The Option Pricing In Jump-diffusion Model

Option pricing theory, the important part of modern finance, has promoted the prosperity of financial market. Together with the portfolio selection theory, the capital asset pricing theory, the effectiveness theory of market and acting issue, it is regarded as one of the five theory modules in modern finance.This dissertation is intended to study option pricing problems, so as to establish the mathematic module of option pricing with jump-diffusion process by means of mathematical tools such as martingale theory and stochastic analysis, to deduce the option pricing equation.This dissertation is divided into four chapters:Chapter 1 is preface, which summarizes the Basic concept, the development of the Option pricing theory and the used knowledge to the mathematics.In Chapter II, jump diffusion model is constructed and the European call option pricing formula is obtained with martingale method in risk-neutral measure. If the parameters of the jump to zero, that is, elimination jump, the formula turned into Black-Scholes formula. Finally, we analyses the parameters of the formula.In Chapter III ,we introduced the Bear Market Warrant(BMW), then we get the pricing formula of the Bear Market Warrant in jump diffusion model .Finally, we calculated the parameter Delta and Gamma.In Chapter IV, we introduced the Bivariate option. Based on the maturity proceeds, it can be divided into two categories: Bivariate cash or nothing option and Bivariate asset or nothing option. Bivariate cash or nothing option include: Bivariate cash or nothing call, Bivariate cash or nothing put, Blend type cash or nothing call and C-Brick option; Bivariate asset or nothing option include: Bivariate asset or nothing call, Bivariate asset or nothing put, Blend type cash or nothing call and A-Brick option.