Risk Magazine Cutting Edge Research Article | The Free Boundary SABR: Natural Extension to Negative Rates
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
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
Authors
Dr. Alexandre Antonov
Dr. Antonov received his PhD degree from the Landau Institute for Theoretical Physics in 1997 and joined Numerix in 1998, where he currently works as a Senior Vice President of Quantitative Research. His activity is concentrated on modeling and numerical methods for interest rates, cross currency, hybrid, credit and CVA. Dr. Antonov is a published author for multiple publications in mathematical finance, including RISK magazine and a frequent speaker at financial conferences.
Dr. Michael Konikov
Dr. Michael Konikov is a Senior Vice President and Head of Quantitative Development at Numerix, where he manages a team responsible for the development and delivery of models in Numerix software. Previously, he worked at Citigroup, Barclays, and Bloomberg in quantitative research and desk quant roles. He completed his PhD in mathematical finance at the University of Maryland College Park, concentrating in particular on the application of pure jump processes to option pricing. Dr. Konikov's publications cover diverse asset classes ranging from equity to interest rates and credit.
