Paul Wilmott On Quantitative Finance

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3 Paul Wilmott On Quantitative Finance

5 Paul Wilmott On Quantitative Finance Second Edition

6 Copyright 2006 Paul Wilmott Published by John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) (for orders and customer service enquiries): Visit our Home Page on All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or ed to permreq@wiley.co.uk, or faxed to (+44) Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA , USA Wiley-VCH Verlag GmbH, Boschstr. 12, D Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Wilmott, Paul. Paul Wilmott on quantitative finance. 2nd ed. p. cm. Includes bibliographical references and index. ISBN (cloth/cd : alk. paper) ISBN (cloth/cd : alk. paper) 1. Derivative securities Mathematical models. 2. Options (Finance) Mathematical models. 3. Options (Finance) Prices Mathematical models. I. Title. HG6024.A3W dc British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-13: (HB) ISBN-10: (HB) Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

7 In memory of Detlev Vogel

9 contents of volume one Visual Basic Code Prolog to the Second Edition xxv xxvii PART ONE MATHEMATICAL AND FINANCIAL FOUNDATIONS; BASIC THEORY OF DERIVATIVES; RISK AND RETURN 1 1 Products and Markets 5 2 Derivatives 25 3 The Random Behavior of Assets 55 4 Elementary Stochastic Calculus 71 5 The Black Scholes Model 91 6 Partial Differential Equations The Black Scholes Formulae and the Greeks Simple Generalizations of the Black Scholes World Early Exercise and American Options Probability Density Functions and First-exit Times Multi-asset Options How to Delta Hedge Fixed-income Products and Analysis: Yield, Duration and Convexity Swaps 251

10 viii contents 15 The Binomial Model How Accurate is the Normal Approximation? Investment Lessons from Blackjack and Gambling Portfolio Management Value at Risk Forecasting the Markets? A Trading Game 359

11 contents ix contents of volume two PART TWO EXOTIC CONTRACTS AND PATH DEPENDENCY An Introduction to Exotic and Path-dependent Derivatives Barrier Options Strongly Path-dependent Derivatives Asian Options Lookback Options Derivatives and Stochastic Control Miscellaneous Exotics Equity and FX Term Sheets 481 PART THREE FIXED-INCOME MODELING AND DERIVATIVES One-factor Interest Rate Modeling Yield Curve Fitting Interest Rate Derivatives Convertible Bonds Mortgage-backed Securities Multi-factor Interest Rate Modeling Empirical Behavior of the Spot Interest Rate The Heath, Jarrow & Morton and Brace, Gatarek & Musiela Models Fixed-income Term Sheets 627 PART FOUR CREDIT RISK Value of the Firm and the Risk of Default Credit Risk 649

12 x contents 41 Credit Derivatives RiskMetrics and CreditMetrics CrashMetrics Derivatives **** Ups 731

13 contents xix contents of volume three PART FIVE ADVANCED TOPICS Financial Modeling Defects in the Black Scholes Model Discrete Hedging Transaction Costs Overview of Volatility Modeling Deterministic Volatility Surfaces Stochastic Volatility Uncertain Parameters Empirical Analysis of Volatility Stochastic Volatility and Mean-variance Analysis Asymptotic Analysis of Volatility Volatility Case Study: The Cliquet Option Jump Diffusion Crash Modeling Speculating with Options Static Hedging The Feedback Effect of Hedging in Illiquid Markets Utility Theory More About American Options and Related Matters Advanced Dividend Modeling Serial Autocorrelation in Returns Asset Allocation in Continuous Time 1051

14 xx contents 67 Asset Allocation Under Threat of a Crash Interest-rate Modeling Without Probabilities Pricing and Optimal Hedging of Derivatives, the Non-probabilistic Model Cont d Extensions to the Non-probabilistic Interest-rate Model Modeling Inflation Energy Derivatives Real Options Life Settlements and Viaticals Bonus Time 1175 PART SIX NUMERICAL METHODS AND PROGRAMS Overview of Numerical Methods Finite-difference Methods for One-factor Models Further Finite-difference Methods for One-factor Models Finite-difference Methods for Two-factor Models Monte Carlo Simulation Numerical Integration Finite-difference Programs Monte Carlo Programs 1311 Appendix A All the Math You Need... and No More (An Executive Summary) 1317 Bibliography 1329 Index 1351

15 visual basic code Implied volatility, Newton Raphson 130 Cumulative distribution for Normal variable 131 The binomial method, European option 286 The binomial method, American option 290 Double knock-out barrier option, finite difference 490 Instalment knock-out barrier option, finite difference 493 Range Note, finite difference 497 Lookback, finite difference 501 Index Amortizing Rate Swap, finite difference 634 Cliquet option, uncertain volatility, finite difference 923 Optimization subroutine 983 Setting up final condition, finite difference 1212 Finite difference time loop, first example 1213 European option, finite difference, three dimensions 1215 American option, finite difference, three dimensions 1219 European or American option, finite difference, two dimensions 1221 Upwind differencing, interest rate 1225 LU decomposition 1234 Matrix solution 1235 Successive over relaxation 1238 Successive over relaxation, early exercise 1246 Jump condition for discrete dividends 1248 Jump condition for path-dependent quantities 1249 Two-factor explicit finite difference 1257 Convertible bond constraint 1257 Box Muller 1269 Cholesky factorization 1276 Numerical integration, Monte Carlo 1287 Halton number generation 1290 Kolmogorov equation, explicit finite difference 1295 Convertible bond time stepping fragment, explicit finite difference 1297 American option, implicit finite difference 1298 Parisian option, explicit finite difference 1299 Passport option, explicit finite difference 1300

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