A Study On Exotic Options Pricing With Change Exercise Price

In recent years, as the financial derivative market have developed more and moreprosperity, the financial derivative products become the important tools for investors tohedge. Options as a sort of financial derivative tools have been applied abroad in the riskmanagement, its pricing problem became one of core problems of finance study.Since the Black-Scholes option pricing model had been brought forward, many schol-ars have made a great lot achievement study on it. As the hypothesis conditions of theoriginal model were more ideal, scholars had weakened hypothesis conditions continuously.They brought forward various options pricing models on the foundation of Black-Scholesoption pricing model. These made the options pricing models are more press close to mar-ket. In these models, most are pricing on options with determinate exercise price, but lesson options with change exercise price. In this thesis, we will research into power-optionand reset options which exercise price obey random di?erential equation. By applyingmartingale method and risk-neutral pricing principle we get the pricing formulas of Eu-ropean call (put) options with power payo?s, reset options and reset options with powerpayo?s, which are all with changing exercise prices and stock with continuous dividend.This thesis is divided into four chapters:In chapter one, we introduce the before scholars work and the main work of thisthesis.In chapter two, we list Brown motion, martingale, Ito? formula, and some other basicconcepts and theories.In chapter three, we get the pricing formula of European call(put) options with powerpayo?s that exercise price obey random di?erential equation.In chapter four, we get the pricing formula of reset option and reset option withpower payo?s that exercise price obey random di?erential equation.