Laplace Transform Identities for Diffusions, with Applications to Rebates and Barrier Options

Hardy Hulley and Eckhard Platen ()

No 203, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms of some functions of first-passage times for the diffusion. These results are applied to the special case of squared Bessel processes with killing or reflecting boundaries. In particular, we demonstrate how the above-mentioned integral identity enables us to derive the transition density of a squared Bessel process killed at the origin, without the need to invert a Laplace transform. Finally, as an application, we consider the problem of pricing barrier options on an index described by the minimal market model.

Keywords: diffusions; transition densities; first-passage times; Laplce transformations; squared bessel processes; minimal market model; real-world pricing; rebates; barrier options (search for similar items in EconPapers)
Date: 2007-10-01
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