Laplace Transform Identities for Diffusions, with Applications to Rebates and Barrier Options
AbstractUsing 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.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 203.
Date of creation: 01 Oct 2007
Date of revision:
diffusions; transition densities; first-passage times; Laplce transformations; squared bessel processes; minimal market model; real-world pricing; rebates; barrier options;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-10-20 (All new papers)
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