An Elementary Introduction to Mathematical Finance

"This mathematically elementary introduction to the theory of options pricing presents the Black-Scholes theory of options as well as such general topics in finance as the time value of money, rate of return on an investment cash flow sequence, utility functions and expected utility maximization, mean variance analysis, value at risk, optimal portfolio selection, optimization models, and the capital assets pricing model. The author assumes no prior knowledge of probability and presents all the necessary preliminary material simply and clearly in chapters on probability, normal random variables, and the geometric Brownian motion model that underlies the Black-Scholes theory. He carefully explains the concept of arbitrage with many examples; he then presents the arbitrage theorem and uses it, along with a multiperiod binomial approximation of geometric Brownian motion, to obtain a simple derivation of the Black-Scholes call option formula. Simplified derivations are given for the delta hedging strategy, the partial derivatives of the Black-Scholes formula, and the nonarbitrage pricing of options both for securities that pay dividends and for those whose prices are subject to randomly occurring jumps. A new approach for estimating the volatility parameter of the geometric Brownian motion is also discussed. Later chapters treat risk-neutral (nonarbitrage) pricing of exotic options - both by Monte Carlo simulation and by multiperiod binomial approximation models for European and American style options"--