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The Concepts and Practice of Mathematical Finance
** by
Mark S. Joshi

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Black-Scholes formula, Brownian motion, correlation coefficient, Credit Default Swap, delta neutral, discrete time, Emanuel Derman, implied volatility, incomplete markets, interest rate derivative, interest rate swap, London Interbank Offered Rate, martingale, millennium bug, quantitative trading / quantitative ﬁnance, short selling, stochastic process, stochastic volatility, the market place, time value of money, transaction costs, value at risk, volatility smile, yield curve, zero-coupon bond

Show that the discount factors P(t1) can be deduced from the rates X j. Such rates are said to be co-terminal. 318 Interest rate derivatives Exercise 13.7 Show that the process for a swap-rate is not log-normal if the underlying forward rates are log-normal. Exercise 13.8 A trigger FRA is a FRA that comes into existence if and only if the forward rate is above H at the start of the FRA. Develop an analytic formula for its price if the forward rate follows geometric Brownian motion. 14 The pricing of exotic interest rate derivatives 14.1 Introduction The critical difference between modelling interest rate derivatives and equity/FX options is that an interest rate derivative is really a derivative of the yield curve and the yield curve is a one-dimensional object whereas the price of a stock or an FX rate is zero-dimensional.

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The bank will therefore try to match maturities in money it receives and pays, in order to avoid these problems, and will use interest rate derivatives when appropriate to reduce risks. 13.2 The simplest instruments 13.2.1 Zero-coupon bonds and present valuing We have talked about swapping a stream of fixed interest payments for a stream of floating ones. This sort of contract is one of the most widely traded and simplest products to price mathematically. Indeed, it can be perfectly hedged in a static model-independent fashion. In this section, we define and price swaps. In general, 13.2 The simplest instruments 303 the best way to analyze an interest rate derivative is in terms of the cashflows involved, and we illustrate this here. All pricing of interest rate derivatives assumes the existence of a continuum of zero-coupon bonds which can be freely bought and sold, including short-selling as necessary.

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Or more generally, since each forward rate has an instantaneous volatility curve, one could make the shape of that curve stochastic. We do not explore these possibilities here but merely suggest the reader bears them in mind when studying the alternative models of stock evolution. 358 The pricing of exotic interest rate derivatives 14.13 Key points The pricing of exotic interest-rate derivatives depends on the evolution of a onedimensional object: the yield curve. The modem approach to pricing exotic interest rate derivatives is to evolve market observable rates. The BGM (or BGM/J) model is based on the evolution of log-normal forward rates. Forward rates only have zero drifts in the martingale measure when the numeraire is a bond with the same payoff time as the forward rate. In general, the drift of a forward rate is both state- and time-dependent.

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How the City Really Works: The Definitive Guide to Money and Investing in London's Square Mile
** by
Alexander Davidson

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accounting loophole / creative accounting, algorithmic trading, asset allocation, asset-backed security, bank run, banking crisis, barriers to entry, Big bang: deregulation of the City of London, capital asset pricing model, central bank independence, corporate governance, Credit Default Swap, dematerialisation, discounted cash flows, diversified portfolio, double entry bookkeeping, Edward Lloyd's coffeehouse, Elliott wave, Exxon Valdez, forensic accounting, global reserve currency, high net worth, index fund, inflation targeting, interest rate derivative, interest rate swap, London Interbank Offered Rate, Long Term Capital Management, margin call, market fundamentalism, Nick Leeson, North Sea oil, Northern Rock, pension reform, Piper Alpha, price stability, purchasing power parity, Real Time Gross Settlement, reserve currency, shareholder value, short selling, The Wealth of Nations by Adam Smith, transaction costs, value at risk, yield curve, zero-coupon bond

In the UK, the average daily turnover in OTC currency and interest rate _________________________________ INTRODUCTION TO DERIVATIVES 65 derivatives was US $643 billion in April 2004, up from US $275 billion in April 2001, according to the Bank for International Settlements. This compared with US $355 billion in the United States, up from US $135 billion over the same period. The 10 largest UK institutions accounted for 80 per cent of total reported turnover in April 2004, up from 74 per cent in 2001. The institutions most active in interest rate derivatives markets were not necessarily active in currency derivatives. Interest rate derivatives (see Chapter 11) and credit derivatives (see Chapter 12) are the largest categories of OTC derivatives, but there are many others. The demand for any one type of OTC derivative may ﬂuctuate. In 2000, the energy derivatives market crashed, partly because of supply and demand dynamics, and partly because of market manipulation by, among others, US energy company Enron.

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______________________________________ INTEREST RATE PRODUCTS 85 Securities lending is a temporary exchange of securities for collateral and is not technically a repo. Institutional investors will lend their bonds for a fee to enhance the income from their ﬁxed interest portfolios. The borrower must provide cash, securities or a letter of credit as collateral to the lender. Interest rate derivatives Interest rate derivatives are the main instrument in the OTC derivatives market. They enable companies that have made large borrowings to protect themselves against adverse interest rate movements, and are a major part of the money markets. In the global OTC derivatives markets at the end of June 2006, interest rate contracts had a notional amount outstanding of US $262.3 trillion, which was more than 70 per cent of the total amount for all OTC derivatives, according to a Bank for International Settlements (BIS) survey, OTC Derivatives Market Activity in the First Half of 2006, November 2006.

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This book is for still for you, To celebrate a wonderful childhood and to look forward to what is to come, With love THIS PAGE INTENTIONALLY LEFT BLANK vi THIS PAGE INTENTIONALLY LEFT BLANK vii THIS PAGE INTENTIONALLY LEFT BLANK viii Contents Acknowledgements Introduction 1 The City of London Introduction The City deﬁned Financial markets The City as a world leader No gain without pain Markets are people The future The next step xlvii 1 4 4 4 5 5 6 8 9 9 2 The Bank of England Introduction Origin Role today Monetary policy Lender of last resort International liaison 10 10 10 11 12 15 17 3 Commercial banking Introduction History Commercial banks today Building societies Raising ﬁnance 18 18 18 19 22 23 THIS PAGE INTENTIONALLY LEFT BLANK x THIS PAGE INTENTIONALLY LEFT BLANK xi THIS PAGE INTENTIONALLY LEFT BLANK xii THIS PAGE INTENTIONALLY LEFT BLANK xiii THIS PAGE INTENTIONALLY LEFT BLANK xiv THIS PAGE INTENTIONALLY LEFT BLANK xv THIS PAGE INTENTIONALLY LEFT BLANK xvi THIS PAGE INTENTIONALLY LEFT BLANK xvii THIS PAGE INTENTIONALLY LEFT BLANK xviii _________________________________________________ CONTENTS xix Credit collection Bad loans and capital adequacy 25 26 4 Introduction to equities Introduction Shares Market indices Stockbrokers The next step 29 29 29 32 33 34 5 How to value shares Introduction Analysts’ forecasts Ratios Discounted cash ﬂow analysis Market inﬂuencers 35 35 35 36 39 40 6 New share issues Introduction Capital raising 42 42 42 7 Investment banking Introduction Overview The initial public offering Specialist types of share issue Bond issues Mergers and acquisitions Disclosure and regulation 47 47 47 47 54 56 56 58 8 Introduction to derivatives Introduction Cash and derivatives Four types of derivative transaction On-exchange versus OTC derivatives Clearing and settlement Hedging and speculation Problems and fraud 60 60 60 61 63 65 67 67 9 Derivatives for retail investors Introduction 69 69 THIS PAGE INTENTIONALLY LEFT BLANK xx THIS PAGE INTENTIONALLY LEFT BLANK xxi THIS PAGE INTENTIONALLY LEFT BLANK xxii THIS PAGE INTENTIONALLY LEFT BLANK xxiii THIS PAGE INTENTIONALLY LEFT BLANK xxiv ________________________________________________ CONTENTS xxv Options Futures Warrants Financial spread betting Contracts for difference 69 71 72 73 76 10 Wholesale market participants Introduction Banks Investors Inter-dealer brokers 78 78 78 79 79 11 Interest rate products Introduction Overview of money markets Debt securities Repos Interest rate derivatives Government bonds 81 81 81 82 84 85 86 12 Credit products Introduction Overview Bonds Credit derivatives The future 89 89 89 90 96 98 13 Commodities Introduction Overview Hard commodities Soft commodities The investment case for commodities Regulation 99 99 99 102 106 107 108 14 Foreign exchange Introduction Global overview In the City The participants Exchange rates 109 109 109 112 113 115 THIS PAGE INTENTIONALLY LEFT BLANK xxvi THIS PAGE INTENTIONALLY LEFT BLANK xxvii Visit Kogan Page online www.kogan-page.co.uk Comprehensive information on Kogan Page titles Features include: � complete catalogue listings, including book reviews and descriptions � sample chapters � monthly promotions � information on NEW and BEST-SELLING titles � a secure shopping basket facility for online ordering Sign up to receive regular e-mail updates on Kogan Page books at www.kogan-page.co.uk/signup.aspx and visit our website: www.kogan-page.co.uk THIS PAGE INTENTIONALLY LEFT BLANK xxix THIS PAGE INTENTIONALLY LEFT BLANK xxx ________________________________________________ CONTENTS Supply and demand Transaction types Electronic trading Default risk Further research XXXI 115 115 117 119 120 15 The London Stock Exchange and its trading systems Introduction Overview Trading facilities Users 121 121 121 122 127 16 Share trading venues and exchanges Introduction Overview Exchanges Multilateral trading facilities Systematic internalisers Dark liquidity pools Consolidation 130 130 130 131 134 137 138 138 17 Post-trade services Introduction Overview Clearing Settlement Safekeeping and custody Cross-border activity The future 140 140 140 141 142 143 144 150 18 Investors Introduction Retail investors Institutional investors 151 151 151 155 19 Pooled investments Introduction Investment funds Investment companies Exchange-traded funds Hedge funds 159 159 159 164 169 169 THIS PAGE INTENTIONALLY LEFT BLANK xxxii THIS PAGE INTENTIONALLY LEFT BLANK xxxiii THIS PAGE INTENTIONALLY LEFT BLANK xxxiv _______________________________________________ CONTENTS xxxv 20 Analysts and research Introduction The analyst Others 172 172 172 177 21 Financial communications Introduction Public relations Investor relations Corporate information ﬂow Journalists 179 179 179 183 185 185 22 Financial services regulation Introduction Overview History of regulation The current regime 190 190 190 190 192 23 Financial fraud Introduction Overview Fraud busters The future 200 200 200 208 215 24 Money laundering Introduction Overview Know your client Action against money launderers The size of the problem 216 216 216 217 217 222 25 Overview of corporate governance Introduction The concept The Cadbury Code The Greenbury Committee The Combined Code The Turnbull Report OECD Principles of Corporate Governance Directors’ Remuneration Report Regulations Higgs and Smith 223 223 223 224 224 225 225 226 226 227 THIS PAGE INTENTIONALLY LEFT BLANK xxxvi THIS PAGE INTENTIONALLY LEFT BLANK xxxvii THIS PAGE INTENTIONALLY LEFT BLANK xxxviii _______________________________________________ CONTENTS The Revised Combined Code Listing Rules The Myners Report Developments across Europe The future XXXIX 227 228 229 230 230 26 Accounting and governance issues Introduction Accounting scandals The Sarbanes–Oxley Act European auditing and disclosure rules Business review International Financial Reporting Standards 232 232 232 233 234 235 237 27 Insurance: the London companies market Introduction Overview London Types of business The underwriting process Regulatory developments Market reform The future 239 239 239 240 240 241 243 245 245 28 Insurance: Lloyd’s of London Introduction Overview How Lloyd’s works Boom to bust More about Lloyd’s today The future 246 246 246 247 250 252 258 29 Reinsurance Introduction Overview Reinsurance contracts Retrocession Financial reinsurance Reinsurance reassessed Capital markets convergence The Reinsurance Directive 260 260 260 261 262 263 264 264 266 THIS PAGE INTENTIONALLY LEFT BLANK xl Visit Kogan Page online Comprehensive information on Kogan Page titles Features include: � complete catalogue listings, including book reviews � sample chapters � monthly promotions � information on NEW and BEST-SELLING titles � a secure shopping basket facility for online ordering Sign up to receive regular e-mail updates on Kogan Page books at www.kogan-page.co.uk/signup.aspx and visit our website: www.kogan-page.co.uk THIS PAGE INTENTIONALLY LEFT BLANK xli THIS PAGE INTENTIONALLY LEFT BLANK xlii _________________________________________________ CONTENTS xliii Offshore reinsurance collateral requirements in the United States Dispute resolution 267 268 30 Retail insurance, savings and domestic property Introduction Overview Products How the products are sold Complaints and compensation The future 269 269 269 273 277 279 280 31 Pensions in ﬂux Introduction Overview The basic state pension Occupational and personal pensions Annuities and unsecured pensions 282 282 282 283 284 288 A word to investors 291 Appendix 1: Useful websites Appendix 2: Further reading 292 297 Index Index of advertisers 302 308 THIS PAGE INTENTIONALLY LEFT BLANK xliv THIS PAGE INTENTIONALLY LEFT BLANK xlv THIS PAGE INTENTIONALLY LEFT BLANK xlvi Acknowledgements This book owes everything to the City professionals who gave freely of their valuable time in providing interviews, source material and other help.

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Frequently Asked Questions in Quantitative Finance
** by
Paul Wilmott

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Albert Einstein, asset allocation, Black-Scholes formula, Brownian motion, butterfly effect, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discrete time, diversified portfolio, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Norbert Wiener, quantitative trading / quantitative ﬁnance, random walk, regulatory arbitrage, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, urban planning, value at risk, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond

See Boyle (1977). 1977 Vasicek So far quantitative finance hadn’t had much to say about pricing interest rate products. Some people were using equity option formulæ for pricing interest rate options, but a consistent framework for interest rates had not been developed. This was addressed by Vasicek. He started by modelling a short-term interest rate as a random walk and concluded that interest rate derivatives could be valued using equations similar to the Black-Scholes partial differential equation. Figure 1-2: Simulations like this can be easily used to value derivatives. Oldrich Vasicek represented the short-term interest rate by a stochastic differential equation of the form The bond pricing equation is a parabolic partial differential equation, similar to the Black-Scholes equation.

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Mike Harrison and David Kreps, in 1979, showed the relationship between option prices and advanced probability theory, originally in discrete time. Harrison and Stan Pliska in 1981 used the same ideas but in continuous time. From that moment until the mid 1990s applied mathematicians hardly got a look in. Theorem, proof everywhere you looked. See Harrison and Kreps (1979) and Harrison and Pliska (1981). 1986 Ho and Lee One of the problems with the Vasicek framework for interest rate derivative products was that it didn’t give very good prices for bonds, the simplest of fixed income products. If the model couldn’t even get bond prices right, how could it hope to correctly value bond options? Thomas Ho and Sang-Bin Lee found a way around this, introducing the idea of yield curve fitting or calibration. See Ho and Lee (1986). 1992 Heath, Jarrow and Morton Although Ho and Lee showed how to match theoretical and market prices for simple bonds, the methodology was rather cumbersome and not easily generalized.

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• European calls, puts and binaries on a single equity: Simulate a single stock path, the payoff for an option, or even a portfolio of options, calculate the expected payoff and present value to price the contract. • Path-dependent option on a single equity: Price a barrier, Asian, lookback, etc. • Options on many stocks: Price a multi-asset contract by simulating correlated random walks. You’ll see how time taken varies with number of dimensions. • Interest rate derivatives, spot rate model: This is not that much harder than equities. Just remember to present value along each realized path of rates before taking the expectation across all paths. • HJM model: Slightly more ambitious is the HJM interest rate model. Use a single factor, then two factors etc. • BGM model: A discrete version of HJM. Numerical integration Occasionally one can write down the solution of an option-pricing problem in the form of a multiple integral.

**
Derivatives Markets
** by
David Goldenberg

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Black-Scholes formula, Brownian motion, capital asset pricing model, commodity trading advisor, compound rate of return, conceptual framework, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, financial innovation, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, law of one price, locking in a profit, London Interbank Offered Rate, Louis Bachelier, margin call, market microstructure, martingale, Norbert Wiener, price mechanism, random walk, reserve currency, risk/return, riskless arbitrage, Sharpe ratio, short selling, stochastic process, stochastic volatility, time value of money, transaction costs, volatility smile, Wiener process, Y2K, yield curve, zero-coupon bond

and B 481; solving for 648 INDEX dollar position in bonds under scenario 1 (over period 2) 483; up state, replication in 480 hedging with forward contracts 33–64; cash commodity prices 35; combinations of positions 50; combining charts to see proﬁts from hedged positions 54–5; commitment prices 41; concept checks: charting payoff to long forward position 39; solution to 62; charting payoff to short forward position 42; solution to 62; charting proﬁts to fully unhedged position 45; solution to 63; charting proﬁts to long spot position sold forward 49; payoff per share to long forward position 39; solution to 61; payoff per share to short forward position 42; proﬁts to fully naked (unhedged) short forward position 50; solution to 64; proﬁts to long spot position sold forward 48–9; proﬁts to naked long spot position 45; wheat price volatility, dealing with 36; decision-making process, protection of potential value 36–7; exercises for learning development of 56–61; forward contracts 37; hedging with 43–5; fully hedged current long spot position, proﬁts to 47–9; fully hedged position, adding proﬁt tables to determine proﬁts from 50–4; futures trading 35; hedged position proﬁts, graphical method for ﬁnding 55; hedgers 37; individual stock forwards: long position 38–9; short position 41–3; key concepts 56; long forward position, payoff to 37–9; motivation for 33–7; naked (unhedged) forward contracts 41; naked (unhedged) long spot position, proﬁts to 45–6; payoff position 37; payoff to long forward position in IBM 40; payoff to short forward position in IBM 43; proﬁt from fully hedged spot position in wheat 53; proﬁts from fully naked (unhedged) spot position in wheat 51; proﬁts from short forward position in wheat 52; proﬁts to long spot position sold forward 49; proﬁts to naked (unhedged) long spot position 46; risk aversion 37; scenarios: adding proﬁt tables to determine proﬁts from fully hedged position 52–4; hedging with forward contracts 44–5; long position contracts 38–9; short position contracts 42; selling a forward contract 40–1, 47–8; settlement price 35; short forward position, payoff to 39–43; spot prices 34–5; uncertainty (volatility), unhedged positions and 45; wheat price uncertainties, dealing with 33–7 hedging with futures contracts 163–209; backwardation, contango and 198–9; basis risk vs. spot price risk 178–82; calendar spreads 199; carrying charge hedging 188–93; convergence, implications for 189; equilibrium (noarbitrage) in full carrying charge market 190–3; overall proﬁts on 189; concept checks: bond equivalent yield (BEY) of actual T-bill 167; solution to 207–8; construction of risk-free arb if r > 0 with no dividends 173; solution to 208; effect of narrowing basis in traditional short hedge 178; solution to 208–9; effect of widening basis in traditional short hedge 176; failure of traditional hedging 184; solution to 209; proﬁts in traditional short hedge and the basis 172; veriﬁcation arb is arb without noninterest carrying charges and is riskless 192–3; solution to 209; veriﬁcation of no current cost in arb 190; veriﬁcation of riskless arb 191; contango and backwardation 198–9; convergence of futures to cash price at expiration 189; correlation effect 165–6; cost-of-carry model, spread and price of storage for 195; equilibrium forward pricing, comparison with equilibrium futures pricing 193–5; equilibrium (no-arbitrage) in full carrying charge market 190–3; classical short selling a commodity 192; Exchange Traded Funds (ETF) 191–2; formal arbitrage opportunity 192; noninterest carrying changes, arb without 192–3; setting up arb 190; unwinding INDEX arb 190–2; exercises for learning development of 205–7; hedging as portfolio theory 165–8; hedging deﬁnitions 168; informational effects 181–2; inter-commodity spreads 199; inter-market spreads 199; interestadjusted marginal carrying costs 196; key concepts 204; long vs. short positions 164; marginal carrying charges 188; minimum variance hedging 185–8; estimation of risk minimization hedge ratio 187–8; OLS regression 187–8; risk minimization hedge ratio, derivation of 186–7; non-traditional (-for-one) hedging theory 182–8; objective of hedging 167–8; OLS regression 181–2, 187–8; one-for-one theory with basis risk 174–8; non-constant basis example with basis narrowing 177; non-constant basis example with basis widening 175–6; one-for-one theory with no basis risk 168–71; basis, concept of 170–1; consistency with no-arbitrage 172–4; constant basis example 168–71; with dividends, r > 0 and r=p, case of 173–4; no dividends and r=0, case of 172–3; speculation on the basis 171; perfectly negatively correlated asset returns 166; portfolio theory, hedging as 165–8; portfolio variance, calculation of 179–81; proﬁts in one-for-one short hedge and basis 171–2; risk reduction with (-forone) hedging 183–5; risk reduction with traditional hedging 179–82; informational effect 181–2; OLS regression 181–2; portfolio variance calculation 179–81; selling hedge 168; short hedge 168; spread basis, deﬁnition of 200–1; spreads as speculative investment 199–203; stock index futures contracts, introduction of 167; storage and price (cost) of 195–7; subsequent inventory sale price, locking in of 195; synthesis of negative correlation, hedging as 165–7; synthetic risk, diversifying away of 167; synthetic treasury bill vs. actual bill 165; systematic, market risk 649 after diversiﬁcation, protection against 168; transportation across time, storage as 195; treasury bill synthesis 166–7 Heston volatility model 587–8 historical data, checking on 9–10 holding period rate of return 237 idiosyncratic risk 225 immediate exercise value 330 implicit bonds 303, 304; implicit ﬂoatingrate bond, valuation of 308 implicit short positions 340 In-the-Money calls 337 In-the-Money covered call writes 421–4 incomplete markets 450–1 independent securities and risks 600 index points 226 individual stock forwards: long position 38–9; short position 41–3 inﬁnitesimal intervals 93 informational effects 181–2 instantaneous yields 90–2, 93–4 insurance features, options and 327 inter-commodity spreads 199 inter-market spreads 199 interest-adjusted marginal carrying costs 196 interest rate derivatives (IRDs): ﬁnancial futures contracts 254; interest-rate swaps 278–80; paying ﬁxed in 278–9; receiving variable in 279–80 interest-rate risk management 9–10 interest-rate swaps 273–319; back stub period 294; cash ﬂows for annual rate swap 302; cash ﬂows in nonintermediated swaps 282–4; commodity forward contracts: paying ﬁxed and receiving ﬂoating in 276; as single period swaps 275–6; concept checks: calculation of implied forward rates (IFRs) 310; solution to 319; graphical representation of swap’s cash ﬂows 283; solution to 318; paying ﬁxed in an interest rate derivative (IRD) 279; solution to 317–18; receiving variable in an interest rate derivative (IRD) 280; strip of forward contracts, short’s position in 650 INDEX 278; solution to 317; swapping ﬁxed for ﬂoating payments 276; solution to 317; credit spreads 298–9; currency swaps, notional value of 274; dealer intermediated plain vanilla swaps 284–93; arbitraging swaps market 292–3; asked side in 286; bid side in 285; dealer’s spread 286; example of 284–6; hedging strategy: implications of 291–2; outline of 288–90; plain vanilla swaps as hedge vehicles 286–92; dealer’s problem, ﬁnding other side to swap 294–8; asked side in 295; bid side in 295; credit spreads in spot market (AA-type ﬁrms) 296; dealer swap schedule (AA-type ﬁrms) 295; selling a swap 296; swap cash ﬂows 298; synthetic ﬂoating-rate ﬁnancing (AA-type ﬁrms) 297; transformation from ﬁxed-rate to ﬂoating rate borrowing 297–8; duration 300; effective date 293; Eurodollar (ED) futures 278; strips of 280–1; exercises for learning development of 315–16; ﬁnancial institutions and use of swaps 299–301; ﬁxed leg 293; ﬁxed payments 278–9; FLIBOR (Futures LIBOR) 278, 287; ﬂoating leg 293; ﬂoating payments 279–80; ﬂoating-rate bond implicit in swap 306; ﬂoating-rate payments as expected cash ﬂows 306; forward contracts, swaps as strips of 274–8; front stub period 294; gap management problem, solutions for 300–1; generic example, ﬁve-year swap 294; implicit bonds 303, 304; implicit ﬂoating-rate bond, valuation of 308; interest rate derivatives (IRDs) 278–80; paying ﬁxed in 278–9; receiving variable in 279–80; key concepts 315; LIBOR (London Interbank Offered Rate) 274–5, 278, 282, 293, 297, 303, 304, 306, 307, 309–10, 311–13; yield curve (spot rates) 304; matching principle 300; mortgage bonds 279; non-dealer intermediated plain vanilla swaps 281–4; notional value of 274; over-the-counter (OTC) bilateral agreements 278; par swap rate 294, 301; paying ﬁxed 293; in interest rate derivatives (IRDs) 278–9; and receiving ﬂoating in commodity forward contracts 276; plain vanilla interest-rate swaps 274; dealer intermediated swaps 284–93; nondealer intermediated swaps 281–4; pricing a swap 294; quality spreads 299; receiving ﬂoating 293; receiving variable in interest rate derivatives (IRDs) 279–80; reset date 293; resetting ﬂoating rate 293; selling short 293; single period swaps, commodity forward contracts as 275–6; strip cash ﬂows, generation of 277; strips of forward contracts 277–8; swap cash ﬂows: decomposition into implicit bonds 303; graphical representation of 318; swap spread 294; swapping ﬁxed for ﬂoating payments 276; swaps as strips of forward contracts 274–8; swaps pricing 301–14; example of 301–3; ﬁxed-rate bond, valuation of 303–5; ﬂoating-rate bond, valuation of 305–8; implied forward rates (IFRs) 309–11; par swap rate 301; interpretations of 311–14; swap at initiation, valuation of 308–9; synthetic ﬁxed-rate bond 291–2; synthetic ﬁxedrate ﬁnancing 290; tenor of swap 293; terminology for 278–81, 293–4; trade date 293; valuation of ﬂoating-rate bonds prior to maturity 306–7; zero sum game, swaps as?

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and B 481; solving for 648 INDEX dollar position in bonds under scenario 1 (over period 2) 483; up state, replication in 480 hedging with forward contracts 33–64; cash commodity prices 35; combinations of positions 50; combining charts to see proﬁts from hedged positions 54–5; commitment prices 41; concept checks: charting payoff to long forward position 39; solution to 62; charting payoff to short forward position 42; solution to 62; charting proﬁts to fully unhedged position 45; solution to 63; charting proﬁts to long spot position sold forward 49; payoff per share to long forward position 39; solution to 61; payoff per share to short forward position 42; proﬁts to fully naked (unhedged) short forward position 50; solution to 64; proﬁts to long spot position sold forward 48–9; proﬁts to naked long spot position 45; wheat price volatility, dealing with 36; decision-making process, protection of potential value 36–7; exercises for learning development of 56–61; forward contracts 37; hedging with 43–5; fully hedged current long spot position, proﬁts to 47–9; fully hedged position, adding proﬁt tables to determine proﬁts from 50–4; futures trading 35; hedged position proﬁts, graphical method for ﬁnding 55; hedgers 37; individual stock forwards: long position 38–9; short position 41–3; key concepts 56; long forward position, payoff to 37–9; motivation for 33–7; naked (unhedged) forward contracts 41; naked (unhedged) long spot position, proﬁts to 45–6; payoff position 37; payoff to long forward position in IBM 40; payoff to short forward position in IBM 43; proﬁt from fully hedged spot position in wheat 53; proﬁts from fully naked (unhedged) spot position in wheat 51; proﬁts from short forward position in wheat 52; proﬁts to long spot position sold forward 49; proﬁts to naked (unhedged) long spot position 46; risk aversion 37; scenarios: adding proﬁt tables to determine proﬁts from fully hedged position 52–4; hedging with forward contracts 44–5; long position contracts 38–9; short position contracts 42; selling a forward contract 40–1, 47–8; settlement price 35; short forward position, payoff to 39–43; spot prices 34–5; uncertainty (volatility), unhedged positions and 45; wheat price uncertainties, dealing with 33–7 hedging with futures contracts 163–209; backwardation, contango and 198–9; basis risk vs. spot price risk 178–82; calendar spreads 199; carrying charge hedging 188–93; convergence, implications for 189; equilibrium (noarbitrage) in full carrying charge market 190–3; overall proﬁts on 189; concept checks: bond equivalent yield (BEY) of actual T-bill 167; solution to 207–8; construction of risk-free arb if r > 0 with no dividends 173; solution to 208; effect of narrowing basis in traditional short hedge 178; solution to 208–9; effect of widening basis in traditional short hedge 176; failure of traditional hedging 184; solution to 209; proﬁts in traditional short hedge and the basis 172; veriﬁcation arb is arb without noninterest carrying charges and is riskless 192–3; solution to 209; veriﬁcation of no current cost in arb 190; veriﬁcation of riskless arb 191; contango and backwardation 198–9; convergence of futures to cash price at expiration 189; correlation effect 165–6; cost-of-carry model, spread and price of storage for 195; equilibrium forward pricing, comparison with equilibrium futures pricing 193–5; equilibrium (no-arbitrage) in full carrying charge market 190–3; classical short selling a commodity 192; Exchange Traded Funds (ETF) 191–2; formal arbitrage opportunity 192; noninterest carrying changes, arb without 192–3; setting up arb 190; unwinding INDEX arb 190–2; exercises for learning development of 205–7; hedging as portfolio theory 165–8; hedging deﬁnitions 168; informational effects 181–2; inter-commodity spreads 199; inter-market spreads 199; interestadjusted marginal carrying costs 196; key concepts 204; long vs. short positions 164; marginal carrying charges 188; minimum variance hedging 185–8; estimation of risk minimization hedge ratio 187–8; OLS regression 187–8; risk minimization hedge ratio, derivation of 186–7; non-traditional (-for-one) hedging theory 182–8; objective of hedging 167–8; OLS regression 181–2, 187–8; one-for-one theory with basis risk 174–8; non-constant basis example with basis narrowing 177; non-constant basis example with basis widening 175–6; one-for-one theory with no basis risk 168–71; basis, concept of 170–1; consistency with no-arbitrage 172–4; constant basis example 168–71; with dividends, r > 0 and r=p, case of 173–4; no dividends and r=0, case of 172–3; speculation on the basis 171; perfectly negatively correlated asset returns 166; portfolio theory, hedging as 165–8; portfolio variance, calculation of 179–81; proﬁts in one-for-one short hedge and basis 171–2; risk reduction with (-forone) hedging 183–5; risk reduction with traditional hedging 179–82; informational effect 181–2; OLS regression 181–2; portfolio variance calculation 179–81; selling hedge 168; short hedge 168; spread basis, deﬁnition of 200–1; spreads as speculative investment 199–203; stock index futures contracts, introduction of 167; storage and price (cost) of 195–7; subsequent inventory sale price, locking in of 195; synthesis of negative correlation, hedging as 165–7; synthetic risk, diversifying away of 167; synthetic treasury bill vs. actual bill 165; systematic, market risk 649 after diversiﬁcation, protection against 168; transportation across time, storage as 195; treasury bill synthesis 166–7 Heston volatility model 587–8 historical data, checking on 9–10 holding period rate of return 237 idiosyncratic risk 225 immediate exercise value 330 implicit bonds 303, 304; implicit ﬂoatingrate bond, valuation of 308 implicit short positions 340 In-the-Money calls 337 In-the-Money covered call writes 421–4 incomplete markets 450–1 independent securities and risks 600 index points 226 individual stock forwards: long position 38–9; short position 41–3 inﬁnitesimal intervals 93 informational effects 181–2 instantaneous yields 90–2, 93–4 insurance features, options and 327 inter-commodity spreads 199 inter-market spreads 199 interest-adjusted marginal carrying costs 196 interest rate derivatives (IRDs): ﬁnancial futures contracts 254; interest-rate swaps 278–80; paying ﬁxed in 278–9; receiving variable in 279–80 interest-rate risk management 9–10 interest-rate swaps 273–319; back stub period 294; cash ﬂows for annual rate swap 302; cash ﬂows in nonintermediated swaps 282–4; commodity forward contracts: paying ﬁxed and receiving ﬂoating in 276; as single period swaps 275–6; concept checks: calculation of implied forward rates (IFRs) 310; solution to 319; graphical representation of swap’s cash ﬂows 283; solution to 318; paying ﬁxed in an interest rate derivative (IRD) 279; solution to 317–18; receiving variable in an interest rate derivative (IRD) 280; strip of forward contracts, short’s position in 650 INDEX 278; solution to 317; swapping ﬁxed for ﬂoating payments 276; solution to 317; credit spreads 298–9; currency swaps, notional value of 274; dealer intermediated plain vanilla swaps 284–93; arbitraging swaps market 292–3; asked side in 286; bid side in 285; dealer’s spread 286; example of 284–6; hedging strategy: implications of 291–2; outline of 288–90; plain vanilla swaps as hedge vehicles 286–92; dealer’s problem, ﬁnding other side to swap 294–8; asked side in 295; bid side in 295; credit spreads in spot market (AA-type ﬁrms) 296; dealer swap schedule (AA-type ﬁrms) 295; selling a swap 296; swap cash ﬂows 298; synthetic ﬂoating-rate ﬁnancing (AA-type ﬁrms) 297; transformation from ﬁxed-rate to ﬂoating rate borrowing 297–8; duration 300; effective date 293; Eurodollar (ED) futures 278; strips of 280–1; exercises for learning development of 315–16; ﬁnancial institutions and use of swaps 299–301; ﬁxed leg 293; ﬁxed payments 278–9; FLIBOR (Futures LIBOR) 278, 287; ﬂoating leg 293; ﬂoating payments 279–80; ﬂoating-rate bond implicit in swap 306; ﬂoating-rate payments as expected cash ﬂows 306; forward contracts, swaps as strips of 274–8; front stub period 294; gap management problem, solutions for 300–1; generic example, ﬁve-year swap 294; implicit bonds 303, 304; implicit ﬂoating-rate bond, valuation of 308; interest rate derivatives (IRDs) 278–80; paying ﬁxed in 278–9; receiving variable in 279–80; key concepts 315; LIBOR (London Interbank Offered Rate) 274–5, 278, 282, 293, 297, 303, 304, 306, 307, 309–10, 311–13; yield curve (spot rates) 304; matching principle 300; mortgage bonds 279; non-dealer intermediated plain vanilla swaps 281–4; notional value of 274; over-the-counter (OTC) bilateral agreements 278; par swap rate 294, 301; paying ﬁxed 293; in interest rate derivatives (IRDs) 278–9; and receiving ﬂoating in commodity forward contracts 276; plain vanilla interest-rate swaps 274; dealer intermediated swaps 284–93; nondealer intermediated swaps 281–4; pricing a swap 294; quality spreads 299; receiving ﬂoating 293; receiving variable in interest rate derivatives (IRDs) 279–80; reset date 293; resetting ﬂoating rate 293; selling short 293; single period swaps, commodity forward contracts as 275–6; strip cash ﬂows, generation of 277; strips of forward contracts 277–8; swap cash ﬂows: decomposition into implicit bonds 303; graphical representation of 318; swap spread 294; swapping ﬁxed for ﬂoating payments 276; swaps as strips of forward contracts 274–8; swaps pricing 301–14; example of 301–3; ﬁxed-rate bond, valuation of 303–5; ﬂoating-rate bond, valuation of 305–8; implied forward rates (IFRs) 309–11; par swap rate 301; interpretations of 311–14; swap at initiation, valuation of 308–9; synthetic ﬁxed-rate bond 291–2; synthetic ﬁxedrate ﬁnancing 290; tenor of swap 293; terminology for 278–81, 293–4; trade date 293; valuation of ﬂoating-rate bonds prior to maturity 306–7; zero sum game, swaps as?

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s 611–12; expected return of hedge portfolio 616–18; hedge portfolio, percentage returns for 616–18; perfect positive correlation, statistics result for 609–11; volatility of hedge portfolio 608–11 concept checks: binomial option pricing model (BOPM): algorithm for determination of B, veriﬁcation of 485; binomial completeness, rule of thumb on 449; binomial model, time modeling in 438; calculation of combination function C(N,j) 444; hedge ratio interpretation 482; hedging a European call option in BOPM (N=2) 477; option price behavior (N=2) 477; solution to 505–6; path 2 contribution analysis 496; path 3 contribution analysis: solution to 506; path structure of binomial process, working with 442; solution to 472; price paths for N-period binomial model 442; solution to 471–2; pricing terminal options 446; underlying stock price uncertainty modeling 438; valuation of option (time=0) using RNVR 490; veriﬁcation of numerical example (N=2) numbers 489; veriﬁcation of option values (N=2) in comparison with replicating portfolio method 493; equivalent martingale measures (EMMs): contingent claim pricing, working with 514; martingale condition, calculation of 525; option pricing, working with 514; two period investment strategy under EMM, proof for (t=0) 521; solution to 639 538; ﬁnancial futures contracts: backwardation and contango, markets in 224; bank borrowing in spot Eurodollar (ED) market 250; ‘buying’ and ‘selling’ Eurodollar (ED) futures 256; calculation of adjusted hedge ratios 245; solution to 269; calculation of optimal (riskminimizing) hedge ratio 240; cash settlement and effective price on S&P 500 spot index units 234; solution to 269; exchange rate risk, currency positions and 218; solution to 268; foreign exchange (FX) risk and jet fuel market 219; solution to 268–9; underlying spot 3-month Eurodollar (ED) time deposit 261; solution to 270; forward market contracting: controlling for counterparty risk 12–13; exploration of forward rates in long-term mortgage market 9–10; exploration of spot rates in long-term mortgage market 11; solution to 29; intermediation by Clearing House 15–16; solution to 29–30; spot markets, dealing with price quotes in 6–7; futures market contracting: price quotes in futures markets 19; hedging a European call option in BOPM (N=2): value conﬁrmation 485; hedging with forward contracts: charting payoff to long forward position 39; solution to 62; charting payoff to short forward position 42; solution to 62; charting proﬁts to fully unhedged position 45; solution to 63; charting proﬁts to long spot position sold forward 49; payoff per share to long forward position 39; solution to 61; payoff per share to short forward position 42; proﬁts to fully naked (unhedged) short forward position 50; solution to 64; proﬁts to long spot position sold forward 48–9; proﬁts to naked long spot position 45; wheat price volatility, dealing with 36; hedging with futures contracts: bond equivalent yield (BEY) of actual T-bill 167; solution to 207–8; construction of risk-free arb if r > 0 with no dividends 173; solution to 208; effect of narrowing 640 INDEX basis in traditional short hedge 178; solution to 208–9; effect of widening basis in traditional short hedge 176; failure of traditional hedging 184; solution to 209; proﬁts in traditional short hedge and the basis 172; veriﬁcation that arb is arb without noninterest carrying charges and is riskless 192–3; solution to 209; veriﬁcation of no current cost in arb 190; veriﬁcation of riskless arb 191; interest-rate swaps: calculation of implied forward rates (IFRs) 310; solution to 319; graphical representation of swap’s cash ﬂows 283; solution to 318; paying ﬁxed in an interest rate derivative (IRD) 279; solution to 317–18; receiving variable in an interest rate derivative (IRD) 280; strip of forward contracts, short’s position in 278; solution to 317; swapping ﬁxed for ﬂoating payments 276; solution to 317; market organization for futures contracts: Globex LOB trading, practicalities in 135–6; solution to 160–1; limit order execution 132; market order with protection, processing with CME Globex 128–9; solution to 160; market price best bids below sell market orders with and without protection, results?

**
How I Became a Quant: Insights From 25 of Wall Street's Elite
** by
Richard R. Lindsey,
Barry Schachter

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Albert Einstein, algorithmic trading, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, asset allocation, asset-backed security, backtesting, bank run, banking crisis, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, business process, buy low sell high, capital asset pricing model, centre right, collateralized debt obligation, corporate governance, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, discounted cash flows, disintermediation, diversification, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, full employment, George Akerlof, Gordon Gekko, hiring and firing, implied volatility, index fund, interest rate derivative, interest rate swap, John von Neumann, linear programming, Loma Prieta earthquake, Long Term Capital Management, margin call, market friction, market microstructure, martingale, merger arbitrage, Nick Leeson, P = NP, pattern recognition, pensions crisis, performance metric, prediction markets, profit maximization, purchasing power parity, quantitative trading / quantitative ﬁnance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Richard Feynman, Richard Stallman, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, sorting algorithm, statistical arbitrage, statistical model, stem cell, Steven Levy, stochastic process, systematic trading, technology bubble, The Great Moderation, the scientific method, too big to fail, trade route, transaction costs, transfer pricing, value at risk, volatility smile, Wiener process, yield curve, young professional

In the fall of 1987, in a most timely fashion, Bob Jarrow came to Berkeley to present the first version of the Heath-Jarrow-Morton (HJM) model of interest rate dynamics and interest rate derivative pricing. Richard Grinold, who was my prethesis advisor, gave me a copy of the HJM paper a couple of weeks before the seminar and told me to dig into it. This represents some of the best academic advice I have ever received since I am not sure that I would have immediately realized the model’s importance and potential for further work by myself. The rest, in some sense, is history. I really enjoyed the paper because I was struggling to understand some of the rather abstract questions in stochastic process theory that it dealt with, and I quickly decided to work on the HJM model for my dissertation. Broadly speaking, the HJM paradigm still represents the state of the art in interest rate derivatives pricing, so having been working with it from the very beginning is definitely high on my list of success factors later in life.

…

Reality, The” (Perold), 73 Independent factors, requirement, 100 Independent model valuation, absence, 168–170 India Institute of Technology (IIT), 188 Inference Corporation, 16, 19 Inflection, point, 60–61 Informationless trades, 73 ING Group, 95 Institute for Quantitative Research in Finance (Q Group), 252–253, 273 Institute of Advanced Study at Princeton (IAS), 121–123 Institutional Investor (II), 196, 274 Insurance company valuation, earnings volatility (role), 103–104 Intellicorp, 16 Interest Rate Derivatives, 231 Interest rates derivative pricing, HJM model, 156 dynamics, HJM model, 156 ensuring. See Positive interest rates movement, understanding, 37–38 Internal VaR models, usage, 99 International Association of Financial Engineers (IAFE), 293, 334–337 financial engineering degree programs, curriculum modeling, 334–335 organization, 330 383 International Congress of Mathematicians, 108 International Securities Exchange (ISE), 329, 336 Intra-day hedging, difficulty, 161 Intuition building, 104 challenge, 105 trust, 105 Investing, future, 46–47 Investment bank, risk management, 236 choice, hierarchy, 260 performance, advancement, 192 process improvement, 69–70 quality control/discipline, application, 73–75 products, focus, 149 science, goal, 42 Investment Advisers Act of 1940, 147 Investment Company Act of 1940, 147 Investment Science (Luenberger), 241 Investment Technology Association, 252 Investor Risk Committee, 293 Investors behavior, micro-theories, 281 portrait, 264–265 ISDA day counting/accrual conventions, 174 Jäckel, Peter, 163–175 Jacobs, Bruce I., 263–283 Jacobs Levy Equity Management, 264 268, 267 Jacobs Levy investment approach, 268–278 Jacobs Levy Markowitz Simulator (JLM Sim), 282 Jarrow, Bob, 140, 156, 319 Jensen, Michael, 266 Jensen’s Inequality, 322 Jones, Bob, 200 Jonsson, Oli, 162 Jorde, Jom, 214 Journal of Portfolio Management, 255, 272–276, 282 JP Morgan, transformation, 102 Jump-diffusion dynamics, 169 Kabiller, David, 202 Kahn, Charlie, 160 Kahn, Ronald N., 29–47, 308 Kalman filter, usage, 188, 239 Kani, Iraj, 123–124 Kapner, Ken, 333 Katz, Gary, 336–337 Kazhdan, David, 119–120 Kazhdan-Lusztig result, 120 Kealhofer, Stephen, 211–225 Kelvin, Lord, 67 Kennecott Copper-Carborundum merger, 290 reporting system, design (foresight), 72–73 risk-controlled stock/bond funds, offering, 71 Kieschnick, Michael, 213 P1: OTE/PGN JWPR007-Lindsey P2: OTE January 1, 1904 6:33 384 KMV Corporation, 218 Knuth, Donald, 171 Kohn, Robert, 132 Kottwitz, Robert, 120 Krail, Bob, 202 Krell, David, 336–337 Kritzman, Mark, 251–261 Kurzweil, Ray, 27–28 Kusuda, Yasuo, 168, 170 Kyle, Peter, 214 Landlands, Robert, 119 Landlands Program, 119–120 Lang, Serge, 287 Lanstein, Ron, 307 Large-cap securities, comparison, 267 Large-scale data analysis, 218 Large-scale matrix inversion, 257 Lattice Trading, 75–76 sale, 79–81 “Law of One Alpha, The,” 274 Lawrence, Colin, 232 LECG, litigation counseling, 218 LeClair, Ray, 82 Leeson, Nick, 194 Lefevre, Edwin, 321 Leinweber, David, 9–28 Leinweber & Co., 9 Leland, Hayne, 158 Leland O’Brien Rubinstein Associates, 278 Leptokurtosis, 193–194 Levy, Kenneth N., 263–283 Levy processes, 169 Lewis, Harry, 13 Lexis database, 146–148 Li, David, 240 Liability Driven Investment (LDI), 148 Liew, John, 201, 202 Lindsey, Rich, 157, 162 Lintner, John, 34 Linux, 18 LISP-based trading systems, flaw, 20 LISP Machines, Inc.

…

There is no good software for identifying options embedded in deals defined by verbose legal documents. Derivatives training gives one a huge advantage; you can find options everywhere if you look hard enough. For example, the essence of the deals I have just described was a strategy of writing out-of-the-money options. (Some successful hedge fund managers run essentially similar strategies!) CIBC My next job was an unhappy sojourn at CIBC Wood Gundy, as vice president for Interest Rate Derivatives. The lowlight of my stay there JWPR007-Lindsey 232 May 7, 2007 17:9 h ow i b e cam e a quant was a dispute between CIBC and a trader over the valuation of his book. The dispute was referred to the unlamented auditing firm Arthur Anderson (put out of business by the Enron fiasco), which independently marked the trader’s book of caps, floors, and swaptions using a flat volatility surface.

**
Fool's Gold: How the Bold Dream of a Small Tribe at J.P. Morgan Was Corrupted by Wall Street Greed and Unleashed a Catastrophe
** by
Gillian Tett

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accounting loophole / creative accounting, asset-backed security, bank run, banking crisis, Black-Scholes formula, Bretton Woods, business climate, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, easy for humans, difficult for computers, financial innovation, fixed income, housing crisis, interest rate derivative, interest rate swap, locking in a profit, Long Term Capital Management, McMansion, mortgage debt, North Sea oil, Northern Rock, Renaissance Technologies, risk tolerance, Robert Shiller, Robert Shiller, short selling, sovereign wealth fund, statistical model, The Great Moderation, too big to fail, value at risk, yield curve

By 1998, Japan was in the throes of a full-blown banking crisis that had left the largest banks desperate to find a way to reduce their risk. In the summer, the team cut a series of billion-dollar deals with lending institutions including Fuji, IKB, Daiwa, and Sanwa. Soon after, Masters arranged a BISTRO structure for Pittsburgh-based bank PNC. Demchak already knew that group well, since PNC was his hometown bank, and he had helped to restructure some troubled interest-rate derivatives deals that PNC had made in the early 1990s. A flurry of other American regional banks and European banks expressed interest. The European banks were usually reluctant to reveal the names of the companies whose loans were included in CDS deals; they feared they would lose customers if companies found out that their bank was buying insurance against its loan book risk. Undaunted, Demchak’s team tweaked the scheme again.

…

But then we learnt to communicate better, as we went along. We just talked, talked, and talked.” The task facing them was daunting. On paper, the wider business climate in 2004 should have been playing to all of J.P. Morgan’s strengths. The new decade was shaping up to be the Era of Credit, and credit was supposed to be J.P. Morgan’s strength. By late 2004, the bank could still claim a leading position in the trading of interest-rate derivatives, foreign exchange, and corporate loans, and a respectable operation in the arena of corporate bonds, too. But the situation in securitization—or the selling of asset-backed securities—looked poor. When J.P. Morgan and Chase had merged, both sides believed the combined bank would dominate the securitization business. Chase was a leader in the business of lending money to low-rated companies (an activity known as leveraged finance) and repackaging those loans into bonds, while J.P.

…

So in the spring of 2006, she met with Nick Studer, one of the consultants at Oliver Wyman, to discuss Wyman’s “gap analysis” on how JPMorgan Chase had fared in 2005. This report essentially asked a clutch of banks to submit data on how their different divisions were performing, which the consultants then used to calculate how the banks looked relative to each other (on an anonymous basis). The 2005 scorecard made dismal reading for JPMorgan Chase. The bank was performing well in some areas, such as foreign exchange or interest-rate derivatives. However, in securitization, the bank’s underperformance was getting worse. Equities and commodities were weak, too. As a result, the total revenue gap between JPMorgan Chase’s investment bank and that of its rivals had surged to around $1.5 billion. More than a billion dollars! Masters was startled and baffled. She knew that it would not be easy to placate equity investors in the bank’s stock if they saw that.

**
Mathematics for Finance: An Introduction to Financial Engineering
** by
Marek Capinski,
Tomasz Zastawniak

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Black-Scholes formula, Brownian motion, capital asset pricing model, cellular automata, delta neutral, discounted cash flows, discrete time, diversified portfolio, interest rate derivative, interest rate swap, locking in a profit, London Interbank Offered Rate, margin call, martingale, quantitative trading / quantitative ﬁnance, random walk, short selling, stochastic process, time value of money, transaction costs, value at risk, Wiener process, zero-coupon bond

Stochastic Interest Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 11.1 Binomial Tree Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 11.2 Arbitrage Pricing of Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 11.2.1 Risk-Neutral Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 11.3 Interest Rate Derivative Securities . . . . . . . . . . . . . . . . . . . . . . . . . . 253 11.3.1 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 x Contents 11.3.2 Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 11.3.3 Caps and Floors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 11.4 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Glossary of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 1 Introduction: A Simple Market Model 1.1 Basic Notions and Assumptions Suppose that two assets are traded: one risk-free and one risky security.

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Inserting the values of the M -bonds into (11.7) and using the formula for the money market account, after some algebraic transformations we obtain B(n, N ; sn ) = [p∗ (n, M ; sn )B(n + 1, N ; sn u) + (1 − p∗ (n, M ; sn )) ×B(n + 1, N ; sn d)] exp{−τ r(n; sn )}. This can be solved for p∗ (n, M ; sn ). It turns out that the solution coincides with the probability p∗ (n, N ; sn ) implied by (11.8), as claimed. Exercise 11.10 Spot an arbitrage opportunity if the bond prices are as in Figure 11.15. 11.3 Interest Rate Derivative Securities The tools introduced above make it possible to price any derivative security based on interest rates or, equivalently, on bond prices. Within the binomial tree 254 Mathematics for Finance Figure 11.15 Data for Exercise 11.10 model the cash ﬂow associated with the derivative security can be replicated using the money market account and a bond with suﬃciently long maturity.

…

Exercise 11.12 In the framework of the above example, value a ﬂoor expiring at time 2 with strike rate 8%, based on the bond prices in Example 11.5. 11.4 Final Remarks We conclude this chapter with some informal remarks on possible ways in which models of the structure of bond prices can be built. This is a complex area and all we can do here is to make some general comments. As we have seen, the theory of interest rates is more complicated than the theory of stock prices. In order to be able to price interest rate derivatives, 260 Mathematics for Finance we need a model of possible movements of bond prices for each maturity. The bond prices with diﬀerent maturities have to be consistent with each other. As we have seen above, the speciﬁcation of a) a model of possible short rates, b) a model of possible values of a bond with the longest maturity (consistent with the initial term structure) determines the structure of possible prices of all bonds maturing earlier.

**
The Devil's Derivatives: The Untold Story of the Slick Traders and Hapless Regulators Who Almost Blew Up Wall Street . . . And Are Ready to Do It Again
** by
Nicholas Dunbar

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asset-backed security, bank run, banking crisis, Basel III, Black Swan, Black-Scholes formula, bonus culture, capital asset pricing model, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delayed gratification, diversification, Edmond Halley, facts on the ground, financial innovation, fixed income, George Akerlof, implied volatility, index fund, interest rate derivative, interest rate swap, Isaac Newton, Kenneth Rogoff, Long Term Capital Management, margin call, market bubble, Nick Leeson, Northern Rock, offshore financial centre, price mechanism, regulatory arbitrage, rent-seeking, Richard Thaler, risk tolerance, risk/return, Ronald Reagan, shareholder value, short selling, statistical model, The Chicago School, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, yield curve

A team of bankers was hired away from Deutsche Bank to run the firm’s credit business. Realizing that there was no future for him at Barclays, Usi jumped before he was pushed. He leveraged the $100 million profit his group was forecast to make that year into a $10 million payoff. On August 3, 2001, Barclays announced that Vince Balducci was replacing Oka Usi. With scant experience in credit (he had previously traded interest rate derivatives at Merrill Lynch and Deutsche Bank), Balducci had inherited Usi’s $15 billion portfolio of hard-to-trade assets and a pipeline of Latinate CDOs, which needed to be sold to investors. Without a decent sales force, and with key expertise gone, how would Balducci deliver the profits that Diamond expected? The answer came from that report on infrastructure improvements in response to the New York Fed examination; it said, “All existing transactions should be supported by fully approved valuation models.”

…

As a former member of the team recalls, “We would listen to the client and shape something around what the client was looking for, and then hedge with the different traders around the different floors of the bank. Often the traders wouldn’t know the full extent of the transaction.” While still an associate—the most junior rank at J.P. Morgan—Vella had impressed his bosses by selling a Bologna-based insurance company interest rate derivatives so complex, they were the financial equivalent of a Gordian knot. He was rewarded with a bigger account: Poste Vita, a Rome-based insurance subsidiary of the Italian post office, which sold long-term structured products to retail investors. Poste Vita was a leader in this booming Italian market, moving billions of euros every year. Such products typically work by combining a money-back guarantee with some exciting upside.

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Morgan (July) WorldCom bankruptcy; CDO investors experience losses IKB creates the Rhineland conduit 2003 Daniel Sparks appointed head of Goldman Sachs mortgage trading Dealers launch corporate credit derivatives indexes Gordian Knot finalizes post-LTCM improvements to Sigma 2004 (January) Moody’s publishes SIV “recipe book” Basel Committee initiates trading book review International Accounting Standards Board (IASB) introduces derivatives fair value accounting globally (April) Poste Italiane reports a €104 million interest rate derivatives loss and sues J.P. Morgan (June) Daniel Sparks visits IKB in Dusseldorf; Goldman issues Abacus 2004 AC-1 The SEC agrees to supervise U.S. securities firms at holding company level, applying the Basel II standards (October) HSH Nordbank (formerly LB Kiel) sues Barclays bank over Corvus CDO 2005 (February) Greg Lippmann meets Steve Kasoff of Elliott Associates and discusses shorting subprime via a CDO (March) Federal Reserve sets up Large Financial Institutions (LFI) committee in response to complaints about lack of access to information; New York Fed criticized over lack of supervision of Citigroup (May) GM and Ford downgraded; J.P.

**
Asset and Risk Management: Risk Oriented Finance
** by
Louis Esch,
Robert Kieffer,
Thierry Lopez

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asset allocation, Brownian motion, business continuity plan, business process, capital asset pricing model, computer age, corporate governance, discrete time, diversified portfolio, implied volatility, index fund, interest rate derivative, iterative process, P = NP, p-value, random walk, risk/return, shareholder value, statistical model, stochastic process, transaction costs, value at risk, Wiener process, yield curve, zero-coupon bond

Konishi, 1996. 3 Hutchinson D. and Pennachi G., Measuring rents and interest rate risk in imperfect ﬁnancial markets: the case of retail bank deposit, Journal of Financial and Quantitative Analysis, 1996, pp. 399–417. 4 Heath D., Jarrow R. and Morton A, Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation, Econometrica, 1992, pp. 77–105. 5 Hull J. and White A., Pricing interest rate derivative securities, Review of Financial Studies, 1990, pp. 573–92. 6 Sanyal A., A continuous time Monte Carlo implementation of the Hull and White one-factor model and the pricing of core deposit, unpublished manuscript, December 1997. 7 The ‘replicating portfolio’ suggests breaking down a stock (for example, total demand deposits at moment t) in ﬂow, each with a speciﬁc maturity date and nominal value.

…

., L’apport de replicating portfolio ou portefeuille répliqué en ALM: méthode contrat par contrat ou par la valeur optimale, Banque et Marchés, mars avril, 2001. Heath D., Jarrow R., and Morton A., Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation, Econometrica, vol. 60, 1992, pp. 77–105. Hotelling H., Relation between two sets of variables, Biometrica, vol. 28, 1936, pp. 321–77. Hull J. and White A., Pricing interest rate derivative securities, Review of Financial Studies, vols 3 & 4, 1990, pp. 573–92. Hutchinson D. and Pennachi G., Measuring rents and interest rate risk in imperfect ﬁnancial markets: the case of retail bank deposit, Journal of Financial and Quantitative Analysis, vol. 31, 1996, pp. 399–417. Mardia K. V., Kent J. T., and Bibby J. M., Multivariate Analysis, Academic Press, 1979. Sanyal A., A Continuous Time Monte Carlo Implementation of the Hull and White One Factor Model and the Pricing of Core Deposit, unpublished manuscript, December 1997.

**
Inside the House of Money: Top Hedge Fund Traders on Profiting in a Global Market
** by
Steven Drobny

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Albert Einstein, asset allocation, Berlin Wall, Bonfire of the Vanities, Bretton Woods, buy low sell high, capital controls, central bank independence, Chance favours the prepared mind, commodity trading advisor, corporate governance, correlation coefficient, Credit Default Swap, diversification, diversified portfolio, family office, fixed income, glass ceiling, high batting average, implied volatility, index fund, inflation targeting, interest rate derivative, inventory management, Long Term Capital Management, margin call, market bubble, Maui Hawaii, Mexican peso crisis / tequila crisis, moral hazard, new economy, Nick Leeson, oil shale / tar sands, oil shock, out of africa, paper trading, Peter Thiel, price anchoring, purchasing power parity, reserve currency, risk tolerance, risk-adjusted returns, risk/return, rolodex, Sharpe ratio, short selling, Silicon Valley, The Wisdom of Crowds, too big to fail, transaction costs, value at risk, yield curve, zero-coupon bond

The sell-off was further compounded as margins were called, leveraged positions unwound, and continued price declines created a vicious cycle of forced selling. (See Figure 2.7.) Corporations on the receiving end of Wall Street’s derivative prowess, such as Procter & Gamble and Gibson Greetings, suffered major losses as their hedges went against them; Orange County, California, the wealthiest county in the United States at the time, declared bankruptcy as interest rate derivative structures imploded; and several well-known global macro funds either closed or went into hiding. Indeed, 1994 was the only down year for the HFR global macro index, which lost 4.3 percent (see Chapter 1). 18 INSIDE THE HOUSE OF MONEY 9.0 8.5 U.S. Treasuries UK Gilts German Bunds 8.0 Yield (%) 7.5 7.0 6.5 Greenspan’s Surprise Rate Hike From 3% to 3.25% 6.0 5.5 r-9 3 ay -9 3 Ju n93 Ju l-9 3 Au g93 Se p93 Oc t-9 No 3 v93 De c93 Ja n94 Fe b9 M 4 ar -9 4 Ap r-9 M 4 ay -9 4 Ju n94 Ju l-9 Au 4 g94 Se p94 Oc t-9 No 4 v94 De c94 Ap M 93 -9 3 ar M b- Fe Ja n- 93 5.0 FIGURE 2.7 Yields: U.S. 10-Year Treasury, UK 10-Year Gilt, and German 10-Year Bund, 1993–1994 Source: Bloomberg.

…

It led to the subsequent bankruptcy of the county. Bob Citron, the county treasurer, was the man ultimately responsible for the $7.5 billion municipal funds portfolio, which financed county schools, certain city and special district projects, and the general workings of the county itself. Citron made heavy investments in reverse repurchase agreements and inverse floaters, the latter an interest rate derivative instrument that pays lower coupons as interest rates rise and higher coupons as interest rates fall. The instrument is thus extremely sensitive to interest rate movements. Citron’s highly leveraged strategy—leverage enhanced through the reverse repurchase agreements—was based on speculation that interest rates would either stay flat or come down. In essence, he borrowed long and loaned out short, as long rates had remained consistently higher than short rates prior to this period.

**
Financial Modelling in Python
** by
Shayne Fletcher,
Christopher Gardner

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Brownian motion, discrete time, interest rate derivative, London Interbank Offered Rate, stochastic volatility, yield curve, zero day, zero-coupon bond

SSRN, 2006. [9] Paul Glasserman. Monte Carlo Methods in Financial Engineering. Springer, 2003. [10] John C. Hull. Options, Futures, and Other Derivatives (Third Edition). Prentice Hall, 1997. [11] Peter Jäckel. Monte Carlo Methods in Finance. John Wiley & Sons, Ltd, 1999. [12] Jaan Kiusalaas. Numerical Methods in Engineering with Python. Cambridge University Press, 2005. [13] Peter Kohl-Landgraf. PDE Valuation of Interest Rate Derivatives. From Theory to Implementation. Books on Demand GmbH, 2008. [14] Hans Peter Langtangen. Python Scripting for Computational Science (Third Edition). Springer, Berlin, Heidelberg, 2008. [15] F.A. Longstaff and E.S. Schwartz. Valuing American options by simulation: a simple least-squares approach. Review of Financial Studies 14: 113–147. 2001. [16] Bernt Øksendal, Stochastic Differential Equations.

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Getting a Job in Hedge Funds: An Inside Look at How Funds Hire
** by
Adam Zoia,
Aaron Finkel

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backtesting, barriers to entry, collateralized debt obligation, commodity trading advisor, Credit Default Swap, credit default swaps / collateralized debt obligations, discounted cash flows, family office, fixed income, high net worth, interest rate derivative, interest rate swap, Long Term Capital Management, merger arbitrage, offshore financial centre, random walk, Renaissance Technologies, risk-adjusted returns, rolodex, short selling, side project, statistical arbitrage, systematic trading, unpaid internship, value at risk, yield curve, yield management

For example, if you are working in trade support or accounting you should get to know Advent/Axys, and if you are working with equities you will want to be proficient in trade support systems such as Eze Castle. Knowledge of Visual Basic (VB) programming and Excel are also important skills to have. If you are currently in operations at an investment bank, we recommend doing what you can to learn more about the products you are working with. For example, if you focus on interest rate derivatives, in addition to being able to explain the operations side of those products, you should understand how they work. If you can do that you should be able to separate yourself from other candidates applying for hedge fund positions. Unfortunately, hedge funds are not known to teach operations processes and skills and, therefore, it’s rare that they will hire someone with no operations experience (Case Study 22 is an exception to that rule, but that person benefited from a strong family contact).

**
Currency Wars: The Making of the Next Gobal Crisis
** by
James Rickards

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Asian financial crisis, bank run, Benoit Mandelbrot, Berlin Wall, Big bang: deregulation of the City of London, Black Swan, borderless world, Bretton Woods, BRICs, British Empire, business climate, capital controls, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, Daniel Kahneman / Amos Tversky, Deng Xiaoping, diversification, diversified portfolio, Fall of the Berlin Wall, family office, financial innovation, floating exchange rates, full employment, game design, German hyperinflation, Gini coefficient, global rebalancing, global reserve currency, high net worth, income inequality, interest rate derivative, Kenneth Rogoff, labour mobility, laissez-faire capitalism, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Mexican peso crisis / tequila crisis, money: store of value / unit of account / medium of exchange, Network effects, New Journalism, Nixon shock, offshore financial centre, oil shock, open economy, paradox of thrift, price mechanism, price stability, private sector deleveraging, quantitative easing, race to the bottom, RAND corporation, rent-seeking, reserve currency, Ronald Reagan, sovereign wealth fund, special drawing rights, special economic zone, The Myth of the Rational Market, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, time value of money, too big to fail, value at risk, War on Poverty, Washington Consensus

Off–balance sheet activities and separate conduit vehicles have created a second shadow banking system as large as the visible system. Between June 2000 and June 2007, just prior to the start of the market collapse, the amount of over-the-counter foreign exchange derivatives went from $15.7 trillion to $57.6 trillion, a 367 percent increase. Between those same dates, the amount of over-the-counter interest rate derivatives went from $64.7 trillion to $381.4 trillion, a 589 percent increase. The amount of over-the-counter equity derivatives went from $1.9 trillion to $9.5 trillion in that same seven-year period, an increase of 503 percent. Under Wall Street’s usual risk evaluation methods, these increases are not troubling. Because they consist of long and short positions, the amounts are netted against each other under the VaR method.

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13 Bankers: The Wall Street Takeover and the Next Financial Meltdown
** by
Simon Johnson,
James Kwak

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Andrei Shleifer, Asian financial crisis, asset-backed security, bank run, banking crisis, Bernie Madoff, Bonfire of the Vanities, bonus culture, capital controls, Carmen Reinhart, central bank independence, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, Edward Glaeser, Eugene Fama: efficient market hypothesis, financial deregulation, financial innovation, financial intermediation, financial repression, fixed income, George Akerlof, Gordon Gekko, greed is good, Home mortgage interest deduction, Hyman Minsky, income per capita, interest rate derivative, interest rate swap, Kenneth Rogoff, laissez-faire capitalism, late fees, Long Term Capital Management, market bubble, market fundamentalism, Martin Wolf, moral hazard, mortgage tax deduction, Ponzi scheme, price stability, profit maximization, race to the bottom, regulatory arbitrage, rent-seeking, Robert Shiller, Robert Shiller, Ronald Reagan, Saturday Night Live, sovereign wealth fund, The Myth of the Rational Market, too big to fail, transaction costs, value at risk, yield curve

The failure of over 2,000 banks between 1985 and 1992 was by far the largest financial sector mass die-off since the Great Depression.2 The government bailout of the S&L industry cost more than $100 billion, and hundreds of people were convicted of fraud.3 In 1990, Michael Milken, the junk bond king, pleaded guilty to six felonies relating to securities transactions. In 1991, Citibank was facing severe losses on U.S. real estate and loans to Latin America and had to be bailed out by an investment from Saudi prince Al-Waleed bin Talal. In 1994, Orange County lost almost $2 billion on complicated interest rate derivatives sold by Merrill Lynch and other dealers; county treasurer Robert Citron pleaded guilty to securities fraud, although no one on the “sell side” of those transactions was convicted of anything. In 1998, Long-Term Capital Management collapsed in the wake of the Russian financial crisis and had to be rescued by a consortium of banks organized by the Federal Reserve. Scandals are a constant refrain throughout the history of the financial services industry.

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The Alpha Masters: Unlocking the Genius of the World's Top Hedge Funds
** by
Maneet Ahuja,
Myron Scholes,
Mohamed El-Erian

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Asian financial crisis, asset allocation, asset-backed security, backtesting, Bernie Madoff, Bretton Woods, business process, call centre, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, en.wikipedia.org, family office, fixed income, high net worth, interest rate derivative, Isaac Newton, Long Term Capital Management, Mark Zuckerberg, merger arbitrage, NetJets, oil shock, pattern recognition, Ponzi scheme, quantitative easing, quantitative trading / quantitative ﬁnance, Renaissance Technologies, risk-adjusted returns, risk/return, rolodex, short selling, Silicon Valley, South Sea Bubble, statistical model, Steve Jobs, systematic trading

At the age of 15, he interned after school at Merrill Lynch; at 18 he had a summer job at Goldman Sachs; at 24 he joined Deutsche Bank and was named vice president at 25, director at 26, and managing director at 27. Weinstein joined Deutsche Bank in January 1998, when the market for credit derivatives—financial contracts for hedging (or speculating) against a company’s default—was in its infancy. “Not only was it brand new, but few people understood the mechanics of how to price a credit default swap,” says Weinstein. A CDS is the most common credit derivative. “Foreign exchange derivatives, interest rate derivatives, equity derivatives—those instruments had been around for 25 years before J. P. Morgan and Deutsche began figuring out how to structure and trade credit default swaps.” This was an ideal situation for young Weinstein. For years, while his peers had all followed equities, Weinstein had been fascinated by the complexity of credit. “If you analyze a company and decide you like the stock, all you can really do is buy the stock or a call option on the stock.

**
My Life as a Quant: Reflections on Physics and Finance
** by
Emanuel Derman

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Berlin Wall, bioinformatics, Black-Scholes formula, Brownian motion, capital asset pricing model, Claude Shannon: information theory, Emanuel Derman, fixed income, Gödel, Escher, Bach, haute couture, hiring and firing, implied volatility, interest rate derivative, Jeff Bezos, John von Neumann, law of one price, linked data, Long Term Capital Management, moral hazard, Murray Gell-Mann, pre–internet, publish or perish, quantitative trading / quantitative ﬁnance, Richard Feynman, Sharpe ratio, statistical arbitrage, statistical model, Stephen Hawking, Steve Jobs, stochastic volatility, technology bubble, transaction costs, value at risk, volatility smile, Y2K, yield curve, zero-coupon bond

In contrast, fixed-income securities such as bonds are ornate mechanisms that promise to spin off future periodic payments of interest and a final return of principal. This specification of detail makes fixed income a much more numerate business than equities, and one much more amenable to mathematical analysis. Every fixed-income securitybonds, mortgages, convertible bonds, and swaps, to name only a few-has a value that it depends on, and is therefore conveniently viewed as a derivative of the market's underlying interest rates. Interest-rate derivatives are naturally attractive products for corporations who, as part of their normal business, must borrow money by issuing bonds whose value changes when interest or exchange rates fluctuate. It is much more challenging to create realistic models of the movement of interest rates, which change in more complex ways than stock prices; interest-rate modeling has thus been the mother of invention in the theory of derivatives for the past twenty years.

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Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues
** by
Alain Ruttiens

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algorithmic trading, asset allocation, asset-backed security, backtesting, banking crisis, Black Swan, Black-Scholes formula, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discounted cash flows, discrete time, diversification, fixed income, implied volatility, interest rate derivative, interest rate swap, margin call, market microstructure, martingale, p-value, passive investing, quantitative trading / quantitative ﬁnance, random walk, risk/return, Sharpe ratio, short selling, statistical model, stochastic process, stochastic volatility, time value of money, transaction costs, value at risk, volatility smile, Wiener process, yield curve, zero-coupon bond

Figure 2.5 A polynomial curve passing through the set of data points Nevertheless, sometimes it is worth using this method, for example when the yield curve can more or less realistically be assimilated to a logarithmic curve. Also, it may prove useful within the context of modeling of derivatives, where the aim is less to draw the most accurate yield curve for market applications than to give mathematical support to a model for interest rates derivatives. But its main raison d'être is when a yield curve must be built from a set of untrustworthy data, hence the drawback of a curve not actually passing through these data is less important. This is the case, for example, of illiquid interest rates markets such as emerging markets. Method #4: Cubic Splines Method In this method, data points are joined two by two by linked segments or “splines” of polynomial curves, actually cubic or order-3 polynomials.

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The Post-American World: Release 2.0
** by
Fareed Zakaria

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affirmative action, agricultural Revolution, airport security, anti-communist, Asian financial crisis, battle of ideas, Berlin Wall, Bretton Woods, BRICs, British Empire, call centre, capital controls, central bank independence, centre right, collapse of Lehman Brothers, conceptual framework, Credit Default Swap, currency manipulation / currency intervention, delayed gratification, Deng Xiaoping, double entry bookkeeping, failed state, Fall of the Berlin Wall, financial innovation, global reserve currency, global supply chain, illegal immigration, interest rate derivative, knowledge economy, Mahatma Gandhi, Martin Wolf, mutually assured destruction, new economy, oil shock, open economy, out of africa, postindustrial economy, purchasing power parity, race to the bottom, reserve currency, Ronald Reagan, Silicon Valley, Silicon Valley startup, South China Sea, Steven Pinker, The Great Moderation, Thomas L Friedman, Thomas Malthus, trade route, Washington Consensus, working-age population, young professional

(Derivatives can be important in bad ways, of course; derivatives based on home loans helped cause the mortgage crisis. But many derivatives are plain-vanilla contracts that help businesses minimize their risks.) And the dominant player on the international derivatives market (estimated at a notional value of $300 trillion) is London. London exchanges account for 49 percent of the foreign-exchange derivatives market and 34 percent of the interest-rate derivatives market. (The United States accounts for 16 percent and 4 percent of these markets, respectively.) European exchanges as a whole represent greater than 60 percent of the interest rate, foreign exchange, equity, and fund-linked derivatives. McKinsey’s interviews with global business leaders indicate that Europe dominates not only in existing derivatives products but also in the innovation of new ones.

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The End of Wall Street
** by
Roger Lowenstein

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Asian financial crisis, asset-backed security, bank run, banking crisis, Berlin Wall, Bernie Madoff, Black Swan, Brownian motion, Carmen Reinhart, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, diversified portfolio, eurozone crisis, Fall of the Berlin Wall, fear of failure, financial deregulation, fixed income, high net worth, Hyman Minsky, interest rate derivative, invisible hand, Kenneth Rogoff, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, Martin Wolf, moral hazard, mortgage debt, Northern Rock, Ponzi scheme, profit motive, race to the bottom, risk tolerance, Ronald Reagan, savings glut, short selling, sovereign wealth fund, statistical model, the payments system, too big to fail, tulip mania, Y2K

g The early CDOs yielded roughly three percentage points more than Treasury bonds—a gap that at least paid homage to the former’s relative riskiness. By 2005-06, the spread had narrowed to one percentage point. h Orange County, Bankers Trust, Barings Bank, Metallgesellschaft, and Sumitomo Corporation each suffered horrendous and unexpected losses from derivative transactions. In the case of Orange County, the treasurer, hoping to enhance the county’s income, borrowed money to invest in interest-rate derivatives. However, in 1994, when interest rates rose, the scheme failed and the county filed for bankruptcy. i Curiously, of the four officials ganging up on Born, only Greenspan was a full-fledged partisan for deregulation. In their first meeting, Greenspan told Born [as she later recounted to Stanford Magazine] that he did not agree with her on the need, even, for laws against fraud—which Greenspan said the market would patrol on its own.

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Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives
** by
Satyajit Das

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accounting loophole / creative accounting, Albert Einstein, Asian financial crisis, asset-backed security, Black Swan, Black-Scholes formula, Bretton Woods, BRICs, Brownian motion, business process, buy low sell high, call centre, capital asset pricing model, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, currency peg, disintermediation, diversification, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, Haight Ashbury, high net worth, implied volatility, index arbitrage, index card, index fund, interest rate derivative, interest rate swap, Isaac Newton, job satisfaction, locking in a profit, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Marshall McLuhan, mass affluent, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, mutually assured destruction, new economy, New Journalism, Nick Leeson, offshore financial centre, oil shock, Parkinson's law, placebo effect, Ponzi scheme, purchasing power parity, quantitative trading / quantitative ﬁnance, random walk, regulatory arbitrage, risk-adjusted returns, risk/return, shareholder value, short selling, South Sea Bubble, statistical model, technology bubble, the medium is the message, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, volatility smile, yield curve, Yogi Berra, zero-coupon bond

This was unsurprising – NCB had always been considered a ‘basket’ case by astute analysts. The investors were first-to-cry when NCB was the first-to-default in these baskets. Remote credit Credit derivatives did not enjoy immediate success and many of the original innovators were disappointed at the lack of growth, a lot left to do other things. It was only in the late 1990s that they took off. Suddenly, people talked of credit derivatives being larger than interest rate derivatives, the biggest part of the derivatives markets. The pioneers had been ahead of their time. The breakthrough was the credit default swap (CDS). The basic idea of a CDS is simple. Assume that a bank has made a loan to a client. The bank now wants to sell the risk on the loan; it has too much exposure to the client, industry or country. This is ‘concentration risk’, the opposite of diversification.

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European Spring: Why Our Economies and Politics Are in a Mess - and How to Put Them Right
** by
Philippe Legrain

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3D printing, Airbnb, Asian financial crisis, bank run, banking crisis, barriers to entry, Basel III, battle of ideas, Berlin Wall, Big bang: deregulation of the City of London, Bretton Woods, BRICs, British Empire, business process, capital controls, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, Celtic Tiger, central bank independence, centre right, cleantech, collaborative consumption, collapse of Lehman Brothers, collective bargaining, corporate governance, credit crunch, Credit Default Swap, crony capitalism, currency manipulation / currency intervention, currency peg, debt deflation, Diane Coyle, Downton Abbey, Edward Glaeser, Elon Musk, en.wikipedia.org, energy transition, eurozone crisis, fear of failure, financial deregulation, first-past-the-post, forward guidance, full employment, Gini coefficient, global supply chain, Growth in a Time of Debt, hiring and firing, hydraulic fracturing, Hyman Minsky, Hyperloop, immigration reform, income inequality, interest rate derivative, Irish property bubble, James Dyson, Jane Jacobs, job satisfaction, Joseph Schumpeter, Kenneth Rogoff, labour market flexibility, labour mobility, liquidity trap, margin call, Martin Wolf, mittelstand, moral hazard, mortgage debt, mortgage tax deduction, North Sea oil, Northern Rock, offshore financial centre, oil shale / tar sands, oil shock, open economy, price stability, private sector deleveraging, pushing on a string, quantitative easing, Richard Florida, rising living standards, risk-adjusted returns, Robert Gordon, savings glut, school vouchers, self-driving car, sharing economy, Silicon Valley, Silicon Valley startup, Skype, smart grid, smart meter, software patent, sovereign wealth fund, Steve Jobs, The Death and Life of Great American Cities, The Wealth of Nations by Adam Smith, too big to fail, total factor productivity, Tyler Cowen: Great Stagnation, working-age population, Zipcar

Hardly anyone went on stag weekends in Barcelona, city breaks in Prague or regular trips to their holiday home in Tuscany before European airspace was opened up. Britain’s financial sector is intimately linked with Europe. The UK’s trade surplus with the EU in financial services was £16.6 billion in 2012, more than a third of the country’s total financial sector surplus, according to The City UK, an industry lobby group.750 London dominates several European financial markets: it has 74 per cent of trade in over-the-counter interest-rate derivatives, 85 per cent of hedge-fund assets and 51 per cent of marine-insurance premiums. Whether or not financial players left London if Britain exited the EU, Britain would have no say in shaping EU financial regulation with which they would have to abide in order to trade with the EU. Given the importance of services exports to the British economy – not just banking, but also insurance, accounting, consultancy, commercial law, advertising, education, healthcare, creative industries such as film, music, design, fashion and publishing, and much else – Britain has a huge stake in trying to drive forward further liberalisation within the EU and in shaping the terms on which it happens.

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Other People's Money: Masters of the Universe or Servants of the People?
** by
John Kay

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Affordable Care Act / Obamacare, asset-backed security, bank run, banking crisis, Basel III, Bernie Madoff, Big bang: deregulation of the City of London, bitcoin, Black Swan, Bonfire of the Vanities, bonus culture, Bretton Woods, call centre, capital asset pricing model, Capital in the Twenty-First Century by Thomas Piketty, cognitive dissonance, corporate governance, Credit Default Swap, cross-subsidies, dematerialisation, diversification, diversified portfolio, Edward Lloyd's coffeehouse, Elon Musk, Eugene Fama: efficient market hypothesis, eurozone crisis, financial innovation, financial intermediation, fixed income, Flash crash, forward guidance, Fractional reserve banking, full employment, George Akerlof, German hyperinflation, Goldman Sachs: Vampire Squid, Growth in a Time of Debt, income inequality, index fund, inflation targeting, interest rate derivative, interest rate swap, invention of the wheel, Irish property bubble, Isaac Newton, London Whale, Long Term Capital Management, loose coupling, low cost carrier, M-Pesa, market design, millennium bug, mittelstand, moral hazard, mortgage debt, new economy, Nick Leeson, Northern Rock, obamacare, Occupy movement, offshore financial centre, oil shock, passive investing, peer-to-peer lending, performance metric, Peter Thiel, Piper Alpha, Ponzi scheme, price mechanism, purchasing power parity, quantitative easing, quantitative trading / quantitative ﬁnance, railway mania, Ralph Waldo Emerson, random walk, regulatory arbitrage, Renaissance Technologies, rent control, Richard Feynman, risk tolerance, road to serfdom, Robert Shiller, Robert Shiller, Ronald Reagan, Schrödinger's Cat, shareholder value, Silicon Valley, Simon Kuznets, South Sea Bubble, sovereign wealth fund, Spread Networks laid a new fibre optics cable between New York and Chicago, Steve Jobs, Steve Wozniak, The Great Moderation, The Market for Lemons, the market place, The Myth of the Rational Market, the payments system, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Tobin tax, too big to fail, transaction costs, tulip mania, Upton Sinclair, Vanguard fund, Washington Consensus, We are the 99%, Yom Kippur War

The explanation is that the new skills that were developed were skills that were related not to the needs of end-users but to the process of intermediation itself. People who traded mortgage-backed securities knew about securities, but very little about mortgages, and less about houses and home-buyers. People who traded shares knew about stock markets, but not about companies and their products. People who traded interest rate derivatives knew about derivatives, but not about politics and government finance. The forces that led to these extensive failures in credit markets in 2007–8 had been evident earlier elsewhere. Robert Shiller received the Nobel Prize in economics for providing in the early 1980s the first careful demonstration of a proposition that seems intuitively obvious to anyone who watches stock markets: volatility is far greater than can be explained by changes in the fundamental value of securities.

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Bad Money: Reckless Finance, Failed Politics, and the Global Crisis of American Capitalism
** by
Kevin Phillips

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algorithmic trading, asset-backed security, bank run, banking crisis, Bernie Madoff, Black Swan, Bretton Woods, BRICs, British Empire, collateralized debt obligation, computer age, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, currency peg, diversification, Doha Development Round, energy security, financial deregulation, financial innovation, fixed income, Francis Fukuyama: the end of history, George Gilder, housing crisis, Hyman Minsky, imperial preference, income inequality, index arbitrage, index fund, interest rate derivative, interest rate swap, Joseph Schumpeter, Kenneth Rogoff, large denomination, Long Term Capital Management, market bubble, Martin Wolf, Menlo Park, mobile money, Monroe Doctrine, moral hazard, mortgage debt, new economy, oil shale / tar sands, oil shock, peak oil, Plutocrats, plutocrats, Ponzi scheme, profit maximization, Renaissance Technologies, reserve currency, risk tolerance, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, short selling, sovereign wealth fund, The Chicago School, Thomas Malthus, too big to fail, trade route

FIGURE P.2 Wild About Derivatives Source : InvesTech Research, Oct. 17, 2008 Because the practices and predicaments of securitization are described in chapter 4 of the main text, these pages will focus on derivatives and securitization—both “exotic finance”—as the fourth great nurturer of the financial sector. To be sure, the notional value shown in Figure P.2 gives a much overstated picture of the real sums at risk in any plausible default scenario. Several attempts have been made in the latter direction. Using 2007 data, the Bank for International Settlements first broke out the notional values: a total of $596 trillion split between interest rate derivatives ($393 trillion), credit default swaps ($58 trillion), and currency derivatives ($56 trillion) with the remainder put into an unallocated category. Then, to assess real-world vulnerability, the BIS set what they called net risk at $14.5 trillion, and put a plausible gross credit exposure at $3.256 trillion.14 Abstract as these trillion-dollar references may seem to laypeople, global fears of a second wave of exotic financial implosions took shape during 2008.

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Makers and Takers: The Rise of Finance and the Fall of American Business
** by
Rana Foroohar

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3D printing, accounting loophole / creative accounting, additive manufacturing, Airbnb, algorithmic trading, Asian financial crisis, asset allocation, bank run, Basel III, bonus culture, Bretton Woods, British Empire, call centre, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, carried interest, centralized clearinghouse, clean water, collateralized debt obligation, corporate governance, corporate social responsibility, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, crowdsourcing, David Graeber, deskilling, Detroit bankruptcy, diversification, Double Irish / Dutch Sandwich, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial deregulation, financial intermediation, Frederick Winslow Taylor, George Akerlof, gig economy, Goldman Sachs: Vampire Squid, Gordon Gekko, greed is good, High speed trading, Home mortgage interest deduction, housing crisis, Howard Rheingold, Hyman Minsky, income inequality, index fund, interest rate derivative, interest rate swap, Internet of things, invisible hand, joint-stock company, joint-stock limited liability company, Kenneth Rogoff, knowledge economy, labor-force participation, labour mobility, London Whale, Long Term Capital Management, manufacturing employment, market design, Martin Wolf, moral hazard, mortgage debt, mortgage tax deduction, new economy, non-tariff barriers, offshore financial centre, oil shock, passive investing, pensions crisis, Ponzi scheme, principal–agent problem, quantitative easing, quantitative trading / quantitative ﬁnance, race to the bottom, Ralph Nader, Rana Plaza, RAND corporation, random walk, rent control, Robert Shiller, Robert Shiller, Ronald Reagan, Second Machine Age, shareholder value, sharing economy, Silicon Valley, Silicon Valley startup, Snapchat, sovereign wealth fund, Steve Jobs, technology bubble, The Chicago School, The Spirit Level, The Wealth of Nations by Adam Smith, Tim Cook: Apple, Tobin tax, too big to fail, trickle-down economics, Tyler Cowen: Great Stagnation, Vanguard fund

When the value of what’s being traded is more than four times the underlying asset that actually exists in the real world, it’s safe to say that a good chunk of what’s happening in the market is purely speculative.44 While some portions of the derivatives markets, including credit default swaps, have contracted sharply since the 2008 crisis, the overall market remains enormous. Globally, the value of all outstanding derivatives contracts (including credit default swaps, interest rate derivatives, foreign exchange rate derivatives, commodities-linked derivatives, and so on) was $630 trillion at the beginning of 2015, while the gross market value of those contracts was $21 trillion.45 One big problem with derivatives is that it’s often difficult to tell apart speculation and healthy hedging of real risks, especially when large, complex institutions are doing it. The commodities market, in which various players may both own raw assets and trade them, is especially tricky.

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The Crisis of Crowding: Quant Copycats, Ugly Models, and the New Crash Normal
** by
Ludwig B. Chincarini

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affirmative action, asset-backed security, automated trading system, bank run, banking crisis, Basel III, Bernie Madoff, Black-Scholes formula, buttonwood tree, Carmen Reinhart, central bank independence, collapse of Lehman Brothers, collateralized debt obligation, collective bargaining, corporate governance, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discounted cash flows, diversification, diversified portfolio, family office, financial innovation, financial intermediation, fixed income, Flash crash, full employment, Gini coefficient, high net worth, hindsight bias, housing crisis, implied volatility, income inequality, interest rate derivative, interest rate swap, labour mobility, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, low skilled workers, margin call, market design, market fundamentalism, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, mortgage debt, Northern Rock, Occupy movement, oil shock, price stability, quantitative easing, quantitative hedge fund, quantitative trading / quantitative ﬁnance, Ralph Waldo Emerson, regulatory arbitrage, Renaissance Technologies, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Reagan, Sharpe ratio, short selling, sovereign wealth fund, speech recognition, statistical arbitrage, statistical model, systematic trading, The Great Moderation, too big to fail, transaction costs, value at risk, yield curve, zero-coupon bond

For Morgan and Lehman it was $88,630 and $55,026, respectively.) LTCM was actually better capitalized than either Morgan or Lehman in 1996, especially considering the ratio of equity to total assets. (Of course, LTCM reduced this equity by $2.7 billion at the beginning of 1998.) LTCM’s off-balance-sheet holdings, such as commodity derivatives, foreign exchange derivatives, equity derivatives, and interest rate derivatives, were similar to those of Lehman or Morgan Stanley, or perhaps a bit smaller. If Lehman and Morgan were large institutions, then LTCM was as well. TABLE 7.1 Size of LTCM versus Morgan Stanley and Lehman Brothers LTCM might even have been better off had it been a larger, more diversified firm. If LTCM had had an investment banking department and an asset management department, these divisions might have buffered the proprietary trading group’s losses.