AI 中文总结
研究复合期权估值问题，提出解析COS方法，通过推导余弦系数闭式表达式，无需中间行权阶段数值积分，适用于多种随机模型，数值实验显示计算效率提高且精度高，还能处理不同不确定性下的嵌套决策结构。
AI 中文摘要
我们开发了一种用于复合期权估值的解析傅里叶余弦（COS）方法。通过推导所有复合阶段余弦系数的闭式表达式，该方法在中间行权阶段无需数值积分，同时保留了基础COS近似的收敛特性。其公式扩展到多阶段复合结构和更广泛的收益类型，适用于具有已知特征函数的广泛随机模型。数值实验表明，与基于积分的实现相比，计算效率提高且精度高。应用于分阶段实物期权问题进一步说明了该方法在处理不同不确定性动态下的嵌套决策结构时的灵活性。
英文摘要
We develop an analytic Fourier cosine (COS) method for the valuation of compound options. By deriving closed-form expressions for the cosine coefficients at all compound stages, the proposed method eliminates the need for numerical quadrature in intermediate exercise stages while retaining the convergence properties of the underlying COS approximation. The formulation extends to multi-stage compound structures and a broader class of payoffs, and remains applicable to a wide class of stochastic models characterized by known characteristic functions, including jump-diffusion dynamics. Numerical experiments demonstrate improved computational efficiency compared with quadrature-based implementations while maintaining high accuracy. Applications to staged real-option problems further illustrate the flexibility of the method in handling nested decision structures under different uncertainty dynamics.
Comments31 pages
