The pricing problem of European option is investigated under the generalized fractional jump-diffusion model. First of all, the generalized fractional jump-diffusion model is proposed, with the assumption that the underlying asset price follows this model, and the explicit solution is derived using the Itô formula. Then, the partial differential equation (PDE) of the European option price is obtained by using the delta-hedging strategy, and the analytical solutions of the European call and put option prices are obtained through the risk-neutral pricing principle. Moreover, the accuracy of closed-form formula for European option pricing is verified by the Monte Carlo simulation. Furthermore, the properties of the pricing formulas are discussed and the impact of main parameters on the option pricing model are analyzed via calculations of Greeks. Finally, the rationality and validity of the established option pricing model are verified by numerical analysis.

在广义分数跳跃扩散模型下研究了欧式期权的定价问题。首先，提出广义分数跳跃扩散模型，假设标的资产价格遵循该模型，并使用Itô公式推导出显式解。然后，利用Delta套期保值策略得到欧式期权价格的偏微分方程（PDE），并根据风险中性定价原理得到欧式看涨期权和看跌期权价格的解析解。此外，通过蒙特卡罗模拟验证了欧式期权定价封闭式公式的准确性。进一步讨论了定价公式的性质，并通过Greeks的计算分析了主要参数对期权定价模型的影响。最后通过数值分析验证了所建立的期权定价模型的合理性和有效性。