Amortized neural inference on bivariate tail dependence and tail asymmetry

We develop an amortized neural inference approach to assess the strength of tail dependence and the degree of asymmetry between the upper and lower tails based on a proposed unified tail dependence parameter for copulas. Extensive simulation studies are conducted for amortized inference with neural Bayes estimators of two full-range tail dependence copulas, to understand its performance under different situations, including training and inference speeds, comparisons of different methods for generating samples for training, comparisons between neural Bayes estimators and maximum likelihood estimators, performance for different sample sizes, performance for assessing tail dependence and tail asymmetry simultaneously, and modeling capacities in various misspecified situations. The proposed method has an ultrafast inference speed and is universally applicable and interpretable, making it useful for many real-world applications. An accompanying R package FastTail is also developed. To demonstrate its usefulness, we conducted an empirical study on stocks and ETFs from 2011 to 2025. The proposed GGEE-GARCH model using the neural Bayes estimators outperformed other commonly used copula GARCH models in predicting the next day Value-at-Risk. While the amortized neural inference approach is implemented for full-range tail dependence copulas, it can be useful for other parametric copulas with intractable likelihood functions, opening windows of opportunities for future development of new copula families with flexible dependence patterns.