A Fractional-Rough Liquidity Model for Bitcoin Options: Implied-Volatility Asymptotics and Market Evidence

Abstract

Bitcoin option prices reflect terminal variance and the cost of managing convex exposure in a market with changing depth and execution quality. This paper asks whether a liquidity state can be separated from fractional rough volatility in Bitcoin option valuation. The contribution is a modelling combination: standard stochastic-calculus and rough-volatility tools are joined to a regime-switching hedging-cost reserve, producing a leading-order at-the-money implied-volatility lift. The empirical design tests a liquidity–IV association and its scale using a 700-contract Deribit snapshot, a 4513-trade 24-h window spanning two UTC dates, a 775,315-trade panel over 92 dates, Ether replication, and placebos. The association is strong in open-interest-weighted specifications and for puts, but is absent for calls; it remains after controlling for option premium. Leave-one-expiry-out validation improves open-interest-weighted RMSE but not unweighted RMSE. A realised-volatility HMM is only a market-stress diagnostic, not an estimated liquidity regime. An empirical one-step hedging exercise does not validate the model’s simulated hedging comparative static. Accordingly, the evidence is associational, put-side, and narrower than a causal or fully structural validation.