Fair volatility in a multifractional world: a new equilibrium benchmark for financial markets

This thesis provides a new perspective in financial modeling: volatility is not the fundamental driver, but merely a symptom of a deeper hidden driver–market regularity. Introducing the Fractional Stochastic Regularity Model, we demonstrate how the stochastic Hurst-Hölder exponent H(t) governs market states, naturally defining a FSRM-"Fair Volatility" benchmark that signals true market efficiency. This original framework unifies rough and persistent regimes, revealing how markets breathe around equilibrium. Validated across global indices, our model provides a powerful new lens for forecasting, risk management, and identifying arbitrage opportunities, finally offering a compass for navigating the complex dynamics of financial markets.