Laplace transform identities for diffusions, with applications to rebates and barrier options

Polska Akademia Nauk
Publication Type:
Conference Proceeding
Banach Centre Publications: Advances in Mathematics of Finance, 2008, pp. 139 - 157
Issue Date:
Full metadata record
Files in This Item:
Filename Description SizeFormat
2008002011.pdf2.87 MBAdobe PDF
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.
Please use this identifier to cite or link to this item: