广义分数布朗运动下的双重Heston跳扩散模型欧式期权定价  

European option pricing under double Heston jump-diffusion model with generalized fractional Brownian motion

作　　者：张赵柳 范小明[1] ZHANG Zhaoliu;FAN Xiaoming(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,Sichuan,China)

机构地区：[1]西南交通大学数学学院,四川成都611756

出　　处：《山东大学学报(理学版)》2025年第3期60-68,共9页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12371178);西南交大创新项目(P113123G02004)。

摘　　要：首先在风险中性概率测度下提出基于广义分数布朗运动的双重Heston跳扩散模型,并通过求解特征函数的偏微分方程组推出该模型相应欧式看涨期权定价公式。通过蒙特卡罗模拟验证欧式期权定价公式的准确性,通过数值分析验证所建立的期权定价模型的合理性和有效性,并讨论广义分数布朗运动参数H及波动率等对期权价格的影响。First,a double Heston jump-diffusion model based on generalized fractional Brownian motion is proposed under the risk-neutral probability measure,and the corresponding European call option pricing formula of the model is introduced by solving the partial differential equation system of the characteristic function.The Monte Carlo simulation verifies the accuracy of the European option pricing formula.The rationality and effectiveness of the established option pricing model are verified by numerical analysis,and the influence of generalized fractional Brownian motion parameter H and volatility on option price is discussed.

关 键 词：期权定价 广义分数布朗运动 双重Heston模型 跳扩散模型 

分 类 号：O211.61[理学—概率论与数理统计] F830.9[理学—数学]