By Dr. Burak Budanur
Two Prime Head of Engineering
About This Report
Scenario analysis of cryptocurrency derivative trades requires synthetic yield curves to represent basis rates throughout the holding duration. The approach extends the Cox-Ingersoll-Ross (CIR) model of interest rates across a range of maturities and incorporates a multivariate Wiener process as stochastic forcing. The result is a model that captures mean-reverting basis dynamics across maturities and reflects the correlations present in the actual training data.
Why Bitcoin Futures Need Their Own Yield Curve Model
Standard interest rate models do not capture the multi-modal distribution of the bitcoin futures basis, the frequency of near-term negative basis rates, or cross-maturity correlations. A bitcoin-specific model is required for accurate scenario analysis of basis trades, calendar spreads, and Deribit inverse options.
The Extended Cox-Ingersoll-Ross Model
Two Prime's extension of the CIR model adapts it for Deribit maturities from 10 to 360 days, incorporates correlated Wiener processes across all maturities, and estimates parameters using the minimum covariance determinant method to handle crypto data outliers. The result is a simulation tool calibrated to live market data.
Model Calibration and Limitations
Calibrated using hourly Deribit BTC futures yield curves from February 2025 to February 2026, the model replicates mean-reverting behavior and inter-maturity correlations. Its key limitation is that it does not capture the multimodality of the bitcoin futures basis distribution across market regimes.
Applications for Institutional Derivatives Traders
The simulation tool enables stress-testing of basis trades, calendar spreads, and options strategies against realistic distributions of future yield curve states. For institutional participants building systematic strategies around the bitcoin basis, it provides a quantitative foundation for risk modeling.
