Computing the Volume of n-Dimensional Copulas
A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put-call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume compu...
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| Published in | Applied mathematical finance. Vol. 16; no. 4; pp. 307 - 314 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Abingdon
Taylor & Francis
01.10.2009
Taylor and Francis Journals Taylor & Francis Ltd |
| Series | Applied Mathematical Finance |
| Subjects | |
| Online Access | Get full text |
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| Abstract | A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put-call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume computation in high-dimensional copulas. We provide an algorithm for the exact computation of the volume of copula functions in cases where the copula function is computable in closed form. We apply the algorithm to the problem of computing the survival of a copula function in the pricing problem of a multivariate digital option, and we provide evidence that this is feasible for baskets of up to 20 underlying assets, with acceptable CPU time performance. |
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| AbstractList | A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put-call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume computation in high-dimensional copulas. We provide an algorithm for the exact computation of the volume of copula functions in cases where the copula function is computable in closed form. We apply the algorithm to the problem of computing the survival of a copula function in the pricing problem of a multivariate digital option, and we provide evidence that this is feasible for baskets of up to 20 underlying assets, with acceptable CPU time performance. A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put-call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume computation in high-dimensional copulas. We provide an algorithm for the exact computation of the volume of copula functions in cases where the copula function is computable in closed form. We apply the algorithm to the problem of computing the survival of a copula function in the pricing problem of a multivariate digital option, and we provide evidence that this is feasible for baskets of up to 20 underlying assets, with acceptable CPU time performance. [PUBLICATION ABSTRACT] |
| Author | Cherubini, Umberto Romagnoli, Silvia |
| Author_xml | – sequence: 1 givenname: Umberto surname: Cherubini fullname: Cherubini, Umberto email: umberto.cherubini@unibo.it organization: Department of Mathematical Economics , University of Bologna – sequence: 2 givenname: Silvia surname: Romagnoli fullname: Romagnoli, Silvia organization: Department of Mathematical Economics , University of Bologna |
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| Cites_doi | 10.1080/13504860210136721a 10.1201/b13150 10.1002/9781118673331 |
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| Copyright | Copyright Taylor & Francis Group, LLC 2009 Copyright Taylor & Francis Group 2009 |
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| References | Cherubini U. (CIT0002) 2004 Cherubini U. (CIT0001) 2002; 9 McNeil A. J. (CIT0004) 2005 CIT0006 Joe H. (CIT0003) 1997 Nelsen R. (CIT0005) 2006 |
| References_xml | – volume: 9 start-page: 69 year: 2002 ident: CIT0001 publication-title: Applied Mathematical Finance doi: 10.1080/13504860210136721a contributor: fullname: Cherubini U. – volume-title: Introduction to Copulas year: 2006 ident: CIT0005 contributor: fullname: Nelsen R. – volume-title: Quantitative Risk Management: Concept, Techniques and Tools year: 2005 ident: CIT0004 contributor: fullname: McNeil A. J. – volume-title: Multivariate Models and Dependence Concepts year: 1997 ident: CIT0003 doi: 10.1201/b13150 contributor: fullname: Joe H. – ident: CIT0006 – volume-title: Copula Methods in Finance year: 2004 ident: CIT0002 doi: 10.1002/9781118673331 contributor: fullname: Cherubini U. |
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| SubjectTerms | Algorithms computational pricing methods Copula functions copula volume Mathematical functions Multivariate analysis multivariate options Parity Put & call options Securities prices Studies |
| Title | Computing the Volume of n-Dimensional Copulas |
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