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.

• Self-contained textbook inspired by Financial Calculus by Baxter and Rennie • Extensive exercises, with solutions available to lecturers from [email protected] • Minimal prerequisites in terms of mathematical sophistication

### Contents

Preface; 1. Single period models; 2. Binomial trees and discrete parameter martingales; 3. Brownian motion; 4. Stochastic calculus; 5. The Black-Scholes model; 6. Different payoffs; 7. Bigger models; Bibliography and further reading; Notation; Index.

### 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 Schrüger, 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