Implementing the SABR Stochastic Volatility Model for Interest Rate Derivatives
The SABR (Stochastic Alpha Beta Rho) model is the industry-standard framework for modeling implied volatility smiles in interest rate derivatives markets. This article covers the model's mathematical structure, the Hagan closed-form implied volatility approximation, calibration to swaption vol cubes, handling of negative rates via Shifted and Normal SABR, and integration with QuantLib, with practical Python implementations throughout.