Advanced Analytics for the SABR Model

58 Pages Posted: 26 Mar 2012 Last revised: 5 Sep 2012

Date Written: March 23, 2012


In this paper, we present advanced analytical formulas for SABR model option pricing. The first technical result consists of a new exact formula for the zero correlation case. This closed form is a simple 2D integration of elementary functions, particularly attractive for numerical implementation. The second result is an effective approximation of the general correlation case. We use a map to the zero correlation case having a nice behavior on strike edges. The map formulas are easily implemented and do not contain any numerical integration.

These formulas are important in volatility surface construction and CMS products replication because they provide correct behavior for far strikes and reduced approximation error. The latter is also helpful for dynamic SABR models.

Keywords: SABR, closed formula, map approximation, swaption price, CMS replication, volatility surface

JEL Classification: C1, C3, C5, C6

Suggested Citation

Antonov, Alexandre and Spector, Michael, Advanced Analytics for the SABR Model (March 23, 2012). Available at SSRN: or

Alexandre Antonov (Contact Author)

Danske Bank - Danske Markets ( email )

Holmens Kanal 2-12
DK-1092 Copenhagen K

Michael Spector

Numerix ( email )

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

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