带跳的非仿射粗糙Heston模型欧式期权定价  

European option pricing of non-affine rough Heston model with jump

作　　者：陶祥兴[1] 章丽琴 TAO Xiangxing;ZHANG Liqin(School of Science,Zhejiang University of Science and Technology,Hangzhou 310023,Zhejiang,China)

机构地区：[1]浙江科技学院理学院,杭州310023

出　　处：《浙江科技学院学报》2023年第3期201-208,共8页Journal of Zhejiang University of Science and Technology

基　　金：国家自然科学基金项目(11771399);浙江省大学生科技创新活动计划(新苗人才计划)(2022R415C028)。

摘　　要：【目的】为使Heston(赫斯顿)模型能更细致地刻画标的资产价格演变规律以应对复杂多变的金融市场,提出了带跳的非仿射粗糙Heston模型。【方法】首先用傅里叶余弦级数(Fourier Cosine Series Expansion,Fourier-Cosine)方法分离期权密度函数和特征函数,用扰动法转化非线性偏积分微分方程,并用Adams-Bashforth-Moulton(亚当斯-巴什福斯-默尔顿)预测-校正法求解分数黎卡提方程,从而得到欧式看涨期权定价公式;然后用蒙特卡洛模拟结果验证解的有效性;最后分析了模型非仿射参数、粗糙参数和跳幅度参数对期权价格的影响,并对比了不同模型的定价结果。【结果】数值解与蒙特卡洛模拟结果相对误差为0.01%~0.2%,非仿射参数、粗糙参数和跳幅度参数对模型有不同程度的影响同时又相互制约。【结论】本模型刻画标的资产价格变化规律更具灵活性和多样性,从而为期权定价提供了理论支撑。[Objective] A non-affine rough Heston model with jump was proposed, enabling the Heston model to more accurately depict the underlying asset price evolution law so as to deal with the complex and changeable financial market. [Method] Firstly, the European call option pricing formula was obtained by separating the density function and the characteristic function of the option using the Fourier-Cosine(Fourier Cosine Series Expansion)method, transforming the nonlinear partial integral differential equation by virtue of the perturbation method and solving the fractional Riccati equation by virtue of the Adams-Bashforth-Moulton predictive correction method;secondly, the validity of the model solution was verified by the Monte Carlo simulation;finally, the influences of the non-affine parameter, the rough parameter and the jump parameter on option prices were analyzed and the pricing results of different models were compared. [Result] The results show that the relative error between the numerical solution and the Monte Carlo simulation result is in the range of 0.01%~0.2%, and the non-affine parameter, the rough parameter and the jump parameter have different degrees of influence on the model and also restrict each other. [Conclusion] The model depicts the underlying asset price movement with more flexibility and diversity, and provides theoretical support for option pricing.

关 键 词：粗糙Heston 跳扩散模型 傅里叶余弦级数方法 非仿射 扰动法 分数黎卡提方程 

分 类 号：F830.9[经济管理—金融学]