Maximum Likelihood Estimation Methods for Copula Models

For Copula models, the likelihood function could be multi-modal, and some traditional optimization algorithms such as simulated annealing (SA) may get stuck in the local mode and introduce bias in parameter estimation. To address this issue, we consider three widely used global optimization approaches, including sequential Monte Carlo simulated annealing (SMC-SA), sequential qudratic programming and generalized simulated annealing, in the estimation of bivariate and R-vine Copula models. Then the accuracy and effectiveness of these algorithms are compared in simulation studies, and we find that SMC-SA provides more robust estimation than SA both for bivariate and R-vine Copulas. Finally, we apply these approaches in real data as well as a large multivariate case for portfolio risk management, and find that SMC-SA performs better than SA in both fitting the data and predicting portfolio risk.