Global Multi-Maturity SPX–VIX Calibration Beyond Markovian Stitching

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Highly relevant to quantitative trading desks dealing with SPX and VIX options. The paper addresses a central practical problem: joint calibration of equity index and volatility derivatives across multiple maturities. The identification of cross-period dependence loss under Markovian stitching directly impacts pricing of multi-period volatility products (VIX spreads, variance swaps), hedge sensitivities, and model risk. The augmented-Bregman solver provides a practical finite-dimensional method for robust calibration. The work is from JPMorganChase's quantitative trading and research division, indicating direct industry applicability.

The global formulation requires handling a (2m-1)-dimensional tensor, which grows exponentially with maturities. The augmented-Bregman solver involves sparse matrix-vector operations, cyclic Bregman-Newton corrections, dual ascent, and penalty scheduling. The finite-grid implementation on 1.2 million cells takes approximately 22 minutes on single-threaded hardware. The theoretical framework (feasibility equivalence, Markovization, entropy decomposition) requires careful implementation to preserve block structure. Misaligned dates add further complexity with free SPX nodes and merged timelines.

The paper provides detailed algorithmic specifications (Algorithm 1), finite-state examples with exact numerical values, and controlled synthetic experiments. However, the market-data surfaces (P-spline-smoothed SPX and VIX from 2026-04-21 snapshot) are proprietary JPMorganChase data. The finite-tree example and controlled feasibility knob are fully specified and reproducible. No public code repository is mentioned.