A Course in Financial Calculus

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Paperback | 15 November 2002

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206 Pages

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24.41 x 16.99 x 1.12

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Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be applied to realistic financial questions.

Industry Reviews

' ... being relatively short and a paperback must make it appealing to students and those who need a quick introduction to the material. ... nicely produced and elegantly laid out. I would consider adopting it as a text for a course in this topic. Publication of the International Statistical Institute 'This is a well written textbook which should be suitable for final year undergraduate and first year graduate students having some background in probability theory.' Klaus Schruger, Zentralblatt MATH ' ... this is a very well-organized text that makes it easy to learn.' Journal of the Royal Statistical Society '... it was necessary to supply the framework of the book with some theory of stochastic analysis and to provide a mathematical explanation of the notions used.' EMS Newsletter

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Preface	p. vii
Single period models	p. 1
Summary	p. 1
Some definitions from finance	p. 1
Pricing a forward	p. 4
The one-step binary model	p. 6
A ternary model	p. 8
A characterisation of no arbitrage	p. 9
The risk-neutral probability measure	p. 13
Exercises	p. 18
Binomial trees and discrete parameter martingales	p. 21
Summary	p. 21
The multiperiod binary model	p. 21
American options	p. 26
Discrete parameter martingales and Markov processes	p. 28
Some important martingale theorems	p. 38
The Binomial Representation Theorem	p. 43
Overture to continuous models	p. 45
Exercises	p. 47
Brownian motion	p. 51
Summary	p. 51
Definition of the process	p. 51
Levy's construction of Brownian motion	p. 56
The reflection principle and scaling	p. 59
Martingales in continuous time	p. 63
Exercises	p. 67
Stochastic calculus	p. 71
Summary	p. 71
Stock prices are not differentiable	p. 72
Stochastic integration	p. 74
Ito's formula	p. 85
Integration by parts and a stochastic Fubini Theorem	p. 93
The Girsanov Theorem	p. 96
The Brownian Martingale Representation Theorem	p. 100
Why geometric Brownian motion?	p. 102
The Feynman-Kac representation	p. 102
Exercises	p. 107
The Black-Scholes model	p. 112
Summary	p. 112
The basic Black-Scholes model	p. 112
Black-Scholes price and hedge for European options	p. 118
Foreign exchange	p. 122
Dividends	p. 126
Bonds	p. 131
Market price of risk	p. 132
Exercises	p. 134
Different payoffs	p. 139
Summary	p. 139
European options with discontinuous payoffs	p. 139
Multistage options	p. 141
Lookbacks and barriers	p. 144
Asian options	p. 149
American options	p. 150
Exercises	p. 154
Bigger models	p. 159
Summary	p. 159
General stock model	p. 160
Multiple stock models	p. 163
Asset prices with jumps	p. 175
Model error	p. 181
Exercises	p. 185
Bibliography	p. 189
Notation	p. 191
Index	p. 193
Table of Contents provided by Syndetics. All Rights Reserved.

A Course in Financial Calculus

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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