Introduction to Option Pricing Theory

Since the appearance of seminal works by R. Merton, and F. Black §and M. Scholes, stochastic processes have assumed an increasingly §important role in the development of the mathematical theory of §finance. This work examines, in some detail, that part of stochastic §finance pertaining to option pricing theory. Thus the exposition is §confined to areas of stochastic finance that are relevant to the §theory, omitting such topics as futures and term-structure. §This self-contained work begins with five introductory chapters §on stochastic analysis, making it accessible to readers with little or §no prior knowledge of stochastic processes or stochastic analysis. §These chapters cover the essentials of Ito's theory of stochastic §integration, integration with respect to semimartingales, Girsanov's §Theorem, and a brief introduction to stochastic differential §equations. §Subsequent chapters treat more specialized topics, including §option pricing in discrete time, continuous time trading, arbitrage, §complete markets, European options (Black and Scholes Theory),§American options, Russian options, discrete approximations, and asset §pricing with stochastic volatility. In several chapters, new results §are presented. A unique feature of the book is its emphasis on §arbitrage, in particular, the relationship between arbitrage and §equivalent martingale measures (EMM), and the derivation of necessary §and sufficient conditions for no arbitrage (NA). §{\it Introduction to Option Pricing Theory} is intended for §students and researchers in statistics, applied mathematics, business, §or economics, who have a background in measure theory and have §completed probability theory at the intermediate level. The work §lends itself to self-study, as well as to a one-semester course at the §graduate level.