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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, buy and hold, 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, lateral thinking, 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.
Trading Risk: Enhanced Profitability Through Risk Control by Kenneth L. Grant
backtesting, business cycle, buy and hold, commodity trading advisor, correlation coefficient, correlation does not imply causation, delta neutral, diversification, diversified portfolio, fixed income, frictionless, frictionless market, George Santayana, implied volatility, interest rate swap, invisible hand, Isaac Newton, John Meriwether, Long Term Capital Management, market design, Myron Scholes, performance metric, price mechanism, price stability, risk tolerance, risk-adjusted returns, Sharpe ratio, short selling, South Sea Bubble, Stephen Hawking, the scientific method, The Wealth of Nations by Adam Smith, transaction costs, two-sided market, value at risk, volatility arbitrage, yield curve, zero-coupon bond
However, there are scenarios under which these portfolios (perhaps due to the demands of the firms that provide leverage to convertible 106 TRADING RISK arbitrage portfolio managers) might suffer from the worst of all possible combinations: The bonds drop in value while the equities experience a contemporaneous rise. It behooves those who either manage or fund convertible arbitrage portfolios to have a clear understanding of the risks associated with these worst-case scenarios. 3. Options Volatility Arbitrage. For those intrepid few wishing to capitalize on subtle and theoretically unsustainable discrepancies in the volatility pricing of options with the same or highly similar underliers, it is prudent to create a scenario analysis that specifically targets conditions under which these mispricings extend themselves. Due to the nonlinear and (often) leveraged nature of options portfolios, this process can often identify exposures that a VaR program or other riskestimation methodology might otherwise miss.
See also Liquidity Market makers, 197, 221–222 Market opportunities, 14, 103–104 Market participation, 102–103, 242–244 Market proximity, 221–222 Market rallies, 74, 158, 173 Market risk, 1–2, 152 Market technician, functions of, 185 Market trends, 22–23 Market volume, 79, 108 Mean, defined, 6 Median P/L, 68 Momentum strategy, 77 Momentum trading, 206–207 Moneyness, 149–150 Monte Carlo simulation, 97–98 Monthly P/L, 41–42, 44 Motivation, importance of, 16–18 Moving averages, 107, 218 Multistrategy trading teams, 129–130 Multivariate normal distribution, 94 Negative correlation, 172–173, 175, 179 Negative P/L, 71, 228 Negative return events, 53 Net market value, 161, 172–174 Netting risk, 129–130 Newton, Sir Isaac, 53–56 90/10 rule, 200–208 Nonlinear pricing, 149, 235 Nonmonetary benefits, 237–242 Nonnormal distribution, 64–65 Normal distribution, 57–58, 64, 116 Number of positions correlation, 161, 174–175 256 OGHET. See Scientific method Optimal f, 245–251 Optimism, importance of, 4 Options: asymmetric payoff functions, 150–151 implications of, generally, 148–149 implied volatility, 86–89, 150 leverage, 151–153 nonlinear pricing dynamics, 149 pricing, 88–89, 106 strike price/underlying price, relationship between, 149–150 volatility arbitrage, 106 Out-of-the-money option, 150 Over-the-counter derivatives, 148 Performance analysis, 7–8 Performance metrics, 16, 35 Performance objectives: “going to the beach,” 32–36 importance of, 19–20, 29 nominal target return, 20, 24–26 optimal target return, 20–24 stop-out level, 20–21, 26–32 Performance ratio, 188–200 Performance success metrics: accuracy ratio (win/loss), 184–186 impact ratio, 186–188 performance ratio, 188–200 profitability concentration (90/10) ratio, 200–208 Planning, importance of, 9.
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, business cycle, buy and hold, 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, G4S, 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, London Interbank Offered Rate, 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, stocks for the long run, 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.
Wealth and Poverty: A New Edition for the Twenty-First Century by George Gilder
"Robert Solow", affirmative action, Albert Einstein, Bernie Madoff, British Empire, business cycle, 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, longitudinal study, 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.