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Computing the Volume of n-Dimensional Copulas

Author

Listed:
  • Umberto Cherubini
  • Silvia Romagnoli

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.

Suggested Citation

  • Umberto Cherubini & Silvia Romagnoli, 2009. "Computing the Volume of n-Dimensional Copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(4), pages 307-314.
    • Handle: RePEc:taf:apmtfi:v:16:y:2009:i:4:p:307-314
    DOI: 10.1080/13504860802597311
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    Citations

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    Cited by:

    1. Jian Zhou & Yanmin Gao, 2012. "Tail Dependence in International Real Estate Securities Markets," The Journal of Real Estate Finance and Economics, Springer, vol. 45(1), pages 128-151, June.
    2. Enrico Bernardi & Silvia Romagnoli, 2016. "Distorted Copula-Based Probability Distribution of a Counting Hierarchical Variable: A Credit Risk Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 285-310, March.
    3. Bernardi, Enrico & Falangi, Federico & Romagnoli, Silvia, 2015. "A hierarchical copula-based world-wide valuation of sovereign risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 155-169.

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