Equilibrium Pricing of Bitcoin Options With Stochastic Volatility, Jumps, and Liquidity Risk

Abstract

We introduce an equilibrium model for Bitcoin options that endogenizes stochastic volatility (SV), correlated jumps, and liquidity risk. Investors with constant relative risk aversion utility over consumption and real-money balances face an exponential penalty for illiquidity, yielding a pricing kernel with jump premia linked to a mean-reverting liquidity index. Under the risk-neutral measure, we obtain closed-form adjustments to drifts and Poisson intensities, leading to a semianalytic fourfold sum of Black–Scholes prices at scenario-specific variances. We derive an affine characteristic function for the logarithm of the real price and implement a fast Fourier-transform inversion for efficient valuation. Comparative statics show that higher liquidity aversion steepens short-term skews and raises deep out-of-the-money premia. Two-stage calibration to Bitcoin option surfaces and high-frequency liquidity measures demonstrates that the model captures observed volatility smiles and term structures more effectively than classical SV and jump-diffusion models.