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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Bibliographic Details
Published inApplied mathematical finance. Vol. 16; no. 4; pp. 307 - 314
Main Authors Cherubini, Umberto, Romagnoli, Silvia
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.10.2009
Taylor and Francis Journals
Taylor & Francis Ltd
SeriesApplied Mathematical Finance
Subjects
Algorithms
computational pricing methods
Copula functions
copula volume
Mathematical functions
Multivariate analysis
multivariate options
Parity
Put & call options
Securities prices
Studies
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Summary: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.
ISSN:1350-486X
1466-4313
DOI:10.1080/13504860802597311