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Frequently Asked Questions in Quantitative Finance by Paul Wilmott
Albert Einstein, asset allocation, beat the dealer, Black-Scholes formula, Brownian motion, butterfly effect, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discrete time, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Myron Scholes, Norbert Wiener, Paul Samuelson, quantitative trading / quantitative ﬁnance, random walk, regulatory arbitrage, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, urban planning, value at risk, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond
I am also especially indebted to James Fahy for making the Forum happen and run smoothly. Mahalo and aloha to my ever-encouraging wife, Andrea. About the author Paul Wilmott is one of the most well-known names in derivatives and risk management. His academic and practitioner credentials are impeccable, having written over 100 research papers on mathematics and finance, and having been a partner in a highly profitable volatility arbitrage hedge fund. Dr Wilmott is a consultant, publisher, author and trainer, the proprietor of wilmott.com and the founder of the Certificate in Quantitative Finance (7city.com/cqf). He is the Editor in Chief of the bimonthly quant magazine Wilmott and the author of the student text Paul Wilmott Introduces Quantitative Finance, which covers classical quant finance from the ground up, and Paul Wilmott on Quantitative Finance, the three-volume research-level epic.
References and Further Reading Avellaneda, M, Levy, A & Parás, A 1995 Pricing and hedging derivative securities in markets with uncertain volatilities. Applied Mathematical Finance 2 73-88 Derman, E & Kani, I 1994 Riding on a smile. Risk magazine 7 (2) 32-39 (February) Dupire, B 1994 Pricing with a smile. Risk magazine 7 (1) 18-20 (January) Heston, S 1993 A closed-form solution for options with stochastic volatility with application to bond and currency options. Review of Financial Studies 6 327-343 Javaheri, A 2005 Inside Volatility Arbitrage. John Wiley & Sons Lewis, A 2000 Option valuation under Stochastic Volatility. Finance Press Lyons, TJ 1995 Uncertain Volatility and the risk-free synthesis of derivatives. Applied Mathematical Finance 2 117-133 Rubinstein, M 1994 Implied binomial trees. Journal of Finance 69 771-818 Wilmott, P 2006 Paul Wilmott On Quantitative Finance, second edition. John Wiley & Sons What is the Volatility Smile?
This is often the case with calibrated models and suggests that the model is still not correct, even though its complexity seems to be very promising. Jump-diffusion models allow the stock (and even the volatility) to be discontinuous. Such models contain so many parameters that calibration can be instantaneously more accurate (if not necessarily stable through time). References and Further Reading Gatheral, J 2006 The Volatility Surface. John Wiley & Sons Javaheri, A 2005 Inside Volatility Arbitrage. John Wiley & Sons Taylor, SJ & Xu, X 1994 The magnitude of implied volatility smiles: theory and empirical evidence for exchange rates. The Review of Futures Markets 13 Wilmott, P 2006 Paul Wilmott On Quantitative Finance, second edition. John Wiley & Sons What is GARCH? Short Answer GARCH stands for Generalized Auto Regressive Conditional Heteroscedasticity. This is an econometric model used for modelling and forecasting time-dependent variance, and hence volatility, of stock price returns.
Expected Returns: An Investor's Guide to Harvesting Market Rewards by Antti Ilmanen
Andrei Shleifer, asset allocation, asset-backed security, availability heuristic, backtesting, balance sheet recession, bank run, banking crisis, barriers to entry, Bernie Madoff, Black Swan, Bretton Woods, buy low sell high, capital asset pricing model, capital controls, Carmen Reinhart, central bank independence, collateralized debt obligation, commoditize, commodity trading advisor, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, debt deflation, deglobalization, delta neutral, demand response, discounted cash flows, disintermediation, diversification, diversified portfolio, dividend-yielding stocks, equity premium, Eugene Fama: efficient market hypothesis, fiat currency, financial deregulation, financial innovation, financial intermediation, fixed income, Flash crash, framing effect, frictionless, frictionless market, George Akerlof, global reserve currency, Google Earth, high net worth, hindsight bias, Hyman Minsky, implied volatility, income inequality, incomplete markets, index fund, inflation targeting, information asymmetry, interest rate swap, invisible hand, Kenneth Rogoff, laissez-faire capitalism, law of one price, Long Term Capital Management, loss aversion, margin call, market bubble, market clearing, market friction, market fundamentalism, market microstructure, mental accounting, merger arbitrage, mittelstand, moral hazard, Myron Scholes, negative equity, New Journalism, oil shock, p-value, passive investing, Paul Samuelson, performance metric, Ponzi scheme, prediction markets, price anchoring, price stability, principal–agent problem, private sector deleveraging, purchasing power parity, quantitative easing, quantitative trading / quantitative ﬁnance, random walk, reserve currency, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, riskless arbitrage, Robert Shiller, Robert Shiller, savings glut, selection bias, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, stochastic volatility, survivorship bias, systematic trading, The Great Moderation, The Myth of the Rational Market, too big to fail, transaction costs, tulip mania, value at risk, volatility arbitrage, volatility smile, working-age population, Y2K, yield curve, zero-coupon bond, zero-sum game
However, in 2005–2007, several sell-side firms offered their customers structured products that were short volatility or variance, often simply by selling one-month or 3-month variance swaps on the S&P 500. Excess return for such a product is proportional to the difference between squared implied volatility and squared realized volatility over the life of the contract. Backtested results were extremely impressive until 2007 but the losses in autumn 2008 were dramatic—and traumatic, prompting many investors to leave these strategies. The Merrill Lynch volatility arbitrage strategy, shown below, lost 12 years’ gradually earned excess returns in less than two months. (All index volatility-selling strategies plummeted in autumn 2008, but leverage made the losses of this index exceptionally high.) Although implied volatilities were high, realized volatilities exceeded them, reaching levels only seen during the 1987 crash. Indeed, volatility-selling strategies have suffered serious losses mainly on these two occasions, but these losses have been extremely large and concentrated in the worst possible times.
Performance and risk statistics of S&P and index option-trading strategies, 1989–2009 Sources: Bloomberg, Chicago Board of Exchange, Bank of America Merrill Lynch. Table 15.1 (based on weekly data) illustrates how 2008 “revealed” the riskiness of various option-trading strategies, while at the same time long-run performance statistics became less appealing. The downfall was even worse for the “pure” volatility arbitrage strategy than for covered-option-writing strategies. Over 1989–2009, the latter still display higher returns and Sharpe ratios than a simple long-equities strategy (first column), but this advantage comes with less appealing tail risk or higher moment exposures: more negative skewness and higher kurtosis. The covered-PUT-writing strategy comes with the best performance statistics and worst risk statistics.
Simulated commodity momentum strategies are based on self-collected commodity futures return series since 1990 and earlier on the Mount Lucas Management Commodities trend index. This composite trend style index applies a simple trend-following rule each week on commodity futures, equity country futures, bond/rate futures, and foreign exchange forwards: go long (short) if the current price is above (below) the 12-month moving average. Data are mainly from Bloomberg. Volatility. Volatility-selling returns are based on the simulated Merrill Lynch Equity Volatility Arbitrage Index since 1989, which tries to gain from the typically positive gap between market-implied volatility and subsequent realized volatility of the S&P 500 index’s Bloomberg ticker MLHFEV1 index. Chapter 15 also analyzes the simulated covered-call-writing indices and put-writing indices (BXM, BXY, PUT in Bloomberg) on the S&P 500 index from the Chicago Board of Exchange, dating back to the 1980s.
Trend Following: How Great Traders Make Millions in Up or Down Markets by Michael W. Covel
Albert Einstein, asset allocation, Atul Gawande, backtesting, beat the dealer, Bernie Madoff, Black Swan, buy low sell high, capital asset pricing model, Clayton Christensen, commodity trading advisor, computerized trading, correlation coefficient, Daniel Kahneman / Amos Tversky, delayed gratification, deliberate practice, diversification, diversified portfolio, Edward Thorp, Elliott wave, Emanuel Derman, Eugene Fama: efficient market hypothesis, Everything should be made as simple as possible, fiat currency, fixed income, game design, hindsight bias, housing crisis, index fund, Isaac Newton, John Meriwether, John Nash: game theory, linear programming, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market fundamentalism, market microstructure, mental accounting, money market fund, Myron Scholes, Nash equilibrium, new economy, Nick Leeson, Ponzi scheme, prediction markets, random walk, Renaissance Technologies, Richard Feynman, Richard Feynman, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, South Sea Bubble, Stephen Hawking, survivorship bias, systematic trading, the scientific method, Thomas L Friedman, too big to fail, transaction costs, upwardly mobile, value at risk, Vanguard fund, volatility arbitrage, William of Occam, zero-sum game
On January 10, 2001, this same reporter sent me an email stating that she was doing a follow-up story to the one in December and wanted a comment. I was impressed that she was essentially acknowledging her mistake and was even willing to set the record straight because, for the record, Dunn made 28 percent in November of 2000 and 29 percent in December of 2000. Henry Convergent styles • World knowable • Stable world • Mean-reverting • Short volatility • Arbitrage-based Divergent styles • World uncertain • Unstable world • Mean-fleeing • Long volatility • Trend Following Mark S. Rzepczynski12 Don’t be fooled by the calm. That’s always the time to change course, not when you’re just about to get hit by the typhoon. The way to avoid being caught in such a storm is to identify the confluence of factors and to change course even though right now the sky is blue, the winds are gentle, and the water seems calm…After all look how calm and sunny it is outside.
Wealth and Poverty: A New Edition for the Twenty-First Century by George Gilder
affirmative action, Albert Einstein, Bernie Madoff, British Empire, capital controls, cleantech, cloud computing, collateralized debt obligation, creative destruction, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, deindustrialization, diversified portfolio, Donald Trump, equal pay for equal work, floating exchange rates, full employment, George Gilder, Gunnar Myrdal, Home mortgage interest deduction, Howard Zinn, income inequality, invisible hand, Jane Jacobs, Jeff Bezos, job automation, job-hopping, Joseph Schumpeter, knowledge economy, labor-force participation, margin call, Mark Zuckerberg, means of production, medical malpractice, minimum wage unemployment, money market fund, money: store of value / unit of account / medium of exchange, Mont Pelerin Society, moral hazard, mortgage debt, non-fiction novel, North Sea oil, paradox of thrift, Paul Samuelson, Plutocrats, plutocrats, Ponzi scheme, post-industrial society, price stability, Ralph Nader, rent control, Robert Gordon, Ronald Reagan, Silicon Valley, Simon Kuznets, skunkworks, Steve Jobs, The Wealth of Nations by Adam Smith, Thomas L Friedman, upwardly mobile, urban renewal, volatility arbitrage, War on Poverty, women in the workforce, working poor, working-age population, yield curve, zero-sum game
As Steve Forbes stresses, the role of currencies is to serve as a standard of value, representing a measuring stick of the worth of goods and services: “Floating the currency is like floating the clock. Let’s say you floated the hour, 60 minutes in an hour one day, 50 the next, 85 the next. You would soon have to have hedges to insure against changes in the measure of time,” just to calculate your hours of work in “real terms.” You would have runaway sales of “hour insurance swaps,” and GDP might even go up for awhile, but real economic progress is not volatility arbitrage. Or, to change the metaphor, U.S. monetary policy resembles a housing policy pronouncement: “If we change the size of a foot from 12 to 15 inches, everyone will have a bigger house.” As Forbes comments, “In the real world, you’ll likely end up with a lot of confusion and fewer homes being built. In the same way, with a fluctuating dollar, you get less long-term investment, more speculation, and misdirected capital.”23 Money is a symbol of productive services rendered.