On simulation of rough Volterra stochastic volatility models

TL;DR

This paper develops and compares efficient Monte Carlo simulation techniques for rough Volterra stochastic volatility models, addressing speed and accuracy issues in derivative pricing applications.

Contribution

It introduces modifications to existing simulation schemes and evaluates their performance, improving the practicality of simulating rough volatility models.

Findings

Hybrid scheme outperforms Cholesky and rDonsker methods in speed and accuracy

Variance reduction techniques have limited effectiveness due to implementation obstacles

Modified simulation methods show improved efficiency in practical scenarios

Abstract

Rough Volterra volatility models are a progressive and promising field of research in derivative pricing. Although rough fractional stochastic volatility models already proved to be superior in real market data fitting, techniques used in simulation of these models are still inefficient in terms of speed and accuracy. This paper aims to present accurate and efficient tools and techniques for Monte-Carlo simulations for a wide range of rough volatility models. In particular, we compare three commonly used simulation methods: the Cholesky method, the Hybrid scheme, and the rDonsker scheme. We also comment on the implementation of variance reduction techniques. In particular, we show the obstacles of the so-called turbocharging technique whose performance is sometimes counter-productive. To overcome these obstacles, we suggest several modifications.