随机利率与双指数跳跃扩散模型下几何平均水平重置期权定价

Pricing Geometric Average Trigger Reset Option with Predetermined Levels Based on Double Exponential Jump-Diffusion Model with Stochastic Interest Rate

在资产收益率满足双指数跳跃扩散模型条件下,用Vasicek随机利率模型刻画市场利率的变动,并充分考虑市场利率对资产收益率的影响,研究了具有几何平均特征的水平重置期权定价问题.通过应用测度变换和多维Fourier逆变换方法,给出了此类重置期权定价的解析公式.最后,通过数值实例分析了模型参数对期权价格的影响.结果表明,上跳概率、跳跃频率和利率的长期平均水平对期权价格有正向影响,上跳和下跳幅度对期权价格有反向影响,而利率的均值回复速率对期权价格的影响会因为利率与资产收益率间的相关系数的影响而呈现出复杂性.

Under the condition that the return on assets satisfies the double exponential jump diffusion model,Vasicek stochastic interest rate model is used to describe the market interest rate dynamic,and fully considering the impact of market interest rates on the return on assets,pricing on the geometric average trigger reset option with predetermined levels have been researched.By applying measure transform and multidimensional fourier inverse transform,an analytical formula for the pricing is given.Finally,the influence of the model parameters on the option price are analyzed by numerical examples.The results show that the long-term average level of the up jump probability,jump frequency and interest rate has a positive influence on the option price,while the up jump and down jump amplitude have a negative influence on the option price,and the influence of the mean rate of interest rate on the option price will be complicated due to the influence of the correlation coefficient between the interest rate and the return on assets.