European Option Valuation Under Double Exponential Jump-Diffusion Model With Variable Jump Intensity

Option pricing under double jump-diffusion model as an important aspect in the incomplete market has unique advantages. For years, people more concentrate on modifying jump distribution, interest or volatility with respect to jump research. As a result of these studies, we can describe real market better. But people pay little attention to jump intensity and they assume that jump intensity is constant. Jump intensity means the number of events that occur within the unit interval or frequency of events. If we apply jump model to asset pricing, jump intensity denotes fluctuating sharply frequency of the underlying asset price. With the increasing development of financial market, jump model with constant jump intensity can not match the actual market situation. After analyzing of the actual financial market data, we can find asset price always fluctuating violently with the impact of unexpected events or other policy factors. The fluctuation by a large margin does not follow certain rules, and does not meet the assumption of constant.The main work of this paper is to calculate European option pricing under jump model from the perspective of variable jump intensity. The paper choices the double exponential jump-diffusion model because it can get analytical solution of a variety of pricing options and give a good explanation of two empirical phenomena which are volatility smile and asymmetric heavier tails and higher peak of return distribution. In addition, this paper selects CIR model to describe the variable jump intensity for the reason that the stochastic model can avoid negative which is not allowed for jump intensity. Finally we acquire the solution of European option pricing by characteristic equation, Fourier transform and so on.