Closed Form Approximations for Diffusion Densities: A Path Integral Approach

Journal of Computational and Applied Mathematics, Vols. 164-165, pp. 337-364, March 2004

39 Pages Posted: 6 Oct 2008

See all articles by Ann De Schepper

Ann De Schepper

University of Antwerp - Faculty of Applied Economics

Marc Goovaerts

Catholic University of Leuven (KUL) - Department of Economics

Marc Decamps

Katholieke Universiteit Leuven (KUL)

Abstract

In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible, leading to analytical expressions for the transition probabilities and for the maximum probability paths. A second part consists of the derivation of an analytical approximation for the transition probability, which is useful in case the path integral is too complex to be calculated. The approximation we present, is based on a convex combination of a new analytical upper and lower bound for the transition probabilities. The fact that the approximation is analytical has some important advantages, e.g. for the investigation of Asian options. Finally, we demonstrate the accuracy of the approximation by means of some graphical illustrations.

Keywords: diffusion processes, transition probability, path integral, comonoticity

Suggested Citation

De Schepper, Ann and Goovaerts, Marc and Decamps, Marc, Closed Form Approximations for Diffusion Densities: A Path Integral Approach. Journal of Computational and Applied Mathematics, Vols. 164-165, pp. 337-364, March 2004, Available at SSRN: https://ssrn.com/abstract=1279226

Ann De Schepper

University of Antwerp - Faculty of Applied Economics ( email )

Prinsstraat 13
Antwerp, B-2000
Belgium

Marc Goovaerts (Contact Author)

Catholic University of Leuven (KUL) - Department of Economics ( email )

Leuven, B-3000
Belgium
+32 0 16 32 7446 (Phone)
+32 0 16 32 3740 (Fax)

Marc Decamps

Katholieke Universiteit Leuven (KUL) ( email )

Oude Markt 13
Leuven, Vlaams-Brabant
Belgium

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