The First Hitting Time With Applications To Exotic Options Pricing

In this dissertation, the evolution and development of option pricing theory is introduced firstly. Then Black-Scholcs option pricing model and its modified models are described. At last, a new approach of exotic option is provided.Chapter 1 is devoted to the evolution and development of option pricing theory : traditional option pricing models and Black-Scholcs option pricing model. In addition, some achievements on the theory domestic and aboard are presented.Chapter 2 introduces some basic knowledge about option pricing: basic concepts and theories about stochastic process theory such as martingale, Brownian motion and Ito stochastic integral, Ito formula and Girsanov theorem. Also with mathematic symbols and formula, such knowledge about financial market is presented.Chapter 3 systematically introduces the Black-Scholcs Option Pricing Formula , including its original paper five different ways to derive its formula. Then some research work of generalization and extension about Black-Scholcs is mentioned. In the end, Black-Scholcs Model is generalized to the usual case. Using martingale method, general pricing formula of European contingent claim is derived, European option and put-call parity is analyzed too.Chapter 4 discusses the pricing of two kinds of exotic options: An European lookback call option and an European up-and-out call option with varied barriers. The pricing formula of the above option arc obtained by the following way: (1) gaining distribution function of the first hitting time by Laplace adverse transform, thus obtaining the distribution function about the underlying asset, then achieving the pricing formula of European lookout option with fixed executive price by means of expectation, (2) with the same way as (1), obtaining the distribution function of the time with varied barriers, then obtaining the pricing formula of European up-and-out option by the way of equivalent martingale measure transform and expectation.