Atomic Implied Volatilities

27 Pages Posted: 6 Oct 2008 Last revised: 30 Nov 2009

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, 2008

Abstract

In this note, we present a novel approach to derive asymptotics for Black implied volatilities under the same generic model as proposed in Antonov and Misirpashaev (2009). We perform a time substitution as used by Duru and Kleinert (1979) to calculate the path integral formulation of the H-atom. We demonstrate that the method provides asymptotic implied volatility formula comparable to the result of Hagan and Woodward (1999) for local volatility models and Hagan et al. (2001) for stochastic volatility models. We also discuss possible application to the pricing of basket options. The method is presented as an alternative to Markov projection as introduced by Piterbarg (2006) and is claimed to be applicable to a wide range of numerical problems arising in finance.

Keywords: SABR model, Duru-Kleinert transformation

Suggested Citation

Decamps, Marc and De Schepper, Ann, Atomic Implied Volatilities (September 1, 2008). Available at SSRN: https://ssrn.com/abstract=1279363 or http://dx.doi.org/10.2139/ssrn.1279363

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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