发表机构
University of Wuppertal（伍珀塔尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在随机局部波动率模型中引入随机相关性，推导RBSDE并采用数据驱动数值方法求解，实现美式期权定价与对冲，并验证了方法的收敛性、准确性和效率。
AI 中文摘要
本文研究了在随机局部波动率（SLV）模型基础上，通过引入由额外随机过程驱动的随机相关性所扩展的模型下美式期权的定价问题。我们通过纳入灵活的随机相关性结构，对SLV模型类别进行了推广。为了在这些扩展模型中对期权进行定价，我们推导了相应的反射前瞻后向随机微分方程（RBSDEs），并采用数据驱动的数值方法求解这些方程，以实现定价和对冲的目的。RBSDE框架能够对期权价格的未来演化进行建模。此外，我们对所提出的数值方法进行了收敛性分析，并给出了数值实验，以展示扩展模型的性能以及基于RBSDE方法的准确性和效率。
英文摘要
In this work, we study the pricing of American options under stochastic local volatility (SLV) models extended by including stochastic correlation driven by an additional stochastic process. We generalize the class of SLV models by incorporating a flexible stochastic correlation structure. To price options within these extended models, we derive the corresponding reflected forward-backward stochastic differential equations (RBSDEs) and employ data-driven numerical methods to solve them for both pricing and hedging purposes. The RBSDE framework enables the modelling of the future evolution of the option price. Furthermore, we conduct a convergence analysis of the proposed numerical method and present numerical experiments that illustrate the performance of the extended models, as well as the accuracy and efficiency of the RBSDE-based approach.
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