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paul WilmottIntroducesQuantitative FinanceSecond EditionPaul WilmottIntroducesQuantitative FinanceSecond 2007 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester,West Sussex PO19 8SQ, EnglandTelephone (+44) 1243 779777 Email (for orders and customer service enquiries): our Home Page on 2007 paul WilmottAll Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmittedin any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, exceptunder the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by theCopyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission inwriting of the Publisher.

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1 paul WilmottIntroducesQuantitative FinanceSecond EditionPaul WilmottIntroducesQuantitative FinanceSecond 2007 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester,West Sussex PO19 8SQ, EnglandTelephone (+44) 1243 779777 Email (for orders and customer service enquiries): our Home Page on 2007 paul WilmottAll Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmittedin any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, exceptunder the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by theCopyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission inwriting of the Publisher.

2 Requests to the Publisher should be addressed to the Permissions Department, JohnWiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed or faxed to (+44) 1243 used by companies to distinguish their products are often claimed as trademarks. All brandnames and product names used in this book are trade names, service marks, trademarks or registeredtrademarks of their respective owners. The Publisher is not associated with any product or vendor mentionedin this publication is designed to provide accurate and authoritative information in regard to the subject mattercovered. It is sold on the understanding that the Publisher is not engaged in rendering professional services.

3 Ifprofessional advice or other expert assistance is required, the services of a competent professional should Wiley Editorial OfficesJohn Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USAJ ossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USAW iley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, GermanyJohn Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, AustraliaJohn Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, ONT, L5R 4J3, CanadaWiley also publishes its books in a variety of electronic formats. Some content that appearsin print may not be available in electronic Logo Design: Richard J.

4 PacificoLibrary of Congress Cataloging-in-Publication DataWilmott, wilmott introduces quantitative finance . 2nd 978-0-470-31958-11. finance Mathematical models. 2. Options ( finance ) Mathematical models. 3. Options ( finance ) Prices Mathematical models. I. Title. II Title: quantitative 2007332 dc222007015893 British Library Cataloguing in Publication DataA catalogue record for this book is available from the British LibraryISBN 978-0-470-31958-1 (PB)Typeset in 10/12pt Helvetica by Laserwords Private Limited, Chennai, IndiaPrinted and bound in Great Britain by Antony Rowe Ltd, Chippenham, WiltshireThis book is printed on acid-free paper responsibly manufactured from sustainable forestryin which at least two trees are planted for each one used for paper a rising StarcontentsPrefacexxiii1 Products and Markets.

5 Equities, Commodities, Exchange Rates,Forwards and time value of and first example of no about of common representations of value of the option before affecting derivative and or and bear and and and the counter Binomial can go down as well as option part of our model didn t we need? should this theoretical price be the market price ? role of did I know to sell12of the stock for hedging? general formula for does this change if interest rates are non-zero? the stock itself correctly priced? real and risk-neutral interest now using asset deviation of asset price equation for the value of an did the probabilitypgo?

6 Binomial asset price back down the the binomial continuous-time Random Behavior of popular forms of analysis we need a model for randomness: Jensen s between equities, currencies, commodities and random walk on a Wiener widely accepted model for equities, currencies, commodities Stochastic motivating Markov martingale differential mean square of stochastic variables and It o s of It o s o and o in higher pertinent motion with lognormal random mean-reverting random another mean-reverting random Black Scholes very special of risk: delta Black Scholes Black Scholes on dividend-paying and Black other ways of deriving the Black Scholes martingale binomial arbitrage in the binomial, Black Scholes and other and interest rates are known, forward prices and futuresprices are the on Differential the Black Scholes equation into historical meaning of the terms in the Black Scholes and initial/final solution to constant coefficient diffusion s analytical Black Scholes Formul and the Greeks of the formul for calls, puts and simple for a for a for a binary for a binary classification of hedging hedge?

7 Two main (Platinum) of Volatility different types of or realized estimation by statistical simplest volatility estimate: constant mean weighted moving simple GARCH future close-close estimators: range-based estimation likelihood simple motivating example: taxi math behind this: find the standard and of the straddle to skews and of the risk reversal to skews and approaches to modeling calibrate or not? volatility volatility and mean-variance analysis of choices of volatility How to Delta if implied and actual volatilities are different? versus actual, delta hedging but using which volatility? 1: Hedge with actual volatility, 2: Hedge with implied volatility, expected profit after hedging using implied variance of profit after hedging using implied with different volatility=Implied volatility>Implied volatility<Implied and cons of hedging with each with actual with implied with another when hedging with implied optimization does implied volatility behave?

8 Summary24511 An Introduction to Exotic and Path-dependent path path order of an Examples of exotic Compounds and Range Barrier Asian Lookback Summary of math/coding Summary26712 Multi-asset lognormal random on many pricing formula for European non-path-dependent options ondividend-paying one asset for another: a similarity of pricing basket of hedging basket Correlation versus Summary28413 Barrier types of barrier Carlo differential barriers in the partial differential equation Out In more features in barrier-style hitting of the of barrier practice: what volatility should I use?

9 Barrier Fixed-income Products and Analysis: Yield, Duration and fixed-income contracts and zero-coupon coupon-bearing money market rate rate bond States of and discretely compounded of yield to maturity (YTM) or internal rate of return (IRR) yield An Time-dependent interest Discretely paid Forward rates and Discrete On a Summary34615 vanilla interest rate swap between swaps and features of swaps types of rate One-factor Interest Rate interest bond pricing equation for the general is the market price of risk? the market price of risk, and risk , Ingersoll & & & and FX forwards and futures when rates are convexity Yield Curve & extended Vasicek model of Hull & fitting.

10 For and Interest Rate and relationship between a caplet and a bond swaps, caps and , captions and amortizing rate features in the index amortizing rate with embedded Some More interest rate Summary40119 The Heath, Jarrow & Morton and Brace, Gatarek & Musiela forward rate spot rate non-Markov nature of market price of and risk relationship between the risk-neutral forward rate driftand Musiela Multi-factor Spreadsheet A simple one-factor example: Ho & Principal Component The power Options on equities, Non-infinitesimal short The Brace, Gatarek & Musiela PVing the Summary42020 Investment Lessons from Blackjack and rules of the of winning at distribution of profit in Kelly you win at roulette?


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