Pricing and Calibration of Bitcoin Inverse Options via rBergomi

This thesis examines the pricing and calibration of inverse cryptocurrency options using rough volatility models, with particular focus on Bitcoin options traded on Deribit between 2022 and 2025. Inverse options, where both collateral and settlement occur in the underlying cryptocurrency rather than fiat currency, represent a distinctive feature of crypto-native derivatives markets and require specialized modeling approaches that account for their unique payoff structures. Traditional stochastic volatility models, particularly the Heston model, systematically fail to capture the empirical dynamics observed in Bitcoin options markets. These failures manifest through insufficient short-term volatility skew generation, incorrect smile behavior at short maturities, and parameter instability across calibration periods. The Bitcoin options market exhibits pronounced volatility smiles, with out-of-the-money puts trading at implied volatilities 10-30 percentage points higher than at-the-money options, reflecting significant demand for downside protection. To address these limitations, the rough Bergomi (rBergomi) model is implemented using the Hybrid Scheme computational framework developed by McCrickerd and Pakkanen (2018). The rough volatility framework, characterized by fractional Brownian motion with Hurst parameter H < 0.5, provides superior short-term skew generation capabilities compared to classical stochastic volatility models.