Multiscaling and rough volatility: An empirical investigation

Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modelling approach is known not to be able to reproduce some of the financial stylised facts, including the dynamics of volatility. In the mathematical finance community, it has therefore emerged a new paradigm, named rough volatility modelling, that represents the volatility dynamics of financial assets as a fractional Brownian motion with Hurst exponent very small, which indeed produces rough paths. At the same time, prices' time series have been shown to be multiscaling, characterised by different Hurst scaling exponents. This paper assesses the interplay, if present, between price multiscaling and volatility roughness, defined as the (low) Hurst exponent of the volatility process. In particular, we perform extensive simulation experiments by using one of the leading rough volatility models present in the literature, the rough Bergomi model. A real data analysis is also conducted to test if the rough volatility model reproduces the same relationship. We find that the model can reproduce multiscaling features of the prices' time series when a low value of the Hurst exponent is used, but it fails to reproduce what the real data says. Indeed, we find that the dependency between prices' multiscaling and the Hurst exponent of the volatility process is diametrically opposite to what we find in real data, namely a negative interplay between the two.