次扩散过程驱动下的回望期权定价  

Option Pricing of Look-Back Options in Sub-Diffusive Regime

作　　者：王欣怡 郭志东 WANG Xinyi;GUO Zhidong(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2022年第3期59-62,共4页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省自然科学青年基金项目(1908085QA29)。

摘　　要：期权定价是金融数学中的重要问题之一,回望期权是一种重要的新型期权。在已有的期权定价模型中,标的资产价格变化的随机驱动源通常为布朗运动和分数布朗运动,它们无法刻画标的资产常值周期性的特征。本文主要把标的资产常值周期性的特征纳入到期权定价模型中,建立了次扩散机制下回望期权的定价模型。运用Δ对冲技巧得到了回望期权在次扩散机制下满足的偏微分方程,进一步利用有限差分法给出了模型下回望期权定价的数值计算结果。结果表明,回望期权价格在次扩散参数取不同值下会随着股票价格的增加而减小,差分时间段取值越大,回望期权价格与真实值越接近。Option pricing is one of the important problems in financial mathematics.Look-back option is an important ex-otic option.In the option pricing models,the random driving sources of the price changes of the underlying assets are usually Brownian motion or fractional Brownian motion,which cannot describe the characteristic of periods of constant values of the underlying assets.In this paper,the characteristic of periods of constant values of the underlying assets is incorporated into the option pricing model,and the pricing model of look-back option in sub-diffusive regime is established.The partial differential equations which look-back option in sub-diffusive regime satisfied are obtained by using the Delta hedging technique.More-over,numerical calculation results are given by using the finite difference method.Our results show that the prices of look back option decrease with the increase of the stock prices under different values of the sub-diffusive parameter.The larger the values of the difference period are,the closer the prices of the look-back option are to the true values.

关 键 词：次扩散过程 Itô公式 回望期权 数值模拟 

分 类 号：F830.9[经济管理—金融学]