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

• Autorzy: Hardy Hulley , Eckhard Platen
• Języki publikacji: EN

Abstrakty

EN

We start with a general time-homogeneous scalar diffusion whose state space is an interval I ⊆ ℝ. If it is started at x ∈ I, then we consider the problem of imposing upper and/or lower boundary conditions at two points a,b ∈ I, where a < x < b. 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.

Kategorie tematyczne

• 47D07: Markov semigroups and applications to diffusion processes
• 44A10: Laplace transform
• 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
• 60J60: Diffusion processes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 83
• Numer: 1
• Strony: 139-157

Daty

wydano

2008

Twórcy

autor

Hardy Hulley

• School of Finance and Economics, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia

autor

Eckhard Platen

• School of Finance and Economics and Department of Mathematical Sciences, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia

Identyfikatory

DOI

10.4064/bc83-0-9