An empirical study on asymmetric jump diffusion for option and annuity pricing

Abstract

In this paper, we present a method for estimating market parameters, modelled by the jump diffusion process. The method proposed is based on an empirical method, while the market parameters are the drift, volatility, jump intensity, and its rate of occurrence. A demonstration on how to use these parameters to estimate the fair price of European call options and annuity will be conducted for the situation where the market is modelled by a jump diffusion process with different intensities and occurrences. The results are compared to conventional options to observe the impact of the jumps. The result shows that financial instruments are expose to higher risks when taking in the consideration of the impacts of the jumps. Also, the asymmetric nature of the jumps will bring different impacts to different financial instruments as most instruments have different behaviours in their up side and down side risks.