A course in financial calculus / Alison Etheridge

This book provides a self-contained first course in financial mathematics. Binomial trees are used to introduce the idea of arbitrage pricing. This involves key definitions and results on martingales and stochastic calculus in discrete time. In Chapter 3 Brownian motion and martingales in continuous time are introduced. In Chapter 4 the construction of stochastic integrals with respect to Brownian motion is sketched. In particular there are sections on Itô's formula, Girsanov's theorem, the Brownian representation theorem as well as the Feynman-Kac representation. Chapter 5 is dealing with the Black Scholes model. In particular, the Black-Scholes price and hedging strategies for European options are derived. Furthermore there are sections on the Black-Scholes currency model, dividends as well as the market price of risk. In Chapter 6 several other types of options are discussed; these include multistage options, lookback and barrier options, Asian as well as American options. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. There are some 140 exercises (without solutions). Many of them contain additional material not covered in the main text (this is concerning e.g. several popular interest rate models). 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. (Zentralblatt)

Bibliogr. p. 189-190. Index