The 4/2-CIR Model Driven by Mixed Fractional Brownian Motion and European Option Pricing

文章以资产价格的特征函数为研究工具，深入探讨了欧式期权的定价公式。在假定资产价格遵循混合双分数布朗运动驱动的4/2模型、随机利率遵循CIR模型以及随机波动率符合Heston模型的前提下，推导出了资产价格满足的广义特征函数的近似解析解表达式。进而，借助广义特征函数，巧妙运用傅里叶变换及其逆变换，成功构建出欧式看涨期权的定价公式，为欧式期权定价研究提供了新的分析思路。The article employs the characteristic function of asset prices as a research tool to delve into the pricing formula of European options. Under the assumptions that asset prices follow the 4/2 model driven by mixed fractional Brownian motion, stochastic interest rates adhere to the Cox-Ingersoll-Ross (CIR) model, and stochastic volatility conforms to the Heston model, an approximate analytical solution expression for the generalized characteristic function of asset prices is derived. Subsequently, by leveraging the generalized characteristic function and skillfully applying Fourier transform and its inverse, the pricing formula for European call options is successfully constructed, offering a novel analytical approach to the study of European option pricing.