Turbocharging Monte Carlo pricing for the rough Bergomi model

TL;DR

This paper introduces a novel variance reduction technique for Monte Carlo simulations to efficiently calibrate the rough Bergomi model, significantly decreasing computation time while maintaining accuracy.

Contribution

It proposes a new composition of variance reduction methods applicable to stochastic volatility models, enabling faster calibration of the rough Bergomi model.

Findings

Achieves approximately 20-fold reduction in runtime for Monte Carlo implied volatility estimation.

Maintains calibration accuracy with specified confidence levels.

Applicable across different correlation regimes.

Abstract

The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, we focus on reducing the runtime-adjusted variance of Monte Carlo implied volatilities, thereby contributing to the model's calibration by simulation. We employ a novel composition of variance reduction methods, immediately applicable to any conditionally log-normal stochastic volatility model. Assuming one targets implied volatility estimates with a given degree of confidence, thus calibration RMSE, the results we demonstrate equate to significant runtime reductions - roughly 20 times on average, across different correlation regimes.