In this Cutting Edge research article published in the September 2015 Issue of Risk Magazine, Alexandre Antonov, Michael Konikov, and Michael Spector present a natural generalization of the SABR model to negative rates—which is very important in the current low-interest-rate environment.

The paper derives an exact formula for the option price in the zero-correlation case and an efficient approximation for general correlation. The simplicity of the approximation permits a straightforward implementation. Moreover, the main formulae from the “absorbing” (standard) SABR approximation can be directly reused.

In this paper, the authors study different Monte Carlo schemes and come up with an efficient one. Finally, they have numerically checked the approximation accuracy for option pricing in this study.

This recent development of the free boundary SABR is a natural, convenient and elegant extension of the classical SABR. It has the same number of parameters as the classical SABR (no shift) and is equipped with an efficient and accurate analytical approximation, crucial for fast calibration.

Authors: Alexandre Antonov, Michael Konikov, and Michael Spector