An introduction to mathematical finance: Options and other topics

This mathematically elementary introduction to the theory of options pricing presents the Black-Scholes theory of options as well as introducing such topics in finance as the time value of money, mean variance analysis, optimal portfolio selection, and the capital assets pricing model. The author assumes no prior knowledge of probability and presents all the necessary preliminary material simply and clearly. He explains the concept of arbitrage with examples, and then uses the arbitrage theorem, along with an approximation of geometric Brownian motion, to obtain a simple derivation of the Black-Scholes formula. In the later chapters he presents real price data indicating that this model is not always appropriate and shows how the model can be generalized to deal with such situations. No other text presents such topics in a mathematically accurate but accessible way. It will appeal to professional traders as well as undergraduates studying the basics of finance.