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A Course in Financial Calculus - Alison Etheridge

A Course in Financial Calculus

Paperback Published: 15th November 2002
ISBN: 9780521890779
Number Of Pages: 206

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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 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.

' ... 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

Prefacep. vii
Single period modelsp. 1
Summaryp. 1
Some definitions from financep. 1
Pricing a forwardp. 4
The one-step binary modelp. 6
A ternary modelp. 8
A characterisation of no arbitragep. 9
The risk-neutral probability measurep. 13
Exercisesp. 18
Binomial trees and discrete parameter martingalesp. 21
Summaryp. 21
The multiperiod binary modelp. 21
American optionsp. 26
Discrete parameter martingales and Markov processesp. 28
Some important martingale theoremsp. 38
The Binomial Representation Theoremp. 43
Overture to continuous modelsp. 45
Exercisesp. 47
Brownian motionp. 51
Summaryp. 51
Definition of the processp. 51
Levy's construction of Brownian motionp. 56
The reflection principle and scalingp. 59
Martingales in continuous timep. 63
Exercisesp. 67
Stochastic calculusp. 71
Summaryp. 71
Stock prices are not differentiablep. 72
Stochastic integrationp. 74
Ito's formulap. 85
Integration by parts and a stochastic Fubini Theoremp. 93
The Girsanov Theoremp. 96
The Brownian Martingale Representation Theoremp. 100
Why geometric Brownian motion?p. 102
The Feynman-Kac representationp. 102
Exercisesp. 107
The Black-Scholes modelp. 112
Summaryp. 112
The basic Black-Scholes modelp. 112
Black-Scholes price and hedge for European optionsp. 118
Foreign exchangep. 122
Dividendsp. 126
Bondsp. 131
Market price of riskp. 132
Exercisesp. 134
Different payoffsp. 139
Summaryp. 139
European options with discontinuous payoffsp. 139
Multistage optionsp. 141
Lookbacks and barriersp. 144
Asian optionsp. 149
American optionsp. 150
Exercisesp. 154
Bigger modelsp. 159
Summaryp. 159
General stock modelp. 160
Multiple stock modelsp. 163
Asset prices with jumpsp. 175
Model errorp. 181
Exercisesp. 185
Bibliographyp. 189
Notationp. 191
Indexp. 193
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521890779
ISBN-10: 0521890772
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 206
Published: 15th November 2002
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.4 x 17.2  x 1.0
Weight (kg): 0.44