In order to describe the self-similarity and long-range dependence of financial asset prices, this paper adopts a new fractional-type process, i.e, the generalized mixed weighted fractional Brownian motion to describe the dynamic change process of risky asset prices. A European option pricing model driven by the generalized mixed weighted fractional Brownian motion is constructed, and explicit solutions to the pricing formulas of European call options and European put options are derived by using the arbitrage-free pricing theory. Finally, through numerical simulation, the influence of the parameter on the option price is analyzed.

中文翻译：

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广义混合加权分数布朗运动中的欧式期权定价

为了描述金融资产价格的自相似性和长期依赖性，本文采用一种新的分数型过程，即广义混合加权分数布朗运动来描述风险资产价格的动态变化过程。构建了广义混合加权分数布朗运动驱动的欧式期权定价模型，并利用无套利定价理论推导了欧式看涨期权和欧式看跌期权定价公式的显式解。最后，通过数值模拟，分析了参数对期权价格的影响。