This paper empirically investigates the relationship between price multiscaling and volatility roughness, defined as the Hurst exponent of the volatility process. Using the rough Bergomi model as a benchmark, the authors simulate price and volatility paths across a range of Hurst exponents H and correlation parameters λ. They estimate scaling and multiscaling properties via the Generalized Hurst Exponent method with an optimal aggregation time determined by Autocorrelation Segmented Regression. The simulations show that the rough Bergomi model generates multiscaling prices only for very low H (below 0.3), and the correlation between volatility roughness and price multiscaling is positive, diminishing as H increases.

In contrast, analysis of 31 global stock indices using realized variance (10-minute frequency) reveals a strong negative correlation between volatility roughness and price multiscaling: Pearson correlation of -0.43 and Spearman correlation of -0.51, both statistically significant. This negative relationship becomes even stronger after removing outliers (robust correlations of -0.61 and -0.65). The model's positive correlation is diametrically opposite to the empirical finding, indicating that the rough Bergomi model cannot reproduce the observed dependency structure. The results highlight the need for new models that simultaneously capture rough volatility and multiscaling with their correct negative interplay, which has implications for risk forecasting and derivative pricing.