Paul wilmott introduces quantitative finance

Contents Cover Half Title page Title page Copyright page Dedication Preface Chapter 1: Products and Markets: Equities, Commodities, Exchange Rates, Forwards and Futures 1.1 Introduction 1.2 Equities 1.3 Commodities 1.4 Currencies 1.5 Indices 1.6 The Time Value of Money 1.7 Fixed-Income Securities 1.8 Inflation-Proof Bonds 1.9 Forwards and Futures 1.10 More About Futures 1.11 Summary Further Reading Exercises Chapter 2: Derivatives 2.1 Introduction 2.2 Options 2.3 Definition of Common Terms 2.4 Payoff Diagrams 2.5 Writing Options 2.6 Margin 2.7 Market Conventions 2.8 The Value of the Option Before Expiry 2.9 Factors Affecting Derivative Prices 2.10 Speculation and Gearing 2.11 Early Exercise 2.12 Put-Call Parity 2.13 Binaries or Digitals 2.14 Bull and Bear Spreads 2.15 Straddles and Strangles 2.16 Risk Reversal 2.17 Butterflies and Condors 2.18 Calendar Spreads 2.19 Leaps and Flex 2.20 Warrants 2.21 Convertible Bonds 2.22 Over the Counter Options 2.23 Summary Further Reading Exercises Chapter 3: The Binomial Model 3.1 Introduction 3.2 Equities Can Go Down as Well as Up 3.3 The Option Value 3.4 Which Part of Our ‘Model’ didn’t We Need! 3.5 Why should this ‘Theoretical Price’ be the ‘Market Price’? 3.6 How did I Know to Sell 1/2 of the Stock for Hedging? 3.7 How does this Change if Interest Rates are Non-Zero! 3.8 Is the Stock Itself Correctly Priced! 3.9 Complete Markets 3.10 The Real and Risk-Neutral Worlds 3.11 And Now Using Symbols 3.12 An Equation for the Value of an Option 3.13 Where did the Probability p Go! 3.14 Counter-Intuitive? 3.15 The Binomial Tree 3.16 The Asset Price Distribution 3.17 Valuing Back Down the Tree 3.18 Programming the Binomial Method 3.19 The Greeks 3.20 Early Exercise 3.21 The Continuous-Time Limit 3.22 Summary Further Reading Welcome to My World Appendix: Another Parameterization Exercises Chapter 4: The Random Behavior of Assets 4.1 Introduction 4.2 The Popular Forms of ‘Analysis’ 4.3 Why We Need A Model for Randomness: Jensen’s Inequality 4.4 Similarities Between Equities, Currencies, Commodities and Indices 4.5 Examining Returns 4.6 Timescales 4.7 Estimating Volatility 4.8 The Random Walk on a Spreadsheet 4.9 The Wiener Process 4.10 The Widely Accepted Model for Equities, Currencies, Commodities and Indices 4.11 Summary Further Reading Exercises Chapter 5: Elementary Stochastic Calculus 5.1 Introduction 5.2 A Motivating Example 5.3 The Markov Property 5.4 The Martingale Property 5.5 Quadratic Variation 5.6 Brownian Motion 5.7 Stochastic Integration 5.8 Stochastic Differential Equations 5.9 The Mean Square Limit 5.10 Functions of Stochastic Variables and Itô’s Lemma 5.11 Interpretation of Itô’s Lemma 5.12 Itô and Taylor 5.13 Itô in Higher Dimensions 5.14 Some Pertinent Examples 5.15 Summary Further Reading Exercises Chapter 6: The Black–Scholes Model 6.1 Introduction 6.2 A Very Special Portfolio 6.3 Elimination of Risk: Delta Hedging 6.4 No Arbitrage 6.5 The Black–Scholes Equation 6.6 The Black–Scholes Assumptions 6.7 Final Conditions 6.8 Options on Dividend-Paying Equities 6.9 Currency Options 6.10 Commodity Options 6.11 Expectations and Black–Scholes 6.12 Some Other Ways of Deriving the Black-Scholes Equation 6.13 No Arbitrage in the Binomial, Black–Scholes and ‘Other’ Worlds 6.14 Forwards and Futures 6.15 Futures Contracts 6.16 Options on Futures 6.17 Summary Further Reading Exercises Chapter 7: Partial Differential Equations 7.1 Introduction 7.2 Putting the Black–Scholes Equation into Historical Perspective 7.3 The Meaning of the Terms in the Black–Scholes Equation 7.4 Boundary and Initial/Final Conditions 7.5 Some Solution Methods 7.6 Similarity Reductions 7.7 Other Analytical Techniques 7.8 Numerical Solution 7.9 Summary Further Reading Exercises Chapter 8: The Black–Scholes Formulae and the Greeks’ 8.1 Introduction 8.2 Derivation of the Formulæ for Calls, Puts and Simple Digitals 8.3 Delta 8.4 Gamma 8.5 Theta 8.6 Speed 8.7 Vega 8.8 Rho 8.9 Implied Volatility 8.10 A Classification of Hedging Types 8.11 Summary Further Reading Exercises Chapter 9: Overview of Volatility Modeling 9.1 Introduction 9.2 The Different Types of Volatility 9.3 Volatility Estimation by Statistical Means 9.4 Maximum Likelihood Estimation 9.5 Skews and Smiles 9.6 Different Approaches to Modeling Volatility 9.7 The Choices of Volatility Models 9.8 Summary Further Reading Appendix: How to Derive BS PDE, Minimum Fuss Exercises Chapter 10: How to Delta Hedge 10.1 Introduction 10.2 What if Implied and Actual Volatilities are Different? 10.3 Implied Versus Actual, Delta Hedging but Using Which Volatility? 10.4 Case I: Hedge with Actual Volatility, σ 10.5 Case 2: Hedge with Implied Volatility, 10.6 Hedging with Different Volatilities 10.7 Pros and Cons of Hedging with Each Volatility 10.8 Portfolios when Hedging with Implied Volatility 10.9 How Does Implied Volatility Behave! 10.10 Summary Further Reading Exercises Chapter 11: An Introduction to Exotic and Path-Dependent Options 11.1 Introduction 11.2 Option Classification 11.3 Time Dependence 11.4 Cashflows 11.5 Path Dependence 11.6 Dimensionality 11.7 The Order of an Option 11.8 Embedded Decisions 11.9 Classification Tables 11.10 Examples of Exotic Options 11.11 Summary of Math/Coding Consequences 11.12 Summary Further Reading Some Formulæ for Asian Options Some Formulæ for Lookback Options Exercises Chapter 12: Multi-Asset Options 12.1 Introduction 12.2 Multidimensional Lognormal Random Walks 12.3 Measuring Correlations 12.4 Options on Many Underlyings 12.5 The Pricing Formula for European Non-Path-Dependent Options on Dividend-Paying Assets 12.6 Exchanging one Asset for Another: A Similarity Solution 12.7 Two Examples 12.8 Realities of Pricing Basket Options 12.9 Realities of Hedging Basket Options 12.10 Correlation Versus Cointegration 12.11 Summary Further Reading Exercises Chapter 13: Barrier Options 13.1 Introduction 13.2 Different Types of Barrier Options 13.3 Pricing Methodologies 13.4 Pricing Barriers in The Partial Differential Equation Framework 13.5 Examples 13.6 Other Features in Barrier-Style Options 13.7 Market Practice: What Volatility Should I Use? 13.8 Hedging Barrier Options 13.9 Summary Further Reading Exercises Chapter 14: Fixed-Income Products and Analysis: Yield, Duration and Convexity 14.1 Introduction 14.2 Simple Fixed-Income Contracts and Features 14.3 International Bond Markets 14.4 Accrued Interest 14.5 Day-Count Conventions 14.6 Continuously and Discretely Compounded Interest 14.7 Measures of Yield 14.8 The Yield Curve 14.9 Price/Yield Relationship 14.10 Duration 14.11 Convexity 14.12 An Example 14.13 Hedging 14.14 Time-Dependent Interest Rate 14.15 Discretely Paid Coupons 14.16 Forward Rates and Bootstrapping 14.17 Interpolation 14.18 Summary Further Reading Exercises Chapter 15: Swaps interpolation intrinsic value Ito’s lemma higher dimensions interpretation multidimensional version Taylor series and Japanese bond market Japanese bonds Japanese candlesticks Japanese government bonds (JGBs) Jensen’s inequality jump condition jump diffusion kappa Kelly criterion key cross currency rates knock-in knock-in option see barrier option knock-out knock-out option see barrier option Laplace transform LEAPS (long-term equity anticipation securities) leverage LIBOR-in-arrears swap linear parabolic partial differential equation local truncation error log x logarithm (log) series lognormal random walk London Interbank Offer Rate (LIBOR) long-dated swaption straddles long position Longstaff & Schwartz regression approach for American options Long Term Capital Management long-term equity anticipation securities (LEAPS) long-term German bonds lookback options formulae for low-discrepancy sequences Macaulay duration MAE All Bond Index maintenance margin margin margin account margin call margin delta margin gamma margin hedging margin theta marginal distributions market conventions market crashes market microstructure modeling combining market microstructure and option theory effect of demand on price imitation market portfolio market price market price of risk risk neutrality and marking to market marking to model Markov chains Markov process Markov property Markowitz model mark-to-market mark-to-model Martingale approach, Black-Scholes equation and Martingale property Martingale variance reduction maturity date maturity of contract maximum likelihood estimation examples standard deviation mean mean-reverting random walk mean square limit mean-variance volatility Merton model meshes Metallgesellschaft Microsoft stock migration model-dependent hedging model independence model-independent hedging modified duration money management money market account monotonicity Monte Carlo methods boundary/final conditions decision features efficiency functional form of coefficients linear or non-linear number of dimensions program of study see also Monte Carlo simulation Monte Carlo simulation advanced techniques advantages American options arithmetic variables basis functions calculating greeks calculation time Cholesky factorization control variate technique generating normal variables generating paths interest rate products lognormal underlying, no path dependency Longstaff & Schwartz regression approach for American options pricing via pros and cons risk vs risk neutral, speculation vs hedging speeding up convergence using random numbers Moody’s moving average cap/floor moving averages moving-window volatility multidimensional lognormal random walks multi-index model New York Mercantile Exchange (NYMEX) Newton–Raphson no-arbitrage principle nodes noise trader non-anticipatory integration non-attainable origin non-Markov process non-path-dependent options on dividend-paying assets, pricing formula non-zero interest rates Normal distribution cumulative distribution function Normal model Normal random walk notes numerical integration basic Monte Carlo integration low-discrepancy sequences program of study regular grid one-factor interest rate modeling one-touch volatility one-way floaters open interest option classification option strategy option value before expiry equation for options on baskets on dividend-paying equities on futures order of on underlyings Orange County order of an option ordinary differential equation oscillators out of the money out-of-the-money calls out-of-the-money puts out-of-the-money strangle out option outside (rainbow) barrier options over-the-counter (OTC) contract over the counter options Pacific Stock Exchange par swap parallel shifts in yield curve parameters Parisian options Parkinson estimate partial differential equation captions and swaptions pricing barriers in pricing via path dependence strong weak path differential equations paw swap payer swaption payoff diagram bear spread binary call option binary put option bull spread butterfly spread call option condor put option risk reversal straddle strangle payoff function Perez Companc daily returns normalized frequency distribution performance measure perpetual warrants Philadelphia Stock Exchange Phlogiston theory Platinum (crash) hedge Poisson process instantaneous risk of default and portfolio hedged of options portfolio management diversification risk-free investment uncorrelated assets portfolio theory portfolio when hedging with implied volatility expectation portfolio optimization variance positive homogeneity positive recovery premium present value price time series price/yield relationship pricing methodologies principal principal components analysis power method probability density function Proctor and Gamble product function profit diagram call put pull to par put delta of formula for gamma of rho of sensitivity to dividend for common contracts speed of contract theta of vega of put-call parity put-call symmetry put option payoff diagram put option value as function of asset and time as function of time as function of underlying asset at fixed time put spread put swaption puttable swap quadratic variation quantitative analysis quasi-random sequences rainbow options random walk on a spreadsheet range notes ratchets real (definition) real world rebalancing rebate receiver swaption recursive stratified sampling reduction of variance reflection principle reflex cap/floor rehedging relative strength index repeated hitting replication repo repo rate resetting of barrier Retail Price Index (RPI) return expected reverse floater reverse repo reward rho sensitivity to dividend yield sensitivity to interest rate rings of Saturn effect risk risk neutrality risk preferences risk reversal sensitivity to smiles and skews risk seeking risk/return diagram RiskMetrics correlation datasets parameters, calculation of volatility volatility estimation risk-neutral expectation risk-neutral probabilities risk-neutral random walk risk-neutral spot rate risk-neutral world risky bonds Rogers & Satchell estimate roll-down options roll-up options rolling cap/floor roulette Russian GKOs Samurai bonds saucer (rounding) tops and bottoms Separate Trading of Registered Interest and Principal of Securities (STRIPS) series series solution share shareholders Sharpe ratio short position short-dated swaption straddles short-term German bonds short-term interest rate similarity reduction simple interest skews sensitivity of risk reversal to sensitivity of straddle to slippage slope of option value smile sensitivity of risk reversal to sensitivity of straddle to Sobol sequence soft barrier option speculation speed of an option splitting pairs spot-forward parity spot interest rate spot price spread spread options SPX volatility Standard & Poor’s Standard & Poor’s 500 (S&P500) standard deviation of asset price change static hedging stationarity step-up swaps, caps and floors sticky delta sticky moneyness rule sticky strike stochastic calculus stochastic differential equation stochastic integration stochastic interest rates stochastic risk of default stochastic variables stochastic volatility stock pricing stock splits straddle sensitivity to smiles and skews strangle stratified sampling strike price STRIPS (Separate Trading of Registered Interest and Principal of Securities) Student function sub-additivity swap curve swaps bonds vs definition swaptions symbols, use of systematic risk tail index Taylor series approximation differentiation and expansion Ito’s lemma technical analysis Bollinger bands double and triple tops and bottoms head and shoulders Japanese candlesticks moving averages oscillators plotting point and figure charts relative strength index resistance saucer (rounding) tops and bottoms support trendlines technical analysis tequila crisis term repo term sheet basket equity swap chooser range accrual note in-out range accrual note on MXN/USD ‘La Tricolore’ capital-guaranteed note for OTC put Sterling/Deutschemark deconvergence swap USD fixed rate note for USD index amortizing swap USD/JPY knock-out installment premium option theoretical price theta time decay time dependence time steps time to expiry time value of money time-dependent intensity term structure of default and time-dependent interest rate timescales tracking, index trading game tranches transition matrix translation invariance Treynor ratio triggers trinomial random walk trinomial trees, bond pricing triple tops and bottoms two-for-one split UK bond market uncertain volatility underlying asset up option up-and in call calculator formula value up-and-in put formula up-and-out call delta formula profit/loss value value, with different volatilities up-and-out put calculator formula value upwind differencing US bond market US Treasuries utility function Value at Risk (VaR) definition for derivatives delta approximation delta/gamma approximation fixed-income portfolios use of valuation models as performance measure for portfolio simulations bootstrapping Monte Carlo for single asset vanilla call option vanilla interest rate swap vanilla options vanilla put option variables variance Vasicek model extended, of Hull and White vega hedging volatility choice and VIX volatility VIX volatility index volatility choice in practice estimating types of volatility, estimation by statistical means constant volatility/moving window expected future volatility exponential weighted moving average (EWMA) GARCH model Garman & Klass incorporating mean reversion Parkinson range-based estimation of volatility Rogers & Satchell time-varying volatility traditional close-to-close measure volatility, modeling asymptotic analysis f volatility calibration deterministic volatility surfaces static hedging stochastic volatility stochastic volatility and mean-variance analysis uncertain volatility volatility trades volume Wall Street Journal Europe warrant wave theory Weibull distribution Wiener process writer of options writing of options Xena Yankee bonds yield definition vs duration measures of yield analysis yield curve yield curve fitting reasons against reasons for yield time series yield to maturity (YTM) zero-coupon bond zeta Index compiled by Annette Musker ... Accompanying Paul Wilmott Introduces Quantitative Finance, Second Edition Appendix E: What You Get if (When) You Upgrade to PWOQF2 Introduction Bibliography Index Paul Wilmott Introduces Quantitative Finance. .. Cataloging-in-Publication Data Wilmott, Paul Paul Wilmott introduces quantitative finance. —2nd ed p cm ISBN 978-0-470-31958-1 Finance Mathematical models Options (Finance) —Mathematical models Options (Finance) —Prices—... Street PWOQF is, I am told, a standard text within the banking industry, but in Paul Wilmott Introduces Quantitative Finance I have specifically the university student in mind The differences between