Transform MCMC schemes for sampling intractable factor copula models

Cyril Bénézet (), Emmanuel Gobet and Rodrigo Targino
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Cyril Bénézet: LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
Emmanuel Gobet: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: In financial risk management, modelling dependency within a random vector X is crucial, a standard approach is the use of a copula model. Say the copula model can be sampled through realizations of Y having copula function C: had the marginals of Y been known, sampling X^(i) , the i-th component of X, would directly follow by composing Y^(i) with its cumulative distribution function (c.d.f.) and the inverse c.d.f. of X^(i). In this work, the marginals of Y are not explicit, as in a factor copula model. We design an algorithm which samples X through an empirical approximation of the c.d.f. of the Y marginals. To be able to handle complex distributions for Y or rare-event computations, we allow Markov Chain Monte Carlo (MCMC) samplers. We establish convergence results whose rates depend on the tails of X, Y and the Lyapunov function of the MCMC sampler. We present numerical experiments confirming the convergence rates and also revisit a real data analysis from financial risk management.

Keywords: Copula models; Markov chain Monte Carlo MCMC methods; sampling (search for similar items in EconPapers)
Date: 2023-03
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-03334526v1
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Published in Methodology and Computing in Applied Probability, 2023, 25 (1), pp.13. ⟨10.1007/s11009-023-09983-4⟩

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Journal Article: Transform MCMC Schemes for Sampling Intractable Factor Copula Models (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03334526

DOI: 10.1007/s11009-023-09983-4

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