Transform MCMC Schemes for Sampling Intractable Factor Copula Models

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.