American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach

Chiarella, C; Ziogas, A

American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach

Chiarella, C Ziogas, A

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Publisher:: Routledge
Publication Type:: Journal Article
Citation:: Applied Mathematical Finance, 2009, 16 (1), pp. 37 - 79
Issue Date:: 2009-01

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Field	Value	Language
dc.contributor.author	Chiarella, C	en_US
dc.contributor.author	Ziogas, A	en_US
dc.date.issued	2009-01	en_US
dc.identifier.citation	Applied Mathematical Finance, 2009, 16 (1), pp. 37 - 79	en_US
dc.identifier.issn	1350-486X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/9965
dc.description.abstract	We consider the American option pricing problem in the case where the underlying asset follows a jump-diffusion process. We apply the method of Jamshidian to transform the problem of solving a homogeneous integro-partial differential equation (IPDE) on a region restricted by the early exercise (free) boundary to that of solving an inhomogeneous IPDE on an unrestricted region. We apply the Fourier transform technique to this inhomogeneous IPDE in the case of a call option on a dividend paying underlying to obtain the solution in the form of a pair of linked integral equations for the free boundary and the option price. We also derive new results concerning the limit for the free boundary at expiry. Finally, we present a numerical algorithm for the solution of the linked integral equation system for the American call price, its delta and the early exercise boundary. We use the numerical results to quantify the impact of jumps on American call prices and the early exercise boundary.	en_US
dc.publisher	Routledge	en_US
dc.relation.ispartof	Applied Mathematical Finance	en_US
dc.relation.isbasedon	10.1080/13504860802221672	en_US
dc.rights	This is an Author's Accepted Manuscript of an article published in Applied Mathematical Finance, 2009, 16 (1), pp. 37 - 79. Copyright Routledge, available online at: https://dx.doi.org/10.1080/13504860802221672.	en_US
dc.subject.classification	Finance	en_US
dc.title	American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	16	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	1502 Banking, Finance and Investment	en_US
utslib.for	0103 Numerical and Computational Mathematics	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
utslib.copyright.status	open_access
pubs.consider-herdc	true	en_US
pubs.issue	1	en_US
pubs.volume	16	en_US

Abstract:

We consider the American option pricing problem in the case where the underlying asset follows a jump-diffusion process. We apply the method of Jamshidian to transform the problem of solving a homogeneous integro-partial differential equation (IPDE) on a region restricted by the early exercise (free) boundary to that of solving an inhomogeneous IPDE on an unrestricted region. We apply the Fourier transform technique to this inhomogeneous IPDE in the case of a call option on a dividend paying underlying to obtain the solution in the form of a pair of linked integral equations for the free boundary and the option price. We also derive new results concerning the limit for the free boundary at expiry. Finally, we present a numerical algorithm for the solution of the linked integral equation system for the American call price, its delta and the early exercise boundary. We use the numerical results to quantify the impact of jumps on American call prices and the early exercise boundary.

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http://hdl.handle.net/10453/9965