The evaluation of discrete barrier options in a path integral framework

Chiarella, C; El-Hassan, N; Kucera, A

The evaluation of discrete barrier options in a path integral framework

Chiarella, C El-Hassan, N Kucera, A

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Publisher:: Springer
Publication Type:: Chapter
Citation:: Computational Methods in Financial Engineering: Essays in Honour of Manfred Gilli, 2008, 1, pp. 117 - 144
Issue Date:: 2008-01

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Field	Value	Language
dc.contributor.author	Chiarella, C	en_US
dc.contributor.author	El-Hassan, N	en_US
dc.contributor.author	Kucera, A	en_US
dc.contributor.editor	Kontoghiorghes, E	en_US
dc.contributor.editor	Rustem, B	en_US
dc.contributor.editor	Winker, P	en_US
dc.date.issued	2008-01	en_US
dc.identifier.citation	Computational Methods in Financial Engineering: Essays in Honour of Manfred Gilli, 2008, 1, pp. 117 - 144	en_US
dc.identifier.isbn	9783540779575	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8029
dc.description.abstract	The pricing of discretely monitored barrier options is a difficult problem. In general, there is no known closed form solution for pricing such options. A path integral approach to the evaluation of barrier options is developed. This leads to a backward recursion functional equation linking the pricing functions at successive barrier points. This functional equation is solved by expanding the pricing functions in Fourier-Hermite series. The backward recursion functional equation then becomes the backward recurrence relation for the coefficients in the Fourier-Hermite expansion of the pricing functions. A very efficient and accurate method for generating the pricing function at any barrier point is thus obtained. A number of numerical experiments with the method are performed in order to gain some understanding of the nature of convergence. Results for various volatility values and different numbers of basis functions in the Fourier-Hermite expansion are presented. Comparisons are given between pricing of discrete barrier option in the path integral framework and by use of finite difference methods.	en_US
dc.publisher	Springer	en_US
dc.relation.ispartof	Computational Methods in Financial Engineering: Essays in Honour of Manfred Gilli	en_US
dc.relation.isbasedon	10.1007/978-3-540-77958-2_7	en_US
dc.rights	This is a post-peer-review, pre-copyedit version of an article published in Computational Methods in Financial Engineering: Essays in Honour of Manfred Gilli. The final authenticated version is available online at: https://dx.doi.org/10.1007/978-3-540-77958-2_7.	en_US
dc.title	The evaluation of discrete barrier options in a path integral framework	en_US
dc.type	Chapter
utslib.location	Germany	en_US
utslib.for	1502 Banking, Finance and Investment	en_US
utslib.citation.edition	1	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
utslib.copyright.status	open_access
pubs.consider-herdc	true	en_US
pubs.edition	1	en_US
pubs.place-of-publication	Germany	en_US

Abstract:

The pricing of discretely monitored barrier options is a difficult problem. In general, there is no known closed form solution for pricing such options. A path integral approach to the evaluation of barrier options is developed. This leads to a backward recursion functional equation linking the pricing functions at successive barrier points. This functional equation is solved by expanding the pricing functions in Fourier-Hermite series. The backward recursion functional equation then becomes the backward recurrence relation for the coefficients in the Fourier-Hermite expansion of the pricing functions. A very efficient and accurate method for generating the pricing function at any barrier point is thus obtained. A number of numerical experiments with the method are performed in order to gain some understanding of the nature of convergence. Results for various volatility values and different numbers of basis functions in the Fourier-Hermite expansion are presented. Comparisons are given between pricing of discrete barrier option in the path integral framework and by use of finite difference methods.

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http://hdl.handle.net/10453/8029