Markovian approximation of the rough Bergomi model for Monte Carlo option pricing

TL;DR

This paper introduces a Markovian approximation of the rough Bergomi model, enabling more efficient Monte Carlo option pricing by leveraging the affine structure and a hybrid scheme for simulation.

Contribution

The paper establishes the affine structure of the rough Bergomi model and proposes a Markovian approximation algorithm for improved computational efficiency.

Findings

The approximation accurately captures the rough Bergomi model's features.

The hybrid scheme enhances simulation speed and accuracy.

The method facilitates easier model calibration.

Abstract

The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its non-Markovianity brings mathematical and computational challenges for model calibration and simulation. To overcome these difficulties, we show that the rBergomi model can be approximated by the Bergomi model, which has the Markovian property. Our main theoretical result is to establish and describe the affine structure of the rBergomi model. We demonstrate the efficiency and accuracy of our method by implementing a Markovian approximation algorithm based on a hybrid scheme.