基于不确定Stein-Stein-CIR模型的欧式看涨期权定价研究

Research on European Call Option Pricing Based on the Uncertain Stein-Stein-CIR Model

摘要: 基于不确定理论，本文建立了不确定Stein-Stein-CIR模型，并研究了欧式看涨期权的定价问题。首先，通过引入Liu过程以描述股票价格动态变化，并结合Peng-Yao模型刻画波动率特征；同时，将利率过程视为不确定CIR过程，从而建立了一个新的不确定股票模型——不确定Stein-Stein-CIR模型。然后，在此基础上，运用不确定微分方程理论，推导出该模型欧式看涨期权的定价公式及数值算法。最后，基于真实市场数据，采用复合Heun方法进行参数估计，并通过假设检验验证估计的合理性。结果表明，不确定Stein-Stein-CIR模型能够准确地反映金融市场，并对欧式看涨期权进行合理的定价。

Abstract: Based on uncertainty theory, this paper establishes an uncertain Stein-Stein-CIR model and investigates the pricing problem of European call options. Firstly, the Liu process is introduced to describe the dynamic changes in stock prices, while the Peng-Yao model is used to characterize volatility characteristics. In addition, the interest rate process is considered as an uncertain CIR process, thereby establishing a new uncertain stock model—the uncertain Stein-Stein-CIR model. Secondly, on this basis, using the theory of uncertain differential equations, the pricing formula and numerical algorithm for European call options under this model are derived. Finally, based on real-world market data, the composite Heun method is used for parameter estimation, and the reasonableness of the estimates are tested through hypothesis testing. The results indicate that the uncertain Stein-Stein-CIR model can more accurately reflect the financial market and can reasonably price European call options.