Pricing BTC and ETH Options with the Rough Bergomi Model

The high volatility of the cryptocurrency options market makes traditional options pricing models unsuitable for its market environment. Although existing studies have shown that basic models are effective, they are based on smooth volatility and have not been fully validated for their applicability to cryptocurrency option markets. This study compares the performance of the rough Bergomi, Kou, and Bates models in the pricing of European-style options on BTC and ETH futures, thereby validating the superiority of the rough volatility model. The results indicate that the rough Bergomi model not only has lower pricing errors but also estimates a Hurst parameter H < 0.5, confirming the roughness of cryptocurrency volatility. Qualitative analysis further indicates that the rough Bergomi model is more accurate in replicating the market-implied volatility smile curve and the skewed power-law timing of the skew toward the positive price range, establishing the model as a superior framework for pricing cryptocurrency derivatives.