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Transform MCMC schemes for sampling intractable factor copula models

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.
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https://hal.archives-ouvertes.fr/hal-03334526
Contributor : Cyril Bénézet Connect in order to contact the contributor
Submitted on : Friday, September 3, 2021 - 10:13:25 PM
Last modification on : Wednesday, September 8, 2021 - 3:32:49 AM

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  • HAL Id : hal-03334526, version 1

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Cyril Bénézet, Emmanuel Gobet, Rodrigo Targino. Transform MCMC schemes for sampling intractable factor copula models. 2021. ⟨hal-03334526⟩

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