次分数跳-扩散模型下的复合期权定价  

Compound Option Pricing under Sub-Fractional Jump-Diffusion Model

作　　者：王竟莘 郭志东 WANG Jingshen;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）》2023年第2期42-48,共7页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省自然科学基金(1908085QA29)。

摘　　要：复合期权是一种重要的奇异期权。在现有期权定价模型中,标的资产价格通常以几何布朗运动作为驱动源,且大多遵循连续随机过程。然而,标的资产价格并非始终都是连续的,可能会发生跳跃且可能具有长程相关性。本文基于风险中性测度假设,探究了在欧式看涨期权情形下,次分数跳-扩散模型的复合期权定价问题。运用伊藤公式和对冲技术得到该模型下满足的偏微分方程,并运用泊松跳跃和累计概率分布函数理论进一步给出了复合期权价格的表达公式。通过数值模拟探究了多个参数对期权价格的影响,并与几个常用模型的期权价格进行了比较。Compound option is an important type of exotic option.In existing option pricing models,the change of under-lying asset price is usually driven by Brownian motion and most follows continuous random process.However,the underlying asset price is not always continuous,and it may jump and have long-range correlation.Based on the assumption of risk-neutral measure,option pricing of compound option under the sub-fractional jump-diffusion model is discussed in the case of call op-tion on a call option.To obtain the partial differential equations satisfied by compound option,we used the Ito formula and del-ta-hedging technique.Moreover,the expression of compound option price is given by using Poisson jumps and cumulative probability distribution function theory.Furthermore,numerical results explore the effect of some parameters on option prices and compare our model with several commonly used models.

关 键 词：期权定价 次分数布朗运动 复合期权 数值模拟 

分 类 号：F830.9[经济管理—金融学]