Rough Heston Models with Variable Vol-of-Vol and Option Pricing

In this paper,a rough Heston model with variable volatility of volatility(vol-of-vol)is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques.Then the nonlinear fractional Ric-cati equation for the characteristic function of the asset log-price is derived.The existence,uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods.Finally the Fourier-cosine methods are combined with the Adams methods to price the options.

带跳的非仿射粗糙Heston模型欧式期权定价

【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。