SPX–VIX Risk Computations Via Perturbed Optimal Transport

Battle Count: 50

Directly addresses a core problem in equity volatility trading: efficient and accurate risk generation for SPX-VIX derivative portfolios. The 60x speedup over full recalibration makes it immediately practical for trading desk risk systems. The hedging backtests demonstrate real P&L improvement over industry-standard SLV models, especially in volatile regimes. The model-independent nature avoids parametric model risk. The framework is developed by JPMorganChase Quantitative Trading & Research, indicating direct applicability to institutional trading. Cross-Greek computation for VIX options with respect to SPX perturbations is a daily operational need for volatility desks.

Requires expertise in: (1) entropic optimal transport and Sinkhorn algorithms, (2) convex optimization and Lagrangian duality, (3) information geometry and Fisher information matrices, (4) discrete probability on product spaces, (5) SSR smile dynamics and Breeden-Litzenberger inversion, (6) numerical linear algebra for large sparse systems. The base calibration (Algorithm 1) involves nested Sinkhorn + Newton/LM loops. The LR method (Algorithm 2) requires computing and inverting the Fisher matrix. The DR method (Algorithm 3) requires conditional kernel extraction and 2D Sinkhorn projection. Grid sizes of N1*NV*N2 can be large, requiring careful memory management. Gauge fixing and regularization (Tikhonov) add implementation subtleties.

The paper provides detailed algorithms (Algorithms 1-3) and mathematical derivations. However, it uses proprietary JPMorganChase market data and internal calibration infrastructure. No code repository is provided. The mathematical framework is fully specified, but empirical validation depends on proprietary SPX-VIX market data and calibration parameters. The SSR parameters (beta_V=1.2) and grid specifications are partially disclosed.