Pricing and Calibration of Bitcoin Inverse Options via the Rough Bergomi Model

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Highly relevant for quantitative trading in cryptocurrency derivatives markets. The paper provides a practical, computationally efficient calibration framework (17s per snapshot) for pricing and hedging Bitcoin inverse options on Deribit, which commands 85-95% of global BTC options volume. The Hybrid+Mixed pipeline's 20-fold speedup makes real-time calibration feasible. The rough volatility finding (H near 0) has direct implications for short-dated option pricing and gamma hedging strategies. The regime-dependent calibration error analysis is critical for risk management during market stress events.

Implementation requires: (1) Monte Carlo simulation of fractional Brownian motion via Hybrid Scheme with kernel weight precomputation; (2) Conditional Monte Carlo pricing with control variates (Mixed Estimator); (3) Black-Scholes inversion via Brent's method for implied volatilities; (4) Global optimization via Differential Evolution + Nelder-Mead; (5) Data processing from Deribit API with filtering and volume-weighted aggregation; (6) Forward variance curve estimation from ATM options. The mathematical framework is sophisticated (Volterra processes, stochastic exponentials, fractional calculus), but the paper provides Algorithm 1 pseudocode and clear parameter specifications. JIT compilation via Numba is recommended for performance.

The paper provides detailed algorithm descriptions (Algorithm 1 for Hybrid Scheme), explicit parameter bounds, optimizer settings (Differential Evolution population 12, max 25 generations, Nelder-Mead refinement), fixed random seeds, JIT-compiled Numba kernels, and clear data filtering criteria. However, no code repository is explicitly linked. The Deribit API is publicly accessible. All mathematical specifications are fully detailed.