Laplace transform identities for diffusions, with applications to rebates and barrier options
- Publisher:
- Polska Akademia Nauk
- Publication Type:
- Conference Proceeding
- Citation:
- Banach Centre Publications: Advances in Mathematics of Finance, 2008, pp. 139 - 157
- Issue Date:
- 2008-01
Open Access
Copyright Clearance Process
- Recently Added
- In Progress
- Open Access
This item is open access.
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: