A New Parameter Estimation Method And Application Of Jump-Diffusion Model

In recent years, great changes in financial markets are caused by continuous improvement and application of options and other financial derivatives pricing model. The success of the application of financial derivatives pricing model depends largely on the model selection of model parameters and estimation method that is appropriate. Jump-diffusion model is a very important pricing model. It has widespread application in the mutation research of option pricing, interest rate and exchange rate and so on. This paper will make some exploratory research on parameter estimation and inspection on jump-diffusion model. So it can enrich the diversity of the estimation method, which has a certain significance and application value.The new estimation method that outlier test idea applied to jump-diffusion model is both novel and simple. The paper has two kinds of jump-diffusion model. One is jump amplitude to obey normal distribution; the other one is positive or negative jump amplitude to obey exponential distribution. Firstly, a new outlier test method is applied to parameter estimation process of jump-diffusion model. The specific approach is as follows. We use outlier test method to find jump points as before. Then the jump process is separated so as to estimate parameters of jump process and diffusion process. Secondly, Monte Carlo simulation analysis is used to inspect the effect of estimation method. We also discuss how to choose K value in the estimation process. Finally, the new estimation method is applied to the rate of return series of Shanghai stock index and Shenzhen composite index to study behavior change about return rate.After simulation analysis, we obtain the estimation results. From two aspects of T statistics and relative error, we know the estimation results are more accurate. It also shows that the estimation method has a certain practical value. In addition, outlier test method of this paper does not depend on the distribution of data. So it has good versatility for the different jump-diffusion model. The empirical analysis of this paper shows that jump-diffusion model which is used to make daily return rate model for Shanghai stock index and Shenzhen composite index has better effect.