An Emppirical Study on Asymmetric Jump DiffusionFor Option and Annuity Pricing

In this research, we are presenting a method for estimation of market parameters modeled by jump diffusion process. As we are concerned about the current pricing model with geometric Brownian motion is not sufficient to capture the events of jump spikes. The method proposed is based on the Gibbs sampling method, while the market parameters are the drift, the volatility, the jump intensity and its rate of occurrence.We have demonstrated that Kou's jump diffusion model is insufficient to observe and to identify the effect on jump spike event onto the market indexes as it assumes jumps are symmetrical to each other for both directions. Asymmetric double normal jump diffusion model is introduced, where the jump component is modified into two different directions instead of fusing as one. The empirical method is used to estimate the parameters of asymmetric double normal jump diffusion model from real market history data. Demonstration on how to use these parameters to estimate the fair price of European call option and annuity will be shown, for the situation where the market is modeled by jump diffusion process with different intensity and occurrence. The results arecompared to conventional options to observe the impact of jump effects. In conclusion, the proposed asymmetric double normal jump diffusion model able to capture the jump distribution of underlying assets in two directions. It can be applied into the pricing model of both European call option and annuity.