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The Free Boundary SABR: Natural Extension to Negative Rates

17 Pages Posted: 30 Jan 2015  

Date Written: January 28, 2015

Abstract

In the current low-interest-rate environment, extending option models to negative rates has become an important issue. This paper describes one such extension of the widely used SABR model. We stress that our solution is more natural and attractive than the shifted SABR.

An exact formula is derived for the option prices in the case of zero correlation between the rate and its volatility. For nonzero correlation, a mapping procedure onto a mimicking zero-correlation model is applied. Analytical results for the suggested free-boundary SABR model are compared with Monte Carlo simulations.

Keywords: SABR, negative rates, low rates, swaption volatility interpoaltion, closed formula, swaption price, CMS replication, volatility surface

JEL Classification: C1, C3, C5, C6

Suggested Citation

Antonov, Alexandre and Konikov, Michael and Spector, Michael, The Free Boundary SABR: Natural Extension to Negative Rates (January 28, 2015). Available at SSRN: https://ssrn.com/abstract=2557046 or http://dx.doi.org/10.2139/ssrn.2557046

Alexandre Antonov (Contact Author)

Numerix ( email )

58 bis rue de la Chaussee d'Antin
Paris, 75009
France

Michael Konikov

Numerix ( email )

99 Park Avenue, 5th Floor
New York, NY 10016
United States

Michael Spector

Numerix ( email )

99 Park Avenue, 5th Floor
New York, NY 10016
United States

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