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.

对于 Copula 模型，似然函数可能是多模态的，一些传统的优化算法如模拟退火 (SA) 可能会陷入局部模式并在参数估计中引入偏差。为了解决这个问题，我们在双变量和 R-vine Copula 模型的估计中考虑了三种广泛使用的全局优化方法，包括顺序蒙特卡罗模拟退火 (SMC-SA)、顺序二次规划和广义模拟退火。然后在仿真研究中比较了这些算法的准确性和有效性，我们发现 SMC-SA 为双变量和 R-vine Copulas 提供了比 SA 更稳健的估计。最后，我们将这些方法应用于真实数据以及投资组合风险管理的大型多元案例中，