随机利率下双指数跳扩散模型欧式期权定价

European option pricing based on double exponential jump-diffusion process model with stochastic interest rate

为了合理刻画股价实际变化趋势,将利率风险引入双指数跳扩散模型,建立了随机利率和双指数跳扩散组合模型,然后在组合模型下利用鞅方法、Fourier逆变换和Feynman-Kac定理给出了欧式看涨期权价格的闭式解,推广了Kou在2002年提出的模型及期权定价问题,所提模型及方法有利于资产收益的经验分析,同时为公司信用风险管理提供理论依据。

This paper aims to provide a rational model which shows the reality of stock return volatility.By introducing interest rate risk into double exponential jump-diffusion model,an integrated model of stochastic interest rate and double exponential jump-diffusion process was established.Based on the proposed integrated model,a closed-form solution for European call option was derived using Martingale method,Fourier inversion transform formula and Feynman-Kac theorm.Also,the model and corresponding option pricing introduced by Kou in 2002 was extended,which are potentially useful for the empirical analysis of assets return and the management of corporate credit risks.