AI 中文总结
本文提出自适应顺序扩散模型（AD-Seq-Vol及AD-Seq-Vol-FT）生成动态隐含波动率曲面，通过减少套利违反并用于对冲，显著降低跟踪误差和尾部风险，尤其在COVID-19期间表现稳定。
AI 中文摘要
我们开发了一个用于动态隐含波动率曲面生成的扩散模型框架，并通过数据驱动对冲评估其经济实用性。该框架包含两个模型。AD-Seq-Vol联合学习标的资产收益与高维隐含波动率曲面的条件演化，通过顺序更新已实现的市场历史来生成自适应的多期情景。AD-Seq-Vol-FT进一步通过后训练惩罚静态无套利条件违反，纳入期权市场结构。利用2000年至2023年的每日SPX期权数据，我们表明所提出的模型能够生成连贯的曲面轨迹，同时捕捉横截面和时间依赖性。AD-Seq-Vol产生的静态套利违反次数和严重程度均少于训练数据和基于GAN的基准，而AD-Seq-Vol-FT将这些违反几乎降至零。随后，我们将生成的条件情景整合到基于优化的对冲框架中。与一系列经典和数据驱动的基准相比，基于扩散模型的对冲策略将跟踪误差维持在接近零的水平，大幅降低尾部风险，并在COVID-19市场动荡期间表现出特别稳定的性能。这些结果确立了自适应顺序扩散模型作为一类具有市场一致性和经济实用性的金融情景生成器的前景。我们的代码可在以下网址获取：此https URL。
英文摘要
We develop a diffusion-model framework for dynamic implied-volatility surface generation and evaluate its economic usefulness through data-driven hedging. The framework consists of two models. AD-Seq-Vol jointly learns the conditional evolution of the underlying asset return and the high-dimensional implied-volatility surface, generating adapted multi-period scenarios by sequentially updating the realized market history. AD-Seq-Vol-FT further incorporates option-market structure through post-training penalties for violations of static no-arbitrage conditions. Using daily SPX option data from 2000 to 2023, we show that the proposed models generate coherent surface trajectories while capturing both cross-sectional and temporal dependence. AD-Seq-Vol produces fewer and less severe static-arbitrage violations than the training data and the GAN-based benchmark, while AD-Seq-Vol-FT reduces these violations to nearly zero. We then integrate the generated conditional scenarios into an optimization-based hedging framework. Compared to a range of classical and data-driven benchmarks, the diffusion-based hedges maintain tracking errors near zero, substantially reduce tail risk, and exhibit particularly stable performance during the COVID-19 market disruption. These results establish Adaptive Sequential Diffusion Models as a promising class of market-consistent and economically useful financial scenario generators. Our code is available at: https://github.com/yinbinhan/volatility-surface-simulation.
