次扩散过程驱动下的欧式障碍期权定价

Option Pricing of European Barrier Options in Sub-Diffusive Regime

障碍期权是一种重要的新型期权,在现有的定价模型中,标的资产价格的驱动源为布朗运动和分数布朗运动,无法描述标的资产常值周期性的特点.本文把标的资产价格变化的常值周期性的特征纳入障碍期权定价模型中,建立了次扩散机制下的欧式障碍期权定价模型.运用Delta对冲技巧和伊藤公式得到了欧式下降敲出看跌障碍期权满足的偏微分方程.应用变量替换的方法,借助Possion公式给出了欧式下降敲出看跌障碍期权的显示定价公式,最后给出了相关数值计算结果.

Barrier option is an important new type of option.In the existing pricing model,the underlying asset price is driven by Brownian motion and fractional Brownian motion,which can not describe the constant periodicity of the underlying asset.In this paper,the constant periodicity of the underlying asset price is incorporated into the option barrier option pricing model.The pricing model of European barrier option under sub-diffusion mechanism is established.The partial differential equation satisfied by the European knockdown put barrier option is obtained by using the Delta hedging technique and It formula.With the method of variable substitution and the Possion formula,the display pricing formula of European knockdown put barrier option is given.Finally,we give the relevant numerical results.