Option Valuation Using the SABR Framework With Stochastic Volatility

Abstract

This thesis investigates the performance of the classical SABR (Stochastic Alpha Beta Rho) (Hagan et al., 2002) model in pricing European call options, compared to the traditional Black-Scholes (1973) model. Through both in-sample and out-of-sample analyses, the study examines how accurately each model prices options under varying market conditions, specifically during a stable pre-COVID-19 period and a highly volatile period at the onset of the pandemic. The analysis demonstrates that the SABR model consistently produces lower root mean square errors ($RMSE) in both stable and volatile markets. SABR particularly outperforms the BS model for options that are out-of-the-money (OTM) and in-the-money (ITM), whereas the BS model remains competitive for at-the-money (ATM) options due to its assumption of constant volatility. The study further shows that SABR’s pricing accuracy significantly improves after model recalibration, highlighting the model’s sensitivity to changing market conditions and the necessity of regular parameter updates.