Pricing Of Two Options Under Double Exponential Jump Diffusion Model

With the development of economic,the theoretical research and application of fi-nancial mathematics have also been developed rapidly and have achieved fruitful results.Double exponential jump diffusion model refers to the introduction of jumps on the ba-sis of the standard diffusion process.The jump reaches by the Poisson process and the jumping amplitude is characterized by double exponential distribution.That is,the asset price is a model which consists of a continuously moved geometric Brownian motion and a process which is discrete and the logarithm of the jump amplitude obeying the Possion jump process of the double exponential distribution.Firstly,this paper gives the pricing formula of compound option under the double exponential jump diffusion model.Then,the paper gives the pricing formula of the capped call option and floored put option under the log-jump diffusion model.Finally,the paper gives the pricing formula of the capped call option and floored put option under the double exponential jump diffusion model,besides,it gives the numerical calculation of the price of the closed call and the guaranteed put in the double exponential jump diffusion model with Mathmatical and Matlab programming.Through data analysis,we know that under the actual situation,the use of double exponential jump diffusion model can better explain the asymmetry of the return of option and peak thick tail characteristics more better.This article is divided into six parts.In the chapter of introduction,we mainly introduce the related background and status of option pricing theory.In chapter 1 we mainly introduce definitions of capped call option?floored put option and compound option,Brownian motion,Poisson process and martingale,and also introduce some properties and related lemmas.In chapter 2,we assume that the underlying asset price is subject to the double exponential jump diffusion process.The risk-free interest rate r and the volatility a are all constant.The pricing formula of the compound option is given by the method of measure transformation.In chapter 3,we assume that the underlying asset price follows the log-jump process,and the risk-free interest rate r and the volatility a are all constant values.The paper gives the formula of capped call option and floored put option by using the method of integral.In chapter 4,we assume that the underlying asset price follows the double exponential jump diffusion process,the risk-free interest rate r and the volatility a are both constant,and the pricing formulas for capped call option and floored put options are given by the method of measure transformation.We calculate the price of the capped call option and the floored put option in the double exponential jump diffusion model by Mathmatical and Matlab programming.The fifth chapter summarizes the main results studied in this paper and puts forward the problems that need to be further solved.