The Application Of The Double Exponential Jump-diffusion Model In China’ Stock And Index Market

Since1973,financial market has developed rapidly after Black and Scholes proposed Black-Scholes model for option pricing. With the perfection of market, Black-Scholes model was found that it was not a good application in financial market. There are the two main reasons. On the one hand, return distribution is asymmetric and excess kurtosis and skewness. On the other hand, the volatility is not a constant. As a matter of fact,it is a convex curve like a smile.Thereafter, Black-Scholes model has been modified for the two problems. Merton pioneered the establishment of the jump-diffusion model in1976. He assumed that the jump size of asset price is obey to normal distribution. However, this model does not well appear the characteristics of the higher peak and fat-tail and the volatility smile of asset return.Kou proposed the double exponential jump-diffusion model in his paper A Jumper-Diffusion Model for Option Pricing. Practise presented this model could give a good explanation of return distribution exhibiting excess kurtosis and skewness and the volatility smile. So this model was widespread and price for option. In this paper, the double exponential jump-diffusion model was used in China’s stock and exponent market. The data of10stocks and2exponents from Shenzhen Stock Exchange and Shanghai Stock Exchange were analysed.Monte Carlo simulation was used in this paper. Maximum likelihood estimation procedures were used to estimate the parameters of the model. Log-normal jump-diffusion(LJD) model and DEJD model that the distribution of jump magnitudes is a mixture of Pareto and Beta were compared by Maximum likelihood results. We could get that the DEJD failed to beat the LJD. Then,a improvement was made in the paper.:jump magnitudes was assumed as a constant. Empirical evidence showed that the latter was more suitable to China market.