基于非对称漂移双 gamma 跳扩散过程的创新幂型期权定价模型∗

摘要

Since the famous B-S pricing model was made,Option Pricing's research has been the focus of attention.But the in-depth study found that the stock's logarithmic returns of the B-S pricing model,which follows the standard Brownian mo-tion,can not explain the fat tail and serial correlation characteristics.So,this paper used the Asymmetrically Displaced Double Gamma Jump-Diffusion Process proposed by Zhang to describe the logarithm yield of assets,(the process was put forward by the ms kou double exponential jump diffusion process promotion),and used the risk neutral Esscher transformation to study the pricing formula of power-type options.Two kinds of innovation power options were designed,and the corresponding pri-cing formula was given based on Asymmetrically Displaced Double Gamma Jump-Diffusion Process.%针对假设股价的对数收益率布朗运动在期权定价时产生的无法解释股价对数收益率的尖峰厚尾和序列相关性的缺陷，采用了 Zhang 提出的非对称漂移双 gamma 跳-扩散过程来描述资产(股价)的对数收益率运动形态(该过程是 kou 提出的双指数跳扩散过程的推广)，并利用 Esscher 风险中性变换，研究了幂型期权的定价公式。还设计了两种创新的幂型期权，在非对称漂移双 gamma 跳-扩散过程下给出了相应的定价公式。