Problem
Research questions and friction points this paper is trying to address.
Global Calibration
Multi-Maturity
SPX-VIX Smile
Markovian Stitching
Conditional Independence
Global Multi-Maturity SPX-VIX Calibration Beyond Markovian Stitching
🤖 AI Summary
本文提出了一种全局框架，用于在多个期限内对SPX-VIX微笑曲线进行联合校准，解决了Markovian拼接带来的限制，并采用增强Bregman镜像下降方案控制误差。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Global Calibration
Non-Markovian Dependence
Augmented Bregman Mirror-Descent
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