AI 中文总结
本文提出一种基于随机Knothe-Rosenblatt的模块化校准方法，通过递归构造鞅精确匹配边际分布并接近参考动力学，适用于随机和路径依赖波动率模型，支持高效Sinkhorn算法及多资产扩展。
AI 中文摘要
欧式期权微笑决定了资产的风险中性边际律，但并未决定其跨期耦合，而后者对许多应用至关重要。Bass鞅构造在所有已校准鞅中选择最接近Bachelier动力学的那一个；它允许在离散到期日进行快速校准，并随着到期日网格细化而恢复Dupire局部波动率（LV）模型。本文为现有的随机和路径依赖波动率模型开发了一种模块化校准覆盖层。我们递归构造一个鞅，使其精确匹配所有规定的边际分布，同时在适应的Knothe-Rosenblatt意义上尽可能接近参考动力学。与Bass LV模型一样，每个校准步骤都适用于高效的鞅Sinkhorn算法。我们发展了理论基础、数值实现，并考虑了向SLV模型的收敛性。我们还针对Heston和Bergomi有限因子路径依赖波动率动力学对该方法进行了基准测试，并开发了多资产扩展。
英文摘要
European option smiles determine the risk-neutral marginal laws of an asset, but not their intertemporal coupling, which is decisive for many applications. The Bass martingale construction selects, among all calibrated martingales, the one closest to Bachelier dynamics; it permits fast calibration at discrete maturities and recovers the Dupire local-volatility (LV) model as the maturity grid is refined. This article develops a modular calibration overlay for existing stochastic and path-dependent volatility models. We sequentially construct a martingale that matches all prescribed marginals exactly while remaining as close as possible, in an adapted Knothe-Rosenblatt sense, to the reference dynamics. As with the Bass LV model, each calibration step is amenable to an efficient Martingale Sinkhorn algorithm. We develop the theoretical foundations, numerical implementation and consider convergence to the SLV model. We also benchmark the method for Heston and Bergomi finite-factor path-dependent volatility dynamics and develop the multi-asset extension.
