Pricing The European Reset Option In Jump Diffussion Model

Since 1973, Fischer Black and Myron Scholes has established firstly the ubiquitous pricing option formula of financial derivatives. Foreign and domestic scholars began to study various financial derivatives market pricing and empirical problems,they acquired a lot of practical significance to the results. In particular, Option pricing theory and applied research have become the core of modern financial mathematics .Option pricing has a basic problem: it's proceeds (pay off) depends on the price movement of basic securities. Classical Black-Scholes option pricing formula (hereafter called B-S model) is established on the geometric Brownian motion. However, the empirical studies show that the geometric Brownian Motion fails to reflect the real market behavior based kurtosis,skewness,and volatility clustering, but there are still some significant events (such as war,natural disasters,coups etc.),which can cause the prices of the securities to jump up and down.The B-S model can not fully reflect on the market such jumps.The compound Poisson process was firstly introduced by Metron in 1976 to characterize the market shares of such unexpected incidents price changes (called Merton jump-diffusion model),he obtained the closed-form solution for an European options which is similar to that in B-S model ,and indicates that the source is not systematic in jumps and no-arbitrage market hypothesis,Application of risk-neutral principles of Black-Scholes option pricing formula.At present,such a jump diffusion model,in the field of financial mathematics and financial engineering,has been concerned by scholars and financial institutions. Such a jump diffusion model was applied to option pricing, but studies in this area have yielded few results.Reset option is a recreative options can be finalized so that the holders have the right to price options, a holder has more profitable opportunities than the standard European option holder has. Based on the stock price subordinated Metron jump diffusion model,and the rate constants for the circumstances,This paper researches the single time point European reset option,more time points European reset option and extreme single asset European reset option pricing by means of martingale method. Moreover, assumed interest at random,this paper gives a single time point European reset option pricing formula, At the same time,this paper also gives the numerical analysis of the various option prices,but the prices of these options was subject to various parameters in the model.And we also compare the different model option prices, main work: Chapter 1:introduction. This chapter presents some of the options-related knowledge,as well as domestic and foreign option pricing Research: this paper proposed options in jump diffusion model for the purpose and significance of the research.Chapter 2: Under the circumstances that the interest rate is constant and that the stock price subjects to jump diffusion process, first,we derived single time point European reset put option pricing formula,Secondly,It is time to promote the single time point European reset option to the more time point reset option. Meanwhile, by means of the application of numerical methods in this chapter,we compare the single time point European reset options with the standard European options and compare the single time point European reset options in terms of jump diffusion model and compare the single time point European reset options of Black-Scholes model,finally,compare the two time point European reset options with the single time point option prices results.Chapter 3:Some results in chapter 2 will be extended assuming that the interest rate subordinated vasicek model,we can derive the single time point European reset options pricing formula from the stochastic,on the other hand , we also study that option prices are affected by a number of important parameters, in the interest rate model.Chapter 4: As defined in this chapter,a kind of extreme reset option,options that allow the finalization n asset prices as the reset in the maximum and allow the income function of the option due date as n assets in the miximum. N assets price is assumed to meet Merton jump diffusion model. We can deduce the asset of two silgle time point European extreme reset option pricing formula and analize the relationships between the assets of two single time points European extreme reset options and the single asset single time point European extreme reset option .Chapter 5: To solve the problem and to follow studies.This chapter summarized the main results and conclusions of this paper,Meanwhile, the conclusions of this paper can be extended to the option pricing formula.