A Study of Basket Option Pricing Based on Uncertainty Index O-U Modeling

一篮子期权是价值取决于一组资产平均价格或加权平均价格的新型期权。文章首先假设标的股票服从不确定指数O-U过程，利率服从不确定均值回归过程，提出一种新型不确定股票模型。其次，推导出该模型下一篮子看涨期权与看跌期权的定价公式，并设计一系列的数值算法计算期权价格。最后，开展数值实验研究期权价格关于参数的敏感度。本文的研究结果拓展了期权定价的理论范式，为衍生证券定价提供了一种新的研究视角。Basket options are new types of options whose value depends on the average or weighted average price of a group of assets. The article first proposes a novel uncertain stock model by assuming that the underlying stock obeys an uncertain exponential O-U process and the interest rate obeys an uncertain mean reversion process. Second, the pricing formulas for a basket of call and put options under this model are derived, and a series of numerical algorithms are designed to calculate the option prices. Finally, numerical experiments are conducted to study the sensitivity of option prices with respect to the parameters. The results of this paper expand the theoretical paradigm of option pricing and provide a new research perspective on the pricing of derivative securities.