Multi-factor approximation of rough volatility models

TL;DR

This paper introduces multi-factor Markovian approximations for rough volatility models, including the rough Heston model, facilitating efficient simulation and risk management of derivatives.

Contribution

It proposes a novel multi-factor approximation method that transforms non-Markovian rough volatility models into tractable Markovian models, enabling practical computations.

Findings

Developed a Markovian approximation for rough volatility models.

Derived a numerical method for fractional Riccati equations.

Applied the approach to the rough Heston model.

Abstract

Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to simulate efficiently such models, which makes risk management of derivatives an intricate task. In this paper, we design tractable multi-factor stochastic volatility models approximating rough volatility models and enjoying a Markovian structure. Furthermore, we apply our procedure to the specific case of the rough Heston model. This in turn enables us to derive a numerical method for solving fractional Riccati equations appearing in the characteristic function of the log-price in this setting.