A Nonparametric Bayesian Estimator of Copula Density with Applications to Financial Market

We propose a nonparametric Bayesian estimator of copula density based on the Logistic Gaussian Process density estimation method. A Gaussian process prior with flexible mean and covariance functions is placed on the underlying latent function. To avoid the typical boundary issues in copula density estimation, a transformation approach is adopted, allowing the latent process to be defined on an unrestricted support and then back-transformed to obtain the posterior copula density. We also develop a sampler to facilitate efficient sampling from the posterior copula distribution. Monte Carlo simulations demonstrate the strong overall and tail performance of the proposed estimator and the efficiency of the posterior sampler. We illustrate the usefulness of the proposed estimator through applications in financial dependence analysis, risk management, and option pricing.