SPX-VIX Risk Computations Via Perturbed Optimal Transport

TL;DR

This paper introduces a novel, efficient, and model-independent framework for generating SPX and VIX risk scenarios using perturbed optimal transport, enabling fast sensitivity analysis and improved hedging performance.

Contribution

It develops a perturbation methodology within optimal transport to compute risk sensitivities without full recalibration, enhancing speed and stability in risk estimation.

Findings

Accurate risk estimates comparable to full recalibration

Significant computational speedup in risk scenario generation

Improved hedging performance over stochastic local volatility models

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.