An Efficient Calibration Framework for Volatility Derivatives under Rough Volatility with Jumps

TL;DR

This paper introduces a fast, structure-preserving calibration framework for rough volatility models with jumps, combining precomputed integrals and neural network approximations to efficiently fit market data like VIX options.

Contribution

The paper proposes a novel calibration approach that maintains the original pricing transform, uses GPU acceleration, and employs neural networks for efficient calibration of jump-inclusive rough volatility models.

Findings

The method achieves high calibration accuracy.

It significantly speeds up the calibration process.

A pure-jump rough volatility model captures VIX dynamics effectively.

Abstract

We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform and (i) split the pricing formula into data-independent inte- grals and a market-dependent remainder; (ii) precompute those data-independent integrals with GPU acceleration; and (iii) approximate only the remaining, market-dependent pricing map with a small neural network. We instantiate the workflow on a rough volatility model with tempered-stable jumps tailored to power-type volatility derivatives and calibrate it to VIX options with a global-to-local search. We verify that a pure-jump rough volatility model adequately captures the VIX dynamics, consistent with prior empirical findings, and demonstrate that our calibration method achieves high accuracy and speed.