报 告 人：马俊美 上海财经大学 教授、博士生导师

报告时间：2025年12月10 15:00 - 16:00  

报告地点：腾讯会议：940-2668-5088

报告摘要:

This talk presents efficient Willow Tree methods for derivative pricing and risk-minimizing hedging in financial engineering. The discussion focuses on two complementary components: a rough-volatility-based Willow Tree method and a model-free, data-driven implied Willow Tree framework. For the rough-volatility component, we work with the Rough Heston model, which captures essential market features but poses substantial numerical challenges due to its non-Markovian structure, especially in the valuation of American options. Our method constructs a three-dimensional affine Volterra process and employs Johnson-curve transformations together with moment-generating functions to build the discrete grid and approximate transition probabilities. This design effectively mitigates the curse of dimensionality associated with simulating rough volatility dynamics. Beyond pricing, it also enables the computation of globally risk-minimizing hedging strategies, thus providing a unified framework for valuation and hedging. The second component develops a data-driven implied Willow Tree method, calibrated directly from market prices of American options. It constructs discrete asset-price nodes and determines transition probabilities entirely from observed data, thereby reconstructing the underlying risk-neutral process without imposing any parametric stochastic model and eliminating model-specification risk. Numerical experiments demonstrate that these Willow Tree methods deliver improved accuracy and computational efficiency compared with traditional approaches, highlighting their practical potential in modern financial engineering.

 

个人简介:

马俊美，上海财经大学数学学院教授、博士生导师，金融数学与数据计算系主任。主要研究方向为复杂衍生品与投资组合问题中的数值定价方法、风险度量模型及高效计算技术。主持国家自然科学基金项目 2 项，参与国家级科研项目 2 项。在 European Journal of Operational Research、Journal of Derivatives、Journal of Computational and Applied Mathematics 等国际权威期刊发表多篇论文，并出版学术专著《金融中的蒙特卡罗模拟加速理论及应用》和《量化投资：MATLAB 数据挖掘技术与实践》等。