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

Hulley, H; Platen, E

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

Hulley, H

Platen, E

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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

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Field	Value	Language
dc.contributor.author	Hulley, H https://orcid.org/0000-0002-6684-8309	en_US
dc.contributor.author	Platen, E https://orcid.org/0000-0003-4595-3123	en_US
dc.contributor.editor	Stettner, L	en_US
dc.date	2007-04-30	en_US
dc.date.issued	2008-01	en_US
dc.identifier.citation	Banach Centre Publications: Advances in Mathematics of Finance, 2008, pp. 139 - 157	en_US
dc.identifier.issn	0137-6934	en_US
dc.identifier.uri	http://hdl.handle.net/10453/10679
dc.description.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.	en_US
dc.publisher	Polska Akademia Nauk	en_US
dc.relation.ispartof	Banach Centre Publications: Advances in Mathematics of Finance	en_US
dc.relation.ispartof	General AMaMeF Conference and Banach Centre Conference	en_US
dc.title	Laplace transform identities for diffusions, with applications to rebates and barrier options	en_US
dc.type	Conference Proceeding
utslib.location	Warszawa, Poland	en_US
utslib.location.activity	Bedlewo, Poland	en_US
utslib.for	010406 Stochastic Analysis and Modelling	en_US
utslib.for	010404 Probability Theory	en_US
utslib.for	010205 Financial Mathematics	en_US
dc.location.activity	Bedlewo, Poland	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Finance Discipline
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access
pubs.consider-herdc	true	en_US
pubs.place-of-publication	Warszawa, Poland	en_US
pubs.start-date	2007-04-30	en_US

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.

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http://hdl.handle.net/10453/10679