TAILIEUCHUNG - Wilmott _ Howison _ Dewynne - The Mathematics Of Fiancial Derivatives Pdf

Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "real-world" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation. The authors present a unified approach to modeling derivative products as partial differential equations, using numerical solutions where appropriate. The authors assume some mathematical background, but. | Published by the Press Syndicate of the University of Cambridge The Pitt Building Trumpington Street Cambridge CB2 1RP 40 West 20th Street New York NY 10011-4211 USA 10 Stamford Road Oakleigh Melbourne 3166 Australia Paul Wilmott Sam Howison Jeff Dewynne 1995 First Published 1995 Reprinted 1996 Printed in the United States of America Library of Congress cataloging-in-publication data available A catalogue record for this book is available from the British Library ISBN 0-521-49699-3 hardback ISBN 0-521-49789-2 paperback Contents Preface page ix Part One Basic Option Theory 1 1 An Introduction to Options and Markets 3 Introduction 3 What is an Option 4 Reading the Financial Press 7 What are Options For 11 Other Types of Option 13 Forward and Futures Contracts 14 Interest Rates and Present Value 15 2 Asset Price Random Walks 18 Introduction 18 A Simple Model for Asset Prices 19 Ito s Lemma 25 The Elimination of Randomness 30 3 The Black-Scholes Model 33 Introduction 33 Arbitrage 33 Option Values Payoffs and Strategies 35 Put-call Parity 40 The Black-Scholes Analysis 41 The Black-Scholes Equation 44 Boundary and Final Conditions 46 The Black-Scholes Formulae 48 Hedging in Practice 51 Implied Volatility 52 v vi Contents i 4 Partial Differential Equations 58 Introduction 58 The Diffusion Equation 59 Initial and Boundary Conditions 66 t Forward versus Backward 68 5 The Black-Scholes Formulas 71 Introduction 71 Similarity Solutions 71 An Initial Value Problem 75 The Formulae Derived 76 I Binary Options 81 Risk Neutrality 83 6 Variations on the Black-Scholes Model 90 Introduction 90 Options on Dividend-paying Assets 90 Forward and Futures Contracts 98 Options on Futures 100 Time-dependent Parameters 101 7 American Options 106 Introduction 106 The Obstacle Problem 108 American Options as Free Boundary Problems 109 .

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