Research preprint · Equity volatility
A Markov Interpretation of Rough Volatility
Gregory Pelts ·
Abstract
An equity-volatility model must explain how the smile moves, as well as where it stands today. We propose a Markov interpretation of rough volatility in which a pair of interdependent financial clocks connects a compact market state to activity at different horizons. The emphasis is on observable consequences: skew stickiness, maturity scaling, persistent volatility and the forward smile. An SPXW prototype fits a broad option cross-section without a separately fitted, state-dependent leverage function. A comparison with Heston calibrated to the same quotes shows that both models generate downside skew and curved call wings, while implying materially different prices for future-reset exposure. The prototype's forward smiles retain the character of the short-tenor spot skew, consistent with a practitioner expectation of persistent smile shape. Published local- and stochastic-local-volatility comparisons place these results in context. The evidence supports a practical pricing framework and identifies tests of its dynamics; vanilla agreement alone does not establish the accuracy of exotic prices or hedges.