Equilibrium Pricing of Bitcoin Options With Stochastic Volatility, Jumps, and Liquidity Risk
提出了一个比特币期权的均衡定价模型，同时考虑随机波动率、跳跃和流动性风险，通过闭式解和快速傅里叶变换实现高效定价，校准结果显示该模型比传统模型更好地捕捉波动率微笑和期限结构。
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.