混合分数布朗运动下带红利支付的混合期权定价研究  

Pricing Hybrid Options with Dividend Payments under Mixed Fractional Brownian Motion

作　　者：郭泉吕 周海艳 GUO Quanlv;ZHOU Haiyan(College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;College of Mathematics and Statistics,Chongqing Three Gorges University,Chongqing 404100,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]重庆三峡学院数学与统计学院,重庆404100

出　　处：《黄山学院学报》2025年第2期1-7,共7页Journal of Huangshan University

摘　　要：为了更加准确地刻画混合期权的价格波动,在标的资产价格服从混合分数布朗运动模型驱动下,假定模型中标的资产有红利支付,且存在随时间变化的无风险利率r(t)与红利率δt,基于风险中性定价原则,运用拟鞅定价理论,推导得出各种混合期权的定价公式。随后,借助Matlab软件,对定价公式中赫斯特指数H、无风险利率r、红利率δ等参数开展数值试验,通过分析各个参数变化趋势,明确其对混合期权价值的影响关系。将为混合期权定价提供一定理论依据,有助于更合理地评估期权价值。To better understand the price variations of hybrid options,this study assumes that the underlying asset price follows a mixed fractional Brownian motion model,incorporating dividend payments and time-varying risk-free and dividend rates.Using the risk-neutral pricing principle and quasimartingale pricing theory,this study derives pricing formulas for various hybrid options.Subsequently,numerical experiments were conducted using Matlab to analyze the effects of parameters such as the Hurst exponent,risk-free rate,and dividend rate on the pricing formulas.By examining the trends in these parameter variations,the impact of each parameter on the value of hybrid options was clarified.This study provides a theoretical basis for hybrid option pricing and aids in more accurately evaluating option values.

关 键 词：混合分数布朗运动 混合期权 红利支付 风险中性定价 拟鞅定价 

分 类 号：O211.6[理学—概率论与数理统计]