Paul Wilmott introduces quantitative finance

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書誌事項

Paul Wilmott introduces quantitative finance

J. Wiley & Sons, 2007

2nd ed

  • : pbk

大学図書館所蔵 件 / 全8件

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注記

Description based on: reprinted October 2007

Includes bibliographical references (p. [659]-681) and index

内容説明・目次

内容説明

Paul Wilmott Introduces Quantitative Finance, Second Edition is an accessible introduction to the classical side of quantitative finance specifically for university students. Adapted from the comprehensive, even epic, works Derivatives and Paul Wilmott on Quantitative Finance, Second Edition, it includes carefully selected chapters to give the student a thorough understanding of futures, options and numerical methods. Software is included to help visualize the most important ideas and to show how techniques are implemented in practice. There are comprehensive end-of-chapter exercises to test students on their understanding.

目次

Preface xxiii 1 Products and Markets: Equities, Commodities, Exchange Rates, Forwards and Futures 1 1.1 Introduction 2 1.2 Equities 2 1.3 Commodities 9 1.4 Currencies 9 1.5 Indices 11 1.6 The time value of money 11 1.7 Fixed-income securities 17 1.8 Inflation-proof bonds 17 1.9 Forwards and futures 19 1.10 More about futures 22 1.11 Summary 24 2 Derivatives 27 2.1 Introduction 28 2.2 Options 28 2.3 Definition of common terms 33 2.4 Payoff diagrams 34 2.5 Writing options 39 2.6 Margin 39 2.7 Market conventions 39 2.8 The value of the option before expiry 40 2.9 Factors affecting derivative prices 41 2.10 Speculation and gearing 42 2.11 Early exercise 44 2.12 Put-call parity 44 2.13 Binaries or digitals 47 2.14 Bull and bear spreads 48 2.15 Straddles and strangles 50 2.16 Risk reversal 52 2.17 Butterflies and condors 53 2.18 Calendar spreads 53 2.19 LEAPS and FLEX 55 2.20 Warrants 55 2.21 Convertible bonds 55 2.22 Over the counter options 56 2.23 Summary 57 3 The Binomial Model 59 3.1 Introduction 60 3.2 Equities can go down as well as up 61 3.3 The option value 63 3.4 Which part of our 'model' didn't we need? 65 3.5 Why should this 'theoretical price' be the 'market price'? 65 3.6 How did I know to sell 1 2 of the stock for hedging? 66 3.7 How does this change if interest rates are non-zero? 67 3.8 Is the stock itself correctly priced? 68 3.9 Complete markets 69 3.10 The real and risk-neutral worlds 69 3.11 And now using symbols 73 3.12 An equation for the value of an option 75 3.13 Where did the probability p go? 77 3.14 Counter-intuitive? 77 3.15 The binomial tree 78 3.16 The asset price distribution 78 3.17 Valuing back down the tree 80 3.18 Programming the binomial method 85 3.19 The greeks 86 3.20 Early exercise 88 3.21 The continuous-time limit 90 3.22 Summary 90 4 The Random Behavior of Assets 95 4.1 Introduction 96 4.2 The popular forms of 'analysis' 96 4.3 Why we need a model for randomness: Jensen's inequality 97 4.4 Similarities between equities, currencies, commodities and indices 99 4.5 Examining returns 100 4.6 Timescales 105 4.7 Estimating volatility 109 4.8 The random walk on a spreadsheet 109 4.9 The Wiener process 111 4.10 The widely accepted model for equities, currencies, commodities and indices 112 4.11 Summary 115 5 Elementary Stochastic Calculus 117 5.1 Introduction 118 5.2 A motivating example 118 5.3 The Markov property 120 5.4 The martingale property 120 5.5 Quadratic variation 120 5.6 Brownian motion 121 5.7 Stochastic integration 122 5.8 Stochastic differential equations 123 5.9 The mean square limit 124 5.10 Functions of stochastic variables and Ito's lemma 124 5.11 Interpretation of Ito's lemma 127 5.12 Ito and Taylor 127 5.13 Ito in higher dimensions 130 5.14 Some pertinent examples 130 5.15 Summary 136 6 The Black-Scholes Model 139 6.1 Introduction 140 6.2 A very special portfolio 140 6.3 Elimination of risk: delta hedging 142 6.4 No arbitrage 142 6.5 The Black-Scholes equation 143 6.6 The Black-Scholes assumptions 145 6.7 Final conditions 146 6.8 Options on dividend-paying equities 147 6.9 Currency options 147 6.10 Commodity options 148 6.11 Expectations and Black-Scholes 148 6.12 Some other ways of deriving the Black-Scholes equation 149 6.13 No arbitrage in the binomial, Black-Scholes and 'other' worlds 150 6.14 Forwards and futures 151 6.15 Futures contracts 152 6.16 Options on futures 153 6.17 Summary 153 7 Partial Differential Equations 157 7.1 Introduction 158 7.2 Putting the Black-Scholes equation into historical perspective 158 7.3 The meaning of the terms in the Black-Scholes equation 159 7.4 Boundary and initial/final conditions 159 7.5 Some solution methods 160 7.6 Similarity reductions 163 7.7 Other analytical techniques 163 7.8 Numerical solution 164 7.9 Summary 164 8 The Black-Scholes Formulae and the 'Greeks' 169 8.1 Introduction 170 8.2 Derivation of the formulae for calls, puts and simple digitals 170 8.3 Delta 182 8.4 Gamma 184 8.5 Theta 187 8.6 Speed 187 8.7 Vega 188 8.8 Rho 190 8.9 Implied volatility 191 8.10 A classification of hedging types 194 8.11 Summary 196 9 Overview of Volatility Modeling 203 9.1 Introduction 204 9.2 The different types of volatility 204 9.3 Volatility estimation by statistical means 205 9.4 Maximum likelihood estimation 211 9.5 Skews and smiles 215 9.6 Different approaches to modeling volatility 217 9.7 The choices of volatility models 221 9.8 Summary 221 10 How to Delta Hedge 225 10.1 Introduction 226 10.2 What if implied and actual volatilities are different? 227 10.3 Implied versus actual, delta hedging but using which volatility? 228 10.4 Case 1: Hedge with actual volatility, 228 10.5 Case 2: Hedge with implied volatility, ~ 231 10.6 Hedging with different volatilities 235 10.7 Pros and cons of hedging with each volatility 238 10.8 Portfolios when hedging with implied volatility 239 10.9 How does implied volatility behave? 241 10.10 Summary 245 11 An Introduction to Exotic and Path-dependent Options 247 11.1 Introduction 248 11.2 Option classification 248 11.3 Time dependence 249 11.4 Cashflows 250 11.5 Path dependence 252 11.6 Dimensionality 254 11.7 The order of an option 255 11.8 Embedded decisions 256 11.9 Classification tables 258 11.10 Examples of exotic options 258 11.11 Summary of math/coding consequences 266 11.12 Summary 267 12 Multi-asset Options 271 12.1 Introduction 272 12.2 Multidimensional lognormal random walks 272 12.3 Measuring correlations 274 12.4 Options on many underlyings 277 12.5 The pricing formula for European non-path-dependent options on dividend-paying assets 278 12.6 Exchanging one asset for another: a similarity solution 278 12.7 Two examples 280 12.8 Realities of pricing basket options 282 12.9 Realities of hedging basket options 283 12.10 Correlation versus cointegration 283 12.11 Summary 284 13 Barrier Options 287 13.1 Introduction 288 13.2 Different types of barrier options 288 13.3 Pricing methodologies 289 13.4 Pricing barriers in the partial differential equation framework 290 13.5 Examples 293 13.6 Other features in barrier-style options 300 13.7 Market practice: what volatility should I use? 302 13.9 Summary 307 14 Fixed-income Products and Analysis: Yield, Duration and Convexity 319 14.1 Introduction 320 14.2 Simple fixed-income contracts and features 320 14.3 International bond markets 324 14.4 Accrued interest 325 14.5 Day-count conventions 325 14.6 Continuously and discretely compounded interest 326 14.7 Measures of yield 327 14.8 The yield curve 329 14.9 Price/yield relationship 329 14.10 Duration 331 14.11 Convexity 333 14.12 An example 335 14.13 Hedging 335 14.14 Time-dependent interest rate 338 14.15 Discretely paid coupons 339 14.16 Forward rates and bootstrapping 339 14.17 Interpolation 344 14.18 Summary 346 15 Swaps 349 15.1 Introduction 350 15.2 The vanilla interest rate swap 350 15.3 Comparative advantage 351 15.4 The swap curve 353 15.5 Relationship between swaps and bonds 354 15.6 Bootstrapping 355 15.7 Other features of swaps contracts 356 15.8 Other types of swap 357 15.9 Summary 358 16 One-factor Interest Rate Modeling 359 16.1 Introduction 360 16.2 Stochastic interest rates 361 16.3 The bond pricing equation for the general model 362 16.4 What is the market price of risk? 365 16.5 Interpreting the market price of risk, and risk neutrality 366 16.6 Named models 366 16.7 Equity and FX forwards and futures when rates are stochastic 369 16.8 Futures contracts 370 16.9 Summary 372 17 Yield Curve Fitting 373 17.1 Introduction 374 17.2 Ho & Lee 374 17.3 The extended Vasicek model of Hull & White 375 17.4 Yield-curve fitting: For and against 376 17.5 Other models 380 17.6 Summary 380 18 Interest Rate Derivatives 383 18.1 Introduction 384 18.2 Callable bonds 384 18.3 Bond options 385 18.4 Caps and floors 389 18.5 Range notes 392 18.6 Swaptions, captions and floortions 392 18.7 Spread options 394 18.8 Index amortizing rate swaps 394 18.9 Contracts with embedded decisions 397 18.10 Some examples 398 18.11 More interest rate derivatives 400 18.12 Summary 401 19 The Heath, Jarrow & Morton and Brace, Gatarek & Musiela Models 403 19.1 Introduction 404 19.2 The forward rate equation 404 19.3 The spot rate process 404 19.4 The market price of risk 406 19.5 Real and risk neutral 407 19.6 Pricing derivatives 408 19.7 Simulations 408 19.8 Trees 410 19.9 The Musiela parameterization 411 19.10 Multi-factor HJM 411 19.11 Spreadsheet implementation 411 19.12 A simple one-factor example: Ho & Lee 412 19.13 Principal Component Analysis 413 19.14 Options on equities, etc. 416 19.15 Non-infinitesimal short rate 416 19.16 The Brace, Gatarek & Musiela model 417 19.17 Simulations 419 19.18 PVing the cashflows 419 19.19 Summary 420 20 Investment Lessons from Blackjack and Gambling 423 20.1 Introduction 424 20.2 The rules of blackjack 424 20.3 Beating the dealer 426 20.4 The distribution of profit in blackjack 428 20.5 The Kelly criterion 429 20.6 Can you win at roulette? 432 20.7 Horse race betting and no arbitrage 433 20.8 Arbitrage 434 20.9 How to bet 436 20.10 Summary 438 21 Portfolio Management 441 21.1 Introduction 442 21.2 Diversification 442 21.3 Modern portfolio theory 445 21.4 Where do I want to be on the efficient frontier? 447 21.5 Markowitz in practice 450 21.6 Capital Asset Pricing Model 451 21.7 The multi-index model 454 21.8 Cointegration 454 21.9 Performance measurement 455 21.10 Summary 456 22 Value at Risk 459 22.1 Introduction 460 22.2 Definition of Value at Risk 460 22.3 VaR for a single asset 461 22.4 VaR for a portfolio 463 22.5 VaR for derivatives 464 22.6 Simulations 466 22.7 Use of VaR as a performance measure 468 22.8 Introductory Extreme Value Theory 469 22.9 Coherence 470 22.10 Summary 470 23 Credit Risk 473 23.1 Introduction 474 23.2 The Merton model: equity as an option on a company's assets 474 23.3 Risky bonds 475 23.4 Modeling the risk of default 476 23.5 The Poisson process and the instantaneous risk of default 477 23.6 Time-dependent intensity and the term structure of default 481 23.7 Stochastic risk of default 482 23.8 Positive recovery 484 23.9 Hedging the default 485 23.10 Credit rating 486 23.11 A model for change of credit rating 488 23.12 Copulas: pricing credit derivatives with many underlyings 488 23.13 Collateralized debt obligations 490 23.14 Summary 492 24 RiskMetrics and CreditMetrics 495 24.1 Introduction 496 24.2 The RiskMetrics datasets 496 24.3 Calculating the parameters the RiskMetrics way 496 24.4 The CreditMetrics dataset 498 24.5 The CreditMetrics methodology 501 24.6 A portfolio of risky bonds 501 24.7 CreditMetrics model outputs 502 24.8 Summary 502 25 CrashMetrics 505 25.1 Introduction 506 25.2 Why do banks go broke? 506 25.3 Market crashes 506 25.4 CrashMetrics 507 25.5 CrashMetrics for one stock 508 25.6 Portfolio optimization and the Platinum hedge 510 25.7 The multi-asset/single-index model 511 25.8 Portfolio optimization and the Platinum hedge in the multi-asset model 519 25.9 The multi-index model 520 25.10 Incorporating time value 521 25.11 Margin calls and margin hedging 522 25.12 Counterparty risk 524 25.13 Simple extensions to CrashMetrics 524 25.14 The CrashMetrics Index (CMI) 525 25.15 Summary 526 26 Derivatives **** Ups 527 26.1 Introduction 528 26.2 Orange County 528 26.3 Proctor and Gamble 529 26.4 Metallgesellschaft 532 26.5 Gibson Greetings 533 26.6 Barings 536 26.7 Long-Term Capital Management 537 26.8 Summary 540 27 Overview of Numerical Methods 541 27.1 Introduction 542 27.2 Finite-difference methods 542 27.3 Monte Carlo methods 544 27.4 Numerical integration 546 27.5 Summary 547 28 Finite-difference Methods for One-factor Models 549 28.1 Introduction 550 28.2 Grids 550 28.3 Differentiation using the grid 553 28.4 Approximating 553 28.5 Approximating 554 28.6 Approximating 557 28.7 Example 557 28.8 Bilinear interpolation 558 28.9 Final conditions and payoffs 559 28.10 Boundary conditions 560 28.11 The explicit finite-difference method 562 28.12 The Code #1: European option 567 28.13 The Code #2: American exercise 571 28.14 The Code #3: 2-D output 573 28.15 Upwind differencing 575 28.16 Summary 578 29 Monte Carlo Simulation 581 29.1 Introduction 582 29.2 Relationship between derivative values and simulations: equities, indices, currencies, commodities 582 29.3 Generating paths 583 29.4 Lognormal underlying, no path dependency 584 29.5 Advantages of Monte Carlo simulation 585 29.6 Using random numbers 586 29.7 Generating Normal variables 587 29.8 Real versus risk neutral, speculation versus hedging 588 29.9 Interest rate products 590 29.10 Calculating the greeks 593 29.11 Higher dimensions: Cholesky factorization 594 29.12 Calculation time 596 29.13 Speeding up convergence 596 29.14 Pros and cons of Monte Carlo simulations 598 29.15 American options 598 29.16 Longstaff & Schwartz regression approach for American options 599 29.17 Basis functions 603 29.18 Summary 603 30 Numerical Integration 605 30.1 Introduction 606 30.2 Regular grid 606 30.3 Basic Monte Carlo integration 607 30.4 Low-discrepancy sequences 609 30.5 Advanced techniques 613 30.6 Summary 614 A All the Math You Need .and No More (An Executive Summary) 617 A. 1 Introduction 618 A. 2 e 618 A. 3 log 618 A. 4 Differentiation and Taylor series 620 A. 5 Differential equations 623 A. 6 Mean, standard deviation and distributions 623 A. 7 Summary 626 B Forecasting the Markets? A Small Digression 627 B. 1 Introduction 628 B. 2 Technical analysis 628 B. 3 Wave theory 637 B. 4 Other analytics 638 B. 5 Market microstructure modeling 640 B. 6 Crisis prediction 641 B. 7 Summary 641 C A Trading Game 643 C. 1 Introduction 643 C. 2 Aims 643 C. 3 Object of the game 643 C. 4 Rules of the game 643 C. 5 Notes 644 C. 6 How to fill in your trading sheet 645 D Contents of CD accompanying Paul Wilmott Introduces Quantitative Finance, second edition 649 E What you get if (when) you upgrade to PWOQF2 653 Bibliography 659 Index 683

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