The SABR Model in a Negative Interest Rate Framework: Theory and Practice

Jökull Ívarsson

Student thesis: Master thesis

Abstract

This thesis focused on the stochastic volatility mode, the SABR model. This model is well known and has been used in financial institutions since its inception. However, the model is unable to work if interest rates are negative. Some refinements have been proposed to change the workings of the model to incorporate negative rates. The thesis looked at these refinements and tested whether the Normal SABR model and the Shifted SABR model were able to produce implied volatilities similar to the ones observed in the market for both caplets and swaptions.
The results showed us that, in a negative interest rate environment, these modifications to the SABR model can produce implied volatilities that are very close to the market volatilities for both caplets and swaptions. Furthermore, the thesis looked at Obłój’s refinement, which states that the SABR model is unable to produce accurate volatilities for options with low strikes and long maturities. It was found that this method was unable to produce better fitting volatilities for those options than the Shifted SABR model.

EducationsMSc in Finance and Investments, (Graduate Programme) Final Thesis
LanguageEnglish
Publication date2020
Number of pages92
SupervisorsPeter Feldhütter