Consistent Single- and Multi-Step Sampling of Multivariate Arrival Times: A Characterization of Self-Chaining Copulas

23 Pages Posted: 29 Apr 2012

See all articles by Damiano Brigo

Damiano Brigo

Imperial College London - Department of Mathematics

Kyriakos Chourdakis

University of Essex - Centre for Computational Finance and Economic Agents

Date Written: April 28, 2012

Abstract

This paper deals with dependence across marginally exponentially distributed arrival times, such as default times in financial modeling or inter-failure times in reliability theory. We explore the relationship between dependence and the possibility to sample final multivariate survival in a long time-interval as a sequence of iterations of local multivariate survivals along a partition of the total time interval. We find that this is possible under a form of multivariate lack of memory that is linked to a property of the survival times copula. This property defines a "self-chaining-copula", and we show that this coincides with the extreme value copulas characterization. The self-chaining condition is satisfied by the Gumbel-Hougaard copula, a full characterization of self chaining copulas in the Archimedean family, and by the Marshall-Olkin copula. The result has important practical implications for consistent single-step and multi-step simulation of multivariate arrival times in a way that does not destroy dependency through iterations, as happens when inconsistently iterating a Gaussian copula.

Keywords: Dependence Modeling, Arrival Times, Sampling, Archimedean Copula, Gumbel-Hougaard Copula, Marshall-Olkin Copula, Self-Chaining Copula, Multi-Step Simulation, Extreme Value Copulas, Copula Iteration, Copula Chaining

JEL Classification: C15, C16

Suggested Citation

Brigo, Damiano and Chourdakis, Kyriakos, Consistent Single- and Multi-Step Sampling of Multivariate Arrival Times: A Characterization of Self-Chaining Copulas (April 28, 2012). Available at SSRN: https://ssrn.com/abstract=2047474 or http://dx.doi.org/10.2139/ssrn.2047474

Damiano Brigo (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www.imperial.ac.uk/people/damiano.brigo

Kyriakos Chourdakis

University of Essex - Centre for Computational Finance and Economic Agents ( email )

Wivenhoe Park
Colchester, Essex CO4 3SQ
United Kingdom

HOME PAGE: http://www.theponytail.net

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