Numerical Methods And Empirical Analysis For Option Pricing In Jump-difusion Markets

As the rapid development of the financial market around the world, many people pay moreattentions on options and it is necessary to do a deeper research on options. The famous the Black-Scholes formula uses Brownian Motion to describe the stock price with a consecutive variation.However, the stock price in reality has a certain discontinuity, so we need to add the jump-diffusion process mapped by Poisson Process based on the evolution of Brownian Motion. It is hard to get the precise analytical solution from the equation according to this assumption, so we study numerical method for solutions.This paper uses Difference Method and Monte Carlo Simulation these two numerical methods to calculate the price of European Option under jump diffusion model, analyze the effect of different coefficients in the methods to the option price and consider about the characters of the method own, such as convergence speed, stability, etc.At last, again by looking for the real trading options on the market and pricing by the methods above, and then compare with the market price to do the empirical analysis, study the advantages and disadvantages of the European Option Pricing under the model assumption and proposenew perspectives in order to broaden the research direction of this article.