Since the appearance of seminal works by R. Merton and F. Black and M.Scholes stochastic processes have assumed an increasingly important role inthe development... » 

Since the appearance of seminal works by R. Merton and F. Black and M.Scholes stochastic processes have assumed an increasingly important role inthe development of the mathematical theory of finance. This work examines insome detail that part of stochastic finance pertaining to option pricingtheory. Thus the exposition is confined to areas of stochastic finance that arerelevant to the theory omitting such topics as futures and termstructure.This selfcontained work begins with five introductory chapters on stochasticanalysis making it accessible to readers with little or no prior knowledge ofstochastic processes or stochastic analysis. These chapters cover theessentials of Itos theory of stochastic integration integration with respectto semimartingales Girsanovs Theorem and a brief introduction to stochasticdifferential equations. Subsequent chapters treat more specialized topicsincluding option pricing in discrete time continuous time trading arbitragecomplete markets European options Black and Scholes Theory Americanoptions Russian options discrete approximations and asset pricing withstochastic volatility. In several chapters new results are presented. A uniquefeature of the book is its emphasis on arbitrage in particular therelationship between arbitrage and equivalent martingale measures EMM andthe derivation of necessary and sufficient conditions for no arbitrage NA.it Introduction to Option Pricing Theory is intended for students andresearchers in statistics applied mathematics business or economics whohave a background in measure theory and have completed probability theory atthe intermediate level. The work lends itself to selfstudy as well as to aonesemester course at the graduate level. «