An Implicit-explicit Computational Method Based On Time Semi-discretization For Pricing Financial Derivatives With Jumps

In recent years,with the rapid development of financial mathematics,stochastic process,random analysis and other disciplines have been widely used in the pricing of maturity rights and interest rate models.The numerical solution of a series of jump diffusion model by partial differential equation and martingale measure solution from SVJ B-S model to Merton jump diffusion model,stochastic volatility model and will be discussed in this paper,to a certain extent,the quantitative analysis of the financial market plays a vital role.This paper mainly discusses the discretization method of European option pricing under the SVJ model of Bates,and gives the linear complementarity problem related to American option.According to the principle of no arbitrage,we first derive a partial differential equation,and use implicit explicit backward difference method and time semi-discretization method to solve the equation numerically.In order to illustrate the effectiveness of the proposed method,the stability of the time semi discrete scheme is also proved.Finally,we use a simulation example to illustrate the effectiveness of the proposed method.