带跳混合高斯模型下交换期权定价的Mellin变换法

Mellin transformation method of exchange option pricing based on Gaussian mixed model with jumps

研究混合高斯模型和跳-扩散环境下交换期权定价,标的资产的变化过程由次分数布朗运动和布朗运动共同刻画.由无套利原理,得到交换期权价值所满足的偏微分方程,进而利用Mellin变换法求得交换期权的解析解.进而得到跳-扩散环境和混合高斯模型下交换期权定价公式.最后进行数值模拟,赫斯特指数和跳跃强度对期权价值有显著影响.

This paper studied the mixed Gaussian model and the exchange option pricing in a jump-diffusion environment.The change process of the underlying asset was jointly described by the sub-fractional Brownian motion and the Brownian motion.According to the principle of no arbitrage,the partial differential equation satisfied with the value of the exchange option was got,and then using Mellin transformation method gained the numerical solution of the exchange option.So the exchange option pricing formula under the jump-diffusion environment and the mixed Gaussian model was obtained.Finally,the numerical simulation was carried out,which illustrated that the Hurst index and the jump intensity have a significant impact on the value of the option.