Equilibrium origins of rough volatility

Ascertain how rough volatility—e.g., log-volatility dynamics driven by fractional Brownian motion with Hurst exponent H < 1/2—can arise endogenously within equilibrium asset-pricing models for equity indexes. Develop an equilibrium framework that explains the emergence of rough volatility consistent with observed market features.

Background

Empirical studies show that equity index volatilities exhibit rough behavior, often modeled via fractional Brownian motion with small Hurst exponent, and rough volatility models can reproduce the power-law term structure of ATM implied volatility skew. While microstructural foundations have been proposed to justify roughness, connecting these features to equilibrium asset-pricing remains unresolved.

The authors highlight that constructing equilibrium models that generate rough volatility and associated skew behavior is an open challenge; they propose ranking mechanisms as a potential ingredient but leave a full equilibrium development for future work.