Numerix Free Boundary SABR Challenges Market Standard Approach - Introduces Superior Way of Managing Negative Rates in Options Models
Numerix, the leading provider of cross-asset analytics for derivatives valuations and risk management, today announces the availability of its latest quantitative research paper, “The Free Boundary SABR: Natural Extension to Negative Rates,” now available. Authored by Numerix quantitative experts, Dr. Alexandre Antonov, Dr. Michael Konikov and Dr. Michael Spector this research outlines how the widely used SABR model can be extended to incorporate a “free boundary” SABR process, more naturally permitting negative rates versus a shifted SABR process, and eliminating the arbitrary lower bound on rates.
In the current low interest rate environment, especially in Europe and Japan where some deposit rates are below zero and many market rates hover in negative territory, financial institutions are finding that their option models do not handle negative rates. And, since dealing with negative strikes and forwards for short maturity caps and swaptions may require firms to modify their whole implementation of cap and swaption volatility surfaces, this has become a critically important issue.
“We see the free boundary approach being proposed by Numerix as a stronger solution for negative rates, however current market practice has gravitated to adding a deterministic positive shift to a rate and then modeling the shifted rate as a SABR process, also known as “shifted SABR,” said Dr. Alexandre Antonov, Senior Vice President of Numerix Quantitative Research. “While providing realistic probabilities of negative rates, the shifted SABR requires the selection of an arbitrary shift parameter, and it introduces an extra non-calibrated parameter for the SABR model.”
The Free Boundary SABR proposed by Numerix has the same number of parameters as the classical SABR with no shift needed, and it’s equipped with an efficient and accurate analytical approximation, crucial for the fast calibration. The full paper, which can be accessed here derives an exact formula for the option price in the zero-correlation case, and an efficient approximation for general correlation.
Dr. Michael Spector, Director of Quantitative Research adds: “The simplicity of the approximation permits a straightforward implementation. Moreover, the main formulae from the “absorbing” (standard) SABR approximation can be directly reused.”
“The shifted SABR can be a painful process – instilling artificial bound for the rates, requiring extra non-calibrated parameters for the SABR and producing singular behavior for the log-normal vol near the shift position,” said Dr. Michael Konikov, Executive Director and Head of Numerix Quantitative Development. “The free boundary approach, our recent development, is a natural, convenient and elegant extension of the classical SABR. It’s not hard to see this approach becoming the new market standard replacing shifted SABR.”
The authors also study different Monte Carlo schemes and come up with the most efficient choice. Finally, they have numerically checked the approximation accuracy for option pricing in this study.