Pricing and Hedging the Smile with SABR: Evidence from the Interest Rate Caps Market

Abstract

This is the first comprehensive study of the SABR (Stochastic Alpha-Beta-Rho) model (Hagan et. al (2002)) on the pricing and hedging of interest rate caps. We implement several versions of the SABR interest rate model and analyze their respective pricing and hedging performance using two years of daily data with seven different strikes and ten different tenors on each trading day. In-sample and out-of-sample tests show that in addition to having stochastic volatility for the forward rate, it is essential to recalibrate daily either the “vol of vol” or the correlation between forward rate and its volatility, although recalibrating both further improves pricing performance. The fully stochastic version of the SABR model exhibits excellent pricing accuracy and more importantly, captures the dynamics of the volatility smile over time very well. This is further demonstrated through examining delta hedging performance based on the SABR model. Our hedging result indicates that the SABR model produces accurate hedge ratios that outperform those implied by the Black model.