# interest rate derivative

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

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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.

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.

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.

pages: 368 words: 32,950

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

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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.

______________________________________ 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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Frequently Asked Questions in Quantitative Finance by Paul Wilmott

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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.

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.

• 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.

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Derivatives Markets by David Goldenberg

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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?

The Fix: How Bankers Lied, Cheated and Colluded to Rig the World's Most Important Number (Bloomberg) by Liam Vaughan, Gavin Finch

“That’s just the way I am.” 2 Toward the end of his course he secured a 10-week internship at UBS in London, working on the collateral-management desk, a mundane but complex station where it was difficult to stand out. But Hayes did, and the Swiss bank offered him a full-time role when he finished his studies. Hayes turned it down in order to find a trading position. That’s where the real excitement was. After graduating in 2001, Hayes got his wish, joining the rapidly expanding RBS as a trainee on the interest-rate derivatives desk. For 20 minutes a day, as a reward for making the tea and collecting dry cleaning, he was allowed to ask the traders anything he wanted. It was an epiphany. Unlike the messy interactions and hidden agendas that characterized day-to-day life, the formula for success in finance was clear: Make Tommy Chocolate 7 money and everything else will follow. It became Hayes’s guiding principle, and he began to read voraciously about markets, options-pricing models, interest rate curves, and other financial arcana.

That night he put Hayes in contact with one of his counterparts in Tokyo. In March 2006, the Japanese central bank had announced plans to curb overheating in the economy by raising interest rates for the first time in more than a decade. The move brought volatility to money markets that had been dormant, spurring a wave of buying and selling in cash, 10 THE FIX forwards and short-term interest-rate derivatives. Keen to capitalize, UBS was putting together a small team of front-end traders, who dealt in instruments that matured within two or three years. Hayes would be the perfect addition. At the time, yen was still considered something of a backwater within the banks, a steppingstone on the way to the big leagues of trading dollars or euros. The market was full of inexperienced traders not savvy enough to know when they were being fleeced.

Adrift with no compass, many of the traders simply parroted the figures the brokers gave them without a second thought. Two banks—WestLB and Citigroup—didn’t deviate from Goodman’s predictions for weeks at a time. Read referred to them as the “sheep”.3 He would later state that he used the description to help convince Hayes he was successfully influencing the rate. Life as a short-end interest-rate derivatives trader during the crisis was pretty good. Markets were highly volatile and that meant wider spreads, which, for market makers like Hayes, meant bigger profits. The difference in the cost of borrowing cash overnight compared with taking out a six-month loan had blown out to unprecedented levels. Whereas the spread between the two rates used to average about 7 basis points, and jumped around by less than 1 basis point day to day, it now stood at closer to 50 basis points.

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

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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.

pages: 311 words: 99,699

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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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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.

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.

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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.

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.

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

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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.

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

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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.

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Financial Modelling in Python by Shayne Fletcher, Christopher Gardner

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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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The Production of Money: How to Break the Power of Banks by Ann Pettifor

What may still seem to many to be a parochial affair involving Barclays, a 300-year-old British bank, rigging an obscure number, is beginning to assume global significance. The number that the traders were toying with determines the prices that people and corporations around the world pay for loans or receive for their savings. It is used as a benchmark to set payments on about \$800 trillion–worth of financial instruments, ranging from complex interest-rate derivatives to simple mortgages. The number determines the global flow of billions of dollars each year. Yet it turns out to have been flawed.8 How the authorities can influence rates For it [loanable funds] is concerned with changes in the demand for bank borrowing, whereas I am concerned with changes in the demand for money; and those who desire to hold money only overlap partially and temporarily with those who desire to be in debt to the banks.

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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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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).

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

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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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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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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.

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

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

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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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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.

The Blockchain Alternative: Rethinking Macroeconomic Policy and Economic Theory by Kariappa Bheemaiah

Furthermore, measures need to be taken to address both the underlying causes and disproportionate debt issuance and the ensuing instability fuelled by fractional banking and shadow The London inter-bank offered rate (LIBOR) is an average interest rate calculated through submissions of interest rates by major banks across the world. LIBOR is used to settle contracts on money market derivatives and is also used as a benchmark to set payments on about \$800 trillion worth of financial instruments, ranging from complex interest-rate derivatives to simple mortgages. Source: The Economist: http://www.economist.com/node/21558281 24 Qualitative easing means targeting certain assets to try to drive up their prices and drive down their yields, whereas quantitative easing is unspecific and intends to drive down interest rates across the whole spectrum of assets. Source: Bloomberg: http://www.bloomberg.com/news/ articles/2014-10-31/what-the-heck-is-japans-qqe2 23 23 Chapter 1 ■ Debt-based Economy: The Intricate Dance of Money and Debt banking.

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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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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.

Adaptive Markets: Financial Evolution at the Speed of Thought by Andrew W. Lo

We were hoping to see rational financial behavior in action and capture its properties so we could compare them to ordinary individuals. Wouldn’t it be fascinating if we could identify unique traits of Homo economicus and explain how and why they differ from the rest of us? As crazy as this sounded (remember, this was back in 1999, before biometrics were cool), the bank agreed to give us access to ten of their foreign-currency and interest-rate derivatives traders who volunteered to be our guinea pigs. To make our measurements, we used portable biofeedback equipment that measured changes in skin conductance, blood pressure, heart rate, respiration, and body temperature of the ten traders If You’re So Rich, Why Aren’t You Smart? • 93 as they worked (see figure 3.3 in the color section). Back then, this clunky equipment was state of the art, but today, these measurements can all be made (and made more accurately) by a single chip and sensor embedded in a wristwatch connected via Bluetooth to your smartphone.