Duru-Kleinert Asymptotic Expansions for Long-Term Foreign Exchange and Swaptions Implied Volatility Smile

15 Pages Posted: 28 Nov 2009 Last revised: 26 Jan 2012

See all articles by Marc Decamps

Marc Decamps

Katholieke Universiteit Leuven (KUL)

Ann De Schepper

University of Antwerp - Faculty of Applied Economics

Date Written: September 1, 2009

Abstract

In this paper, we develop asymptotic formulas for long-dated Foreign Exchange (FX) and swaptions implied volatilities. We extend the method exposed in Decamps and De Schepper (2009b) to a generic model with time-dependent parameters. Imposing a condition on the skew, we derive averaging formulas for the parameters. The method is applied to the pricing of FX options when the domestic and foreign interest rate curves are driven by Gaussian short-term rate models and to the pricing of swaptions in the Libor market model.

Keywords: FX option, Duru-Kleinert transformation, Parameter averaging

Suggested Citation

Decamps, Marc and De Schepper, Ann, Duru-Kleinert Asymptotic Expansions for Long-Term Foreign Exchange and Swaptions Implied Volatility Smile (September 1, 2009). Available at SSRN: https://ssrn.com/abstract=1514294 or http://dx.doi.org/10.2139/ssrn.1514294

Marc Decamps (Contact Author)

Katholieke Universiteit Leuven (KUL) ( email )

Oude Markt 13
Leuven, Vlaams-Brabant
Belgium

Ann De Schepper

University of Antwerp - Faculty of Applied Economics ( email )

Prinsstraat 13
Antwerp, B-2000
Belgium

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