发表机构
Global Technology Applied Research, JPMorganChase; Quantitative Trading & Research, JPMorganChase（摩根大通全球技术应用研究; 摩根大通量化交易与研究）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出超越马尔可夫拼接的全球多期限SPX-VIX校准框架，采用增强Bregman镜像下降方案，实现了更高的校准精度与更小的残差。
AI 中文摘要
我们开发了一个用于跨多个期限联合校准标普500（SPX）-VIX波动率微笑的全局框架，消除了马尔可夫拼接带来的条件独立性限制。精确的局部可行性与全局可行性等价：每个全局可行的概率律都存在一个块保留型SPX马尔可夫化，其保持每个月度（S_i,V_i,S_{i+1}）概率律不变。然而，拼接得到的概率律可能仅为全局可行路径概率律的严格子集，因为马尔可夫化会丢弃当前SPX水平之外的更早历史依赖关系。因此，相邻的波动率微笑无法识别这种依赖关系，具有相同月度校准的概率律对多期索赔的定价可能存在差异。在标准马尔可夫参考下，相对熵会选择拼接的最小信息完备形式；非马尔可夫依赖则需要跨期信息、合适的目标函数或依赖历史的先验。对于有限离散化，我们提出了增强Bregman镜像下降方案，该方案在保持对可观测报价矩拟合的同时控制鞅和离散度残差。在受控不可行仿射系统中，该方案通过暴露条件行的差异，使指定边际的偏差比循环行投影小约25倍。一个精确的有限状态示例验证了块保留特性，并展示了马尔可夫化后出现的显著跨期价格变化。在平滑的SPX和VIX表面上，数值计算呈现出有限预算惩罚路径：在报告的扫描范围内，拟合最差的微笑误差始终低于0.70波动率点，而大部分条件诊断指标则显著改善。
英文摘要
We develop a global framework for joint S&P 500 (SPX)-VIX smile calibration across multiple maturities without the conditional-independence restriction induced by Markovian stitching. Exact local and global feasibility are equivalent: every globally feasible law has a block-preserving SPX-Markovization that leaves each monthly $(S_i,V_i,S_{i+1})$ law unchanged. Nevertheless, stitched laws can form a strict subset of globally feasible path laws because Markovization discards dependence on earlier history beyond the current SPX level. Adjacent smiles therefore cannot identify this dependence, and laws with identical monthly calibrations can price multi-period claims differently. Under the standard Markov reference, relative entropy selects the stitched minimum-information completion; non-Markov dependence requires cross-period information, an appropriate objective, or a history-dependent prior. For finite discretizations, we introduce an augmented-Bregman mirror-descent scheme. It preserves the fit to observable quote moments while controlling martingale and dispersion residuals. In a controlled infeasible affine system, this split keeps prescribed marginals about $25$ times tighter than cyclic row projection by exposing the discrepancy in the conditional rows. An exact finite-state example verifies block preservation and exhibits material cross-period price changes after Markovization. On smoothed SPX and VIX surfaces, numerical calculations illustrate a finite-budget penalty path: the worst fitted-smile error remains below $0.70$ volatility points across the reported sweep while the bulk conditional diagnostics improve substantially.
