Multiscaling in the Rough Bergomi Model: A Tale of Tails

TL;DR

This paper investigates the source of multiscaling in the rough Bergomi model, finding it primarily arises from fat-tailed return distributions rather than temporal correlations, with implications for financial modeling and risk management.

Contribution

The paper introduces a novel two-stage statistical testing procedure to distinguish between multiscaling caused by roughness or fat tails in the rBergomi model.

Findings

Multiscaling in rBergomi mainly results from fat-tailed distributions.

The proposed method effectively differentiates between sources of multiscaling.

Results validated using synthetic multifractal processes.

Abstract

The rough Bergomi (rBergomi) model, characterised by its roughness parameter $H$, has been shown to exhibit multiscaling behaviour as $H$ approaches zero. Multiscaling has profound implications for financial modelling: it affects extreme risk estimation, influences optimal portfolio allocation across different time horizons, and challenges traditional option pricing approaches that assume uniscaling behaviours. Understanding whether multiscaling arises primarily from the roughness of volatility paths or from the resulting fat-tailed returns has important implications for financial modelling, option pricing, and risk management. This paper investigates the real source of this multiscaling behaviour by introducing a novel two-stage statistical testing procedure. In the first stage, we establish the presence of multiscaling in the rBergomi model against an uniscaling fractional Brownian motion process. We quantify multiscaling by using weighted least squares regression that accounts for heteroscedastic estimation errors across moments. In the second stage, we apply shuffled surrogates that preserve return distributions while destroying temporal correlations. This is done by using distance-based permutation tests robust to asymmetric null distributions. In order to validate our procedure, we check the robustness of the results by using synthetic processes with known multifractal properties, namely the Multifractal Random Walk (MRW) and the Fractional L\'evy Stable Motion (FLSM). We provide compelling evidence that multiscaling in the rBergomi model arises primarily from fat-tailed return distributions rather than memory effects. Our findings suggest that the apparent multiscaling in rough volatility models is largely attributable to distributional properties rather than genuine temporal scaling behaviour.