SPX-VIX Risk Computations Via Perturbed Optimal Transport

2026-03-11

AI Summary

This study addresses the challenge of efficiently generating joint risk scenarios for the S&P 500 (SPX) and the CBOE Volatility Index (VIX) without repeated recalibration, to accurately assess portfolio exposure under market shocks. The authors propose a perturbation-based optimal transport method grounded in Fisher information linearization: first, an entropy-regularized martingale optimal transport framework jointly calibrates the implied volatility surfaces of SPX and VIX; then, leveraging the Skew Stickiness Ratio (SSR) dynamics, SPX shocks are mapped to perturbations in forward variance and the VIX distribution. Dimensionality reduction techniques are incorporated to enhance numerical stability. This approach eliminates the computational burden of traditional recalibration while maintaining high accuracy, and backtesting demonstrates superior hedging performance compared to stochastic local volatility models.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

We propose a model independent framework for generating SPX and VIX risk scenarios based on a joint optimal transport calibration of their market smiles. Starting from the entropic martingale optimal transport formulation of Guyon, we introduce a perturbation methodology that computes sensitivities of the calibrated coupling using a Fisher information linearization. This allows risk to be generated without performing a full recalibration after market shocks. We further introduce a dimension reduction method based on perturbed optimal transport that produces fast and stable risk estimates while preserving the structural properties of the calibrated model. The approach is combined with Skew Stickiness Ratio(SSR) dynamics to translate SPX shocks into perturbations of forward variance and VIX distributions. Numerical experiments show that the proposed method produces accurate risk estimates relative to full recalibration while being computationally much faster. A backtesting study also demonstrates improved hedging performance compared with stochastic local volatility models.

Problem

• SPX-VIX risk
• optimal transport
• model calibration
• risk scenarios
• market shocks

Innovation

• Perturbed Optimal Transport
• Model-Independent Risk
• Fisher Information Linearization
• Skew Stickiness Ratio
• Dimension Reduction