A copula-based model for air pollution portfolio risk and its efficient simulation

This paper introduces a portfolio approach for quantifying pollution risk in the presence of PM_2.5 concentration in cities. The model used is based on a copula dependence structure. For assessing model parameters, we analyze a limited data set of PM_2.5 levels of Beijing, Tianjin, Chengde, Hengshui, and Xingtai. This process reveals a better fit for the t-copula dependence structure with generalized hyperbolic marginal distributions for the PM_2.5 log-ratios of the cities. Furthermore, we show how to efficiently simulate risk measures clean-air-at-risk and conditional clean-air-at-risk using importance sampling and stratified importance sampling. Our numerical results show that clean-air-at-risk at 0.01 probability level reaches up to 352μgm-3 (initial PM_2.5 concentrations of cities are assumed to be 100μgm-3) for the constructed sample portfolio, and that the proposed methods are much more efficient than a naive simulation for computing the exceeding probabilities and conditional excesses.