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

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.

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.

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The Spider Network: The Wild Story of a Math Genius, a Gang of Backstabbing Bankers, and One of the Greatest Scams in Financial History by David Enrich

It benefited from impeccable timing, coinciding with London’s growth as a crucial trading and broking hub. Michael Spencer, as CEO, had gobbled up smaller competitors and steered the firm into new markets, although interest-rate derivatives remained one of the company’s core focal points and profit sources. He had recruited similarly ambitious brokers from other London firms, men like David Casterton, who would come to form his inner circle. Before long, ICAP had a hand in a substantial fraction of all interest-rate derivatives transactions and employed nearly three thousand people in dozens of countries. Dressed as a City dandy in red suspenders, gold cuff links, and colorful Hermès ties, Spencer had spawned the world’s biggest interdealer brokerage.

.* In the early 2000s, an essential element of Goodwin’s expansion strategy was building an army of traders and salesmen to establish RBS as a vital, everyday presence in global markets, helping hedge funds, pensions, insurance companies, and other clients buy and sell a wide variety of securities, currencies, and other assets. The plan worked. By 2003, Hayes and the rest of his team of interest-rate derivatives traders were hitting their strides. They had amassed gargantuan positions; RBS’s books that year were jammed with £5.3 trillion of interest-rate derivatives, compared to £3.7 trillion two years earlier. Worldwide, there were more than one hundred traders in the squad—in London, Tokyo, New York, Singapore, and elsewhere—and as the profits poured in, RBS’s management pulled out the stops to impress them.

The City was about to undergo the violent tremors of Margaret Thatcher’s deregulatory revolution, and hungry young traders and brokers were in high demand. Spencer resurfaced at a smaller brokerage firm called Charles Fulton. By now, despite his money-losing ways, he was developing an expertise in a fast-growing corner of the markets called interest-rate derivatives. When Charles Fulton converted into a publicly traded company in 1985, Spencer took his earnings—about \$200,000—and with a few colleagues decided to create a new brokerage firm that would specialize in matching up buyers and sellers of interest-rate swaps and other derivatives. They launched Intercapital in May 1986.

Mathematical Finance: Theory, Modeling, Implementation by Christian Fries

.: Markov dimension of some models. 156 This work is licensed under a Creative Commons License. http://creativecommons.org/licenses/by-nc-nd/2.5/deed.en Comments welcome. ©2004, 2005, 2006 Christian Fries Version 1.3.19 [build 20061210]- 13th December 2006 http://www.christian-fries.de/finmath/ 12.2. INTEREST RATE PRODUCTS PART 3: EXOTIC INTEREST RATE DERIVATIVES 12.2. Interest Rate Products Part 3: Exotic Interest Rate Derivatives Motivation (“Why exotic derivatives?”): A simple European option with payoff max(L(T ) − K, 0) may be interpreted as an insurance against an increase of the interest rate L(T ). It pays in case of an increasing interest rate the corresponding compensation.

The Black Model for a Caplet 149 11. Pricing of a Quanto Caplet (Modeling the FFX) 151 11.1. Choice of Numéraire . . . . . . . . . . . . . . . . . . . . . . . . . . 151 12. Exotic Derivatives 12.1. Prototypical Product Properties . . . . . . . . . . . . . . . . . 12.2. Interest Rate Products Part 3: Exotic Interest Rate Derivatives 12.2.1. Structured Bond, Structured Swap, Zero Structure . . 12.2.2. Bermudan Callables and Cancelable . . . . . . . . . . 12.2.3. Compound Options . . . . . . . . . . . . . . . . . . . 12.2.4. Trigger Products . . . . . . . . . . . . . . . . . . . . 12.2.5. Structured Coupons . . . . . . . . . . . . . . . . . . . 12.2.6.

Partial Proxy Simulation Schemes . . . . . . . . . . . . . . . . . . . 252 15 This work is licensed under a Creative Commons License. http://creativecommons.org/licenses/by-nc-nd/2.5/deed.en Comments welcome. ©2004, 2005, 2006 Christian Fries Version 1.3.19 [build 20061210]- 13th December 2006 http://www.christian-fries.de/finmath/ Contents V. Pricing Models for Interest Rate Derivatives 253 17. Market Models 17.1. LIBOR Market Model . . . . . . . . . . . . . . . . . . . . . . . . 17.1.1. Derivation of the Drift Term . . . . . . . . . . . . . . . . . 17.1.2. The Short Period Bond P(T m(t)+1 ; t) . . . . . . . . . . . . . 17.1.3. Discretization and (Monte Carlo) Simulation . . . . . . . . 17.1.4.

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Barometer of Fear: An Insider's Account of Rogue Trading and the Greatest Banking Scandal in History by Alexis Stenfors

The sky was unusually clear that day, and I looked briefly out of the window to my left. I never wanted to go through this again, would never put myself in a position where I had to go through this again. That, then, was my answer. *** Six months earlier, after 15 years working in the foreign exchange and interest rate derivatives markets, I had been labelled a ‘rogue trader’. I had gone to India on holiday, and on the second day (it was 17 February 2009) I made a phone call to my manager at Merrill Lynch, who, as it happened, was also away from the office, telling him I wanted to talk. He said he was in a ski lift in Switzerland, and told me that he would call back in two or three hours.

LIBOR was not an isolated incident. Other benchmarks that were supposed to reflect how banks lend to each other were also manipulated, such as the Euro Interbank Offered Rate (EURIBOR) and the Tokyo Interbank Offered Rate (TIBOR). As was the lesser-known ISDAfix, a widely used reference rate for complex interest rate derivatives. Even the largest market on earth – the \$5.1 trillion-a-day foreign exchange market – was found to have been subject to a conspiracy between banks. It appears, then, as if banks have used their power to secretly abuse markets, manipulate benchmarks and defraud customers in virtually all the markets in which I had actively been a trader for 15 years.

I had just written an essay entitled ‘Exchange-rate Risks and Hedging Strategies’, and sent an application to the second-largest bank in Frankfurt: Dresdner Bank. They seemed to like that I was interested in derivatives and foreign exchange markets and invited me to an interview. A month later, I found myself in the back office for interest rate derivatives. I rented a cheap room in the Bahnhofsviertel, just a few blocks from the central station and within walking distance from the bank. It struck me that the heroin addicts who inhabited the red light district and the park next to it did not seem to pay any attention to the swarms of bankers in dark suits who walked past them every morning.

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Frequently Asked Questions in Quantitative Finance by Paul Wilmott

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.

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.

• 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.

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Derivatives Markets by David Goldenberg

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 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 (risk-minimizing) 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 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 non-interest 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?

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

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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The City by Tony Norfield

However, the volume of trading on exchanges is a small fraction of that in the OTC market. UK and US financial centres together account for 70 per cent of the world market in OTC interest rate derivatives, illustrating once more the extreme concentration of global trading. The US and the UK are also the leading issuers of international debt securities – to which a lot of this derivatives trading is linked – giving them easy access to investment funds from across the world. Table 8.4 OTC interest rate derivatives turnover, April 2013 (\$ billion)* FRAs Swaps Options Other Total % World Total UK 472.7 795.8 76.5 2.7 1347.7 48.9% US 141.6 382.5 102.1 1.9 628.2 22.8% France 56.6 141.7 3.9 – 202.2 7.3% Germany 77.2 23.0 1.2 – 101.3 3.7% Japan 2.7 55.9 8.6 – 67.1 2.4% Australia 18.2 46.7 1.3 – 66.2 2.4% Denmark 18.8 39.5 0.9 0.1 59.4 2.2% Singapore 13.5 22.8 0.9 – 37.1 1.3% Canada 6.8 25.2 2.0 – 34.0 1.2% Switzerland 13.7 18.9 0.0 – 32.6 1.2% Netherlands 13.6 14.9 0.2 – 28.7 1.0% Hong Kong 2.0 23.7 2.0 0.1 27.9 1.0% Other 45.2 75.3 5.5 0.1 126.1 4.6% Total 882.4 1,665.7 205.4 5.1 2,758.6 100.0% Note: *Single currency derivatives, daily average turnover.

THE CITY THE CITY London and the Global Power of Finance Tony Norfield First published by Verso 2016 © Tony Norfield 2016 All rights reserved The moral rights of the author have been asserted 1 3 5 7 9 10 8 6 4 2 Verso UK: 6 Meard Street, London W1F 0EG US: 20 Jay Street, Suite 1010, Brooklyn, NY 11201 versobooks.com Verso is the imprint of New Left Books ISBN-13: 978-1-78478-366-2 ISBN: 978-1-78478-367-9 (US EBK) ISBN: 978-1-78478-365-5 (UK EBK) British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress Typeset in Minion Pro by MJ & N Gavan, Truro, Cornwall Printed in the UK by CPI Mackays For Alice and Lucy Contents List of Tables and Charts Preface 1Britain, Finance and the World Economy 2The Anglo-American System 3Finance and the Major Powers 4Power and Parasitism 5The World Hierarchy 6Profit and Finance 7The Imperial Web 8Inside the Machine 9Eternal Interests, Temporary Allies Notes Select Bibliography Index List of Tables and Charts Tables 3.1UK, Germany, France – patterns of trade, 1980 and 1990 3.2Financial market shares of major powers, 1980–2001 5.1Corporate control by controlling company, 2007 6.1UK monetary financial institutions’ financial balance sheet 7.1Financial services export revenues, 2000–13 7.2Equity market capitalisation and turnover, 2013 8.1UK current account balance and net components, 1987–2014 8.2External positions of banks, end-2014 8.3Foreign exchange turnover, 1995–2013 8.4OTC interest rate derivatives turnover, April 2013 8.5UK financial account net annual flows, 1987–2014 8.6Net external position of UK MFIs by location, 2000–14 Charts 5.1The global pecking order, 2013–14 6.1Leverage ratios of major international banks, 2007–11 6.2Leverage ratios of major UK banks, 1960–2010 6.3US corporate rate of profit, 1948–2013 6.4US Federal Reserve holdings of Treasury and mortgage securities 8.1Key components of the UK current account, 1987–2014 8.2UK net foreign investment stock position, 1987–2014 8.3Returns on UK foreign investment assets and liabilities, 1990–2014 Preface The head of eurobond trading at Bank of America International in London was an intense and exacting man, not known for his sense of humour.

Improvements in knowledge do not change these relationships of the capitalist economy, the very relationships that lead to economic disasters. The financial system develops as an integral part of capitalism. For example, while financial operations include trading in company shares on the stock market, or in foreign exchange rates or interest rate derivatives, these things do not occur in a vacuum, or simply on a financier’s whim. They are rooted in capitalist production and commerce. This book will show how these things happen, explaining the role finance plays for the major capitalist countries and their corporations, especially on a world scale.

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

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.

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.

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.

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

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.

Aside from falling squarely in the “solution looking for problem” camp (a natural part of life, according to the Garbage Can Model), my main hesitation with actually trying to pursue these as primary research topics was the realization that I was still pretty far from being a mathematician, and so specializing in an exotic area of applied mathematics might not be a sensible move. 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.

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. In my five years at Berkeley, I met a few other people of critical importance to my career path, and life in general. It might be appropriate to start with my wife, Laura Quigg, who was a fellow student in the finance PhD program.

The Global Money Markets by Frank J. Fabozzi, Steven V. Mann, Moorad Choudhry

The ﬁxed-rate payer is effectively long a 6-month forward contract on 6-month LIBOR. The ﬂoating-rate payer is effectively short a 6- 232 THE GLOBAL MONEY MARKETS month forward contract on 6-month LIBOR. There is therefore an implicit forward contract corresponding to each exchange date. Consequently, interest rate swaps can be viewed as a package of more basic interest rate derivative instruments—forwards. The pricing of an interest rate swap will then depend on the price of a package of forward contracts with the same settlement dates in which the underlying for the forward contract is the same reference rate. While an interest rate swap may be nothing more than a package of forward contracts, it is not a redundant contract for several reasons.

The ALM manager must choose the level of trade-off between risk and expected return. Gap management also assumes that the proﬁle of the banking book can be altered with relative ease. This was not always the case, and even today may still present problems, although the availability of a liquid market in off-balance sheet interest-rate derivatives has eased this problem somewhat. However, historically it has always been difﬁcult to change the structure of the book, as many loans cannot be liquidated instantly and ﬁxed-rate assets and liabilities cannot be changed to ﬂoating-rate ones. Client relationships must also be observed and maintained, a key banking issue.

For cash products on the banking book, the capital charge calculations (risk-adjusted exposure) is given by: principal value × risk weighting × capital charge [8%] calculated for each instrument. The sum of the exposures is taken. Firms may use netting or portfolio modelling to reduce the total principal value. The capital requirements for off-balance sheet instruments are lower because for these instruments the principal is rarely at risk. Interest-rate derivatives such as forward rate agreements (FRAs) of less than one Bank Regulatory Capital 301 year’s maturity have no capital requirement at all, while a long-term currency swap requires capital of between 0.08% and 0.2% of the nominal principal.4 The BIS makes a distinction between banking book transactions as carried out by retail and commercial banks (primarily deposits and lending) and trading book transactions as carried out by investment banks and securities houses.

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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

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.

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.

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.

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The Bank That Lived a Little: Barclays in the Age of the Very Free Market by Philip Augar

The reply shocked him: ‘Why would we hold something for them? They’ve never done anything for us.’ Diamond gave them a long icy stare: ‘They are us. That’s the whole point.’ Diamond made connections that other people missed. He probed and challenged, asking different questions until he got the whole picture. He wondered why BZW’s interest rate derivatives business used the same amount of capital as Morgan Stanley’s equivalent yet made only a fraction of the profit. He and his head of derivatives sat in a meeting room while Diamond scrawled big ideas and potential linkages on a whiteboard. Diamond kept asking questions about the cost base, risk management, product design, sales team but he still couldn’t work out why BZW was less profitable to such an extent than its competitors.

He would not have been so carefree had he known that he had just been a victim of what Barrett several years before had called cross-selling and up-selling. Karl’s basic banking business was not profitable enough for Barclays; they wanted to sell him financial products made in other parts of the bank, in this case interest rate derivatives invented by Barclays Capital. When Varley grouped retail and corporate banking together under Seegers he removed any organizational barriers to cross-selling and Barclays went at it with a will, organizing presentation evenings for people like Carol with titles such as ‘Financial Products for Derivatives Virgins’ and loading on extra high sales credits for those who could sell them.

The FSA’s fine was the largest ever imposed by the British regulator and its summary of the issues was brutal: Barclays’ breaches of the FSA’s requirements encompassed a number of issues, involved a significant number of employees and occurred over a number of years. Barclays’ misconduct included: making submissions … that took into account requests from Barclays’ interest rate derivatives traders. These traders were motivated by profit and sought to benefit Barclays’ trading positions; seeking to influence the … submissions of other banks contributing to the rate setting process; and reducing its LIBOR submissions during the financial crisis as a result of senior management’s concerns over negative media comment.

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

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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Stigum's Money Market, 4E by Marcia Stigum, Anthony Crescenzi

The notional amount of FRAs outstanding at the end of 2005 was \$14.483 trillion, according to the BIS, an increase of about \$8 trillion from 2000.4 The average daily turnover in FRAs was over \$233 billion at the end of June 2004, about three times the tally from six years earlier, although that total represented a smaller percentage of the daily turnover in all OTC interest rate derivatives, at 22.7% compared to 26.4% in 2001.5 Similarly, the notional amount of FRAs outstanding fell to 8.1% of all OTC interest rate derivates compared to 10.1% in 2001. An Example A buyer of a FRA might be a borrower who seeks protection against a rise in interest rates; a seller might be a lender who seeks protection against a fall in interest rates. The precise mechanics of a FRA are best illustrated with an example.

If the counterparty is willing, the TABLE 19.4 Amounts outstanding of over-the-counter (OTC) derivatives by risk category and instrument (in billions of dollars) TABLE 19.5 Notional amounts outstanding of OTC single-currency interest-rate derivatives by instrument, maturity, and counterparty (in billions of U.S. dollars) TABLE 19.6 Amounts outstanding of OTC single-currency interest-rate derivatives by currency (in billions of U.S. dollars) TABLE 19.7 Notional amounts outstanding of OTC foreign-exchange derivatives by instrument, maturity, and counterparty (in billions of U.S. dollars) TABLE 19.8 Amounts outstanding of OTC foreign-exchange derivatives by currency (in billions of U.S. dollars) TABLE 19.9 Notional amounts of credit default swaps outstanding at the end of 2005 (in billions of U.S. dollars) initial agreement can be torn up and a cash payment made reflecting the current market value of the swap.

At the end of 2005 the notional value of over-the-counter interest-rate swaps outstanding was \$173 trillion, according to data from the Bank for International Settlements (BIS) in its quarterly review dated June 2006. Interest-rate swaps represented a large portion of the \$215 trillion in interest-rate derivatives outstanding and of the \$285 trillion in the total amount of over-the-counter derivatives contracts outstanding. Calendar Spreads in Eurodollars For a speculator who does not particularly like to take outright positions in the market but likes to trade relative values between calendar months, the Eurodollar contract is also excellent.

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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

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?

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.

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.

Where Does Money Come From?: A Guide to the UK Monetary & Banking System by Josh Ryan-Collins, Tony Greenham, Richard Werner, Andrew Jackson

Japan’s plan to borrow from banks deserves praise. Financial Times, 9 February 2000 27 Prieg, L., Greenham, T. and Ryan-Collins, J., (2011). Quid Pro Quo: Redressing the Privileges of the Banking Industry. London: nef 28 Bank for International Settlements, (2010). Triennial central bank Survey of Foreign Exchange and Over-The-Counter Interest Rate Derivatives Market Activity in April 2010. Report on global foreign exchange market activity in 2010. BIS – Monetary and Economic Department, p. 6 29 Bank for International Settlements (2010). op. cit. p. 12 30 Ostry D. et al., (2010). Capital Inflows: The Role of Controls. IMF Staff Position Note, 19 February 2010, SPN/10/04 31 Lyonnet, V.

Basel: BIS – Monetary and Economic Department Bank for International Settlements (2010). Supervisory Guidance for Managing Settlement Risk in Foreign Exchange Transactions., Basel: BIS – Monetary and Economic Department Bank for International Settlements (2010). Triennial Central Bank Survey of Foreign Exchange and Over-The-Counter Interest Rate Derivatives Market Activity in April 2010. Basel: BIS – Monetary and Economic Department Bank of England (2003). Strengthening financial infrastructure – Financial Stability Review: June 2003. London: Bank of England. Retrievable from http://www.bankofengland.co.uk/publications/psor/index.htm Bank of England (2009).

Layered Money: From Gold and Dollars to Bitcoin and Central Bank Digital Currencies by Nik Bhatia

Users that provide BTC as collateral to Lightning Network in order to facilitate transactions can potentially earn income from providing this liquidity. This is a historically unprecedented way to earn a return on capital without ever relinquishing custody of it because collateral providers don’t actually part ways with their BTC when dedicating it to Lightning Network. Interest rates derived from this type of activity could function as a reference rate in the Bitcoin world because of Lightning Network’s uniquely counterparty-free nature. The very concept of the time value of money is changing as these new technologies permeate the monetary landscape. Alternative Cryptocurrencies Bitcoin copycats were inevitable.

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

(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.

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.

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

., 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.

., 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.

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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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Financial Modelling in Python by Shayne Fletcher, Christopher Gardner

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.

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Sabotage: The Financial System's Nasty Business by Anastasia Nesvetailova, Ronen Palan

Partly as a response to the varied needs of global businesses, a large secondary derivatives market has emerged, whereby derivative contracts are traded with third parties. The value of outstanding financial derivatives is more than US\$500tn. Some estimates put the overall size of the derivatives market at over \$1.2 quadrillion. Interest rate derivatives comprise more than 90 per cent of all contracts. Derivatives are purchased for the flexibility they offer (parties can buy or sell in the future, but are not obliged to) and protection from changes in the market conditions (the price is pre-specified in the contract). But particular types of derivatives can provide something else.

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

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

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.

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The Greed Merchants: How the Investment Banks Exploited the System by Philip Augar

In support of Mr Buffett: Bill Gross, the manager of PIMCO, one of the world’s largest bond funds; shareholders in Procter & Gamble; Gibson Greetings; ‘Freddie Mac’ and Enron; the citizens of Orange County; and countless others who have lost huge amounts of value through derivatives and who believe that the \$218 trillion of global derivatives contracts presently outstanding contains hidden losses that will in due course come to haunt their owners. The enormous size of the market – \$201 trillion in interest rate derivatives, \$12 trillion in credit derivatives and \$5 trillion in equity derivatives, according to a recent survey by the International Swaps and Derivatives Association35 – illustrates both sides of the argument. If anything went wrong, the consequences could be life threatening to the organization or country involved; on the other hand a market this size would not exist and flourish if it served no purpose.

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The Post-American World: Release 2.0 by Fareed Zakaria

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

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

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.

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

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

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.

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Crashed: How a Decade of Financial Crises Changed the World by Adam Tooze

By 2007, 35 percent of the global turnover in foreign exchange, running at a staggering \$1 trillion per day, was conducted between computer systems in the City of London.22 European banks were the biggest players in the business. London was also the hub for the over-the-counter (OTC) interest rates derivatives business, a means of hedging against the risk of interest rate fluctuations and an essential complement to repo deals. Of an annual turnover in interest rate derivatives in excess of \$600 trillion, London claimed 43 percent, to New York’s 24 percent.23 A decade after Thatcher’s Big Bang, with Britain’s native banking industry under intense competitive pressure, Tony Blair’s New Labour government set about further streamlining the City’s regulatory system.24 Nine specialist regulators were combined into a single agency, the Financial Services Authority (FSA).

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

Different tiers of the instrument are then marketed to different investors and the process creates liquidity in the market as it enables smaller investors to purchase shares in a larger asset pool. 20Source : http://​www.​statista.​com/​statistics/​268750/​global-gross-domestic-product-gdp/​ 21Strong-form efficiency is the strongest design of market efficiency and states that all information in a market, whether public or private, is accounted for in a stock’s price. 22Dynamic stochastic general equilibrium modelling (DSGE) is an applied branch of general equilibrium theory that attempts to explain aggregate economic phenomena, such as economic growth, business cycles, and the effects of monetary and fiscal policy. 23The 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 24Qualitative 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.

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Value of Everything: An Antidote to Chaos The by Mariana Mazzucato

Moran, ‘Urine lab flaunted piles of gold', San Diego Union-Tribune, 24 October 2015; J. Montgomery, ‘Bankruptcy court must clarify Millennium Labs fraud release', Law 360, 20 March 2017. 26. Barba and de Vivo, ‘An “unproductive labour” view of finance' p. 1491. 27. A. Hutton and E. Kent, The Foreign Exchange and Over-the-counter Interest Rate Derivatives Market in the United Kingdom (London: Bank of England, 2016), p. 225. 28. Bank for International Settlements, Basel III phase-in arrangements: http://www.bis.org/bcbs/basel3/basel3_phase_in_arrangements.pdf 29. Jordan Weissmann, ‘How Wall Street devoured corporate America', The Atlantic, 5 March 2013: https://www.theatlantic.com/business/archove/2-13/03/how-wall- street-devoured-corporate-america/273732/ 30.

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

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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Dark Towers: Deutsche Bank, Donald Trump, and an Epic Trail of Destruction by David Enrich

The success or failure of many of his trades hinged on tiny movements in something known as Libor (an acronym for the London interbank offered rate). Each day the world’s biggest banks estimated how much it would cost them to borrow money from other banks. Their estimates were averaged together, and the result was Libor. Libor served as the basis for trillions of dollars of interest-rate derivatives, which were the primary instruments that Bittar was using to make his market bets. Bittar had realized it was surprisingly easy to manipulate Libor. Since the benchmark was an average of banks’ estimated borrowing costs, all you had to do was to get a few banks to move their estimates up or down.

Financial Statement Analysis: A Practitioner's Guide by Martin S. Fridson, Fernando Alvarez

Form Type: 10-K Filed On: 9/11/2009 Years Ended July 25, 2009 Cash flows from operating activities: Net income \$6,134 Adjustments to reconcile net income to net cash provided by operating activities: Depreciation, amortization, and other noncash items 1,768 Employee share-based compensation expense 1,140 Share-based compensation expense related to acquisitions and investments 91 Provision for doubtful accounts 54 Deferred income taxes (574) Excess tax benefits from share-based compensation (22) In-process research and development 63 Net losses (gains) on investments 80 Change in operating assets and liabilities, net of effects of acquisitions: Accounts receivable 610 Inventories 187 Lease receivables, net (222) Accounts payable (208) Income taxes payable and receivable 768 Accrued compensation 175 Deferred revenue 572 Other assets (780) Other liabilities 61 Net cash provided by operating activities 9,897 Cash flows from investing activities: Purchases of investments (41,225) Proceeds from sales of investments 20,473 Proceeds from maturities of investments 12,352 Acquisition of property and equipment (1,005) Acquisition of businesses, net of cash and cash equivalents acquired (426) Change in investments in privately held companies (89) Other (39) Net cash used in investing activities \$(9,959) Cash flows from financing activities: Issuance of common stock 863 Repurchase of common stock (3,611) Issuance of long-term debt 3,991 Repayment of long-term debt (500) Settlement of interest rate derivatives related to long-term debt (42) Excess tax benefits from share-based compensation 22 Other (134) Net cash provided by (used in) financing activities 589 Net increase in cash and cash equivalents 527 Cash and cash equivalents, beginning of fiscal year 5,191 Cash and cash equivalents, end of fiscal year 5,718 Prior to that time, going as far back as the introduction of double-entry bookkeeping in Italy during the fifteenth century, financial analysts had muddled through with only the balance sheet and the income statement.

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

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The End of Wall Street by Roger Lowenstein

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.

pages: 400 words: 121,988

Trading at the Speed of Light: How Ultrafast Algorithms Are Transforming Financial Markets by Donald MacKenzie

To a substantial extent, especially in the case of sovereign bonds, markets are bifurcated, with separate electronic systems for interdealer trading (of which BrokerTec is a leading example) and for trading between dealers and clients (such as Bloomberg FIT). TABLE 4.2. Proportion of trading that is dealer-intermediated in selected markets (2015 unless otherwise indicated) US shares 17% European shares (2018) 19% US Treasurys 65% UK Gilts 90% German Bunds >95% Foreign exchange 60% Interest-rate derivatives (e.g., swaps) 90% Sources: Anderson et al. (2015), Cave (2018). Trading Treasurys It is striking that the trading of shares and of sovereign bonds has become so different, because it was traditionally quite similar. Shares and bonds were bought and sold on the trading floors of exchanges such as the New York Stock Exchange, its London equivalent, and the Paris Bourse.

The Trade Lifecycle: Behind the Scenes of the Trading Process (The Wiley Finance Series) by Robert P. Baker

Interest rate participants We can divide the market on interest rate products into three groups of participants: Central Banks (such as Bank of England, Federal Reserve) – these organisations inject cash into their country’s money supply, set the lowest level of interest rate (known as the base rate) and are lenders of last resort Asset Classes 35 Banks (who are generally lenders of money) Commercial organisations such as industrial companies (who generally need to borrow money). All interest rates derive from the base rate. This is the rate the central bank will charge for secured overnight lending. Banks will lend to each other at a slightly higher interest rate than this base rate. The average interest rates at which banks are currently lending is known as LIBOR (London Interbank Offer Rate).

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

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.

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

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.

Virtual Competition by Ariel Ezrachi, Maurice E. Stucke

The consulting firm claimed it wasn’t liable, as the law applied to the competitors who conspired, and not to those who merely helped to organize the cartel meetings or provide ser vices in the context of the anticompetitive agreements. The General Court and the European Court of Justice upheld the Commission’s decision (T-27/10 AC-Treuhand v. Commission, C-194/14 P AC Treuhand v. Commission). 9. European Commission, Antitrust: Commission Fines Broker ICAP €14.9 Million for Participation in Several Cartels in Yen Interest Rate Derivatives Sector, IP/15/4104 (Brussels: European Commission, February 4, 2015), http://europa.eu/rapid/press-release _ IP-15-4104 _en.htm. 10. United States v. Apple, Inc., 952 F. Supp. 2d 638 (S.D.N.Y. 2013), aff ’d, 791 F.3d 290 (2d Cir. 2015). Apple and its coconspirators changed the wholesale business model used at the time by Amazon, leading to higher prices for e-books.

pages: 497 words: 150,205

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

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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How Money Became Dangerous by Christopher Varelas

It would be a year and a half before I returned to New York. * * * The mess had been many years in the making, all centered on what people had assumed to be the Midas touch of longtime Orange County treasurer and tax collector Robert Citron. Salomon’s first encounter with Citron was many years earlier, when our head of interest rate derivative sales, Michael Corbat, flew out for a meeting. The flamboyant Citron arrived wearing a loose-fitting, canary-yellow suit. Corbat (who would become CEO of Citigroup in 2012) was less than impressed with Citron’s understanding of the investments he’d made. Corbat dialed back to the New York office from a pay phone to report that Bob Citron had no idea what he was doing and that Salomon would not be pursuing business with the county.

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

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 as they worked (see figure 3.3 in the color section).

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Buffett by Roger Lowenstein

Consciously paying more for a stock than its calculated value—in the hope that it can soon be sold for a still-higher price—should be labeled speculation.…22 The world has largely lost sight of that distinction. The treasurer of Orange County, California, thought nothing of borrowing heavily and then speculating with the funds for public schools, roads, and waterworks on esoteric interest-rate derivatives, as a consequence of which the county recently went into bankruptcy. Indeed, the notion of intrinsic value is itself something of a lost ideal. In a world of shifting benchmarks and changing “spots,” value is not intrinsic but ephemeral; the painting cannot be appreciated until the critic weighs in, and beauty is truly up to the beholder.

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

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.

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Liberalism at Large: The World According to the Economist by Alex Zevin

The last point loomed largest, as it had ever since the Economist first made the case for turning towards Europe and away from the sterling area: the American, Japanese, Swiss and other non-EU financial firms based in the City, gaining access to customers in all twenty-seven member states, had made London supreme – with 70 per cent of the market for euro-denominated interest-rate derivatives and 90 per cent of the prime brokerage market servicing hedge funds. Nor would free trade suddenly take a step forward, since ‘the slow, grinding history of trade liberalisation shows that mercantilists tend to have the upper hand’; besides, ‘obstacles to growth’ had less to do with Brussels bureaucrats than Britain, with ‘too few new houses, poor infrastructure and a skills gap’.2 A week on, the outcome was ‘a senseless, self-inflicted blow’ and ‘tragic split’ – ‘the tumbling of the pound’ presaging a recession, ‘a permanently less vibrant economy’, ‘extra austerity’, and the potential breakup of the EU as well as the UK.