Rough-Heston Local-Volatility Model

TL;DR

This paper extends the rough-Heston stochastic volatility model by incorporating a local-volatility component, analyzing its small-time behavior to improve calibration and fit to market data.

Contribution

It introduces a local-volatility extension to the rough-Heston model with singular Volterra processes, preserving key stylized facts and providing asymptotic analysis for calibration.

Findings

Derived small-time asymptotics of the implied local-volatility function.

Provided a calibration scheme based on the asymptotic analysis.

Extended the rough-Heston model to include local volatility while maintaining market fit.

Abstract

In industrial applications it is quite common to use stochastic volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a local volatility term. Here, we consider the case of singular Volterra processes, and we extend them by adding a local-volatility term to their Markov lift by preserving the stylized results implied by these models on plain-vanilla options. In particular, we focus on the rough-Heston model, and we analyze the small time asymptotics of its implied local-volatility function in order to provide a proper extrapolation scheme to be used in calibration.