Edgeworth Expansions of Stochastic Trading Time

25 Pages Posted: 10 Nov 2009 Last revised: 17 May 2010

See all articles by Marc Decamps

Marc Decamps

Katholieke Universiteit Leuven (KUL)

Ann De Schepper

University of Antwerp - Faculty of Applied Economics

Date Written: November 10, 2009

Abstract

Under most local and stochastic volatility models the underlying forward is assumed to be a positive function of a time-changed Brownian motion. It relates nicely the implied volatility smile to the so-called activity rate in the market. Following Young and DeWitt-Morette (1986), we propose to apply the Duru-Kleinert process-cum-time transformation in path integral to formulate the transition density of the forward. The method leads to asymptotic expansions of the transition density around a Gaussian kernel corresponding to the average activity in the market conditional on the forward value. The approximation is numerically illustrated for pricing vanilla options under the CEV model and the popular normal SABR model. The asymptotics can also be used for Monte Carlo simulations or backward integration schemes.

Keywords: Stochastic volatility, Fourier transform, Duru-Kleinert transformation, Edgeworth expansions

Suggested Citation

Decamps, Marc and De Schepper, Ann, Edgeworth Expansions of Stochastic Trading Time (November 10, 2009). Available at SSRN: https://ssrn.com/abstract=1503698 or http://dx.doi.org/10.2139/ssrn.1503698

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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