Dynamics of Value at Risk: Copula -VAR Approach Optimized with PSO Meta-Heuristic Algorithm

The estimation of an accurate measure of the Value-at-Risk is still a topic of interest in financial research and among risk management practitioners Despite the simple concept of VaR, measuring it is a very challenging statistical problem; because of normal distribution assumption, time-varying conditional quantiles, and the main limit of this approach consists into considering linearly conditioned quantiles. CAViaR model and its extent to the multivariate CAViaR approach (MCAViaR) have solved some of these shortcomings. To this end, Copula functions were introduced. This approach provides a flexible non-linear multivariate representation among quantiles. An important parameter of Copula functions is the degree of dependency between tail distributions, the incorrect estimation of which also leads to inaccurate interpretation. One way to estimate the dependency parameter is to use the optimization process; such as meta-heuristic algorithms due to their very high accuracy. Among the meta-heuristic algorithms, the Particle Swarm Optimization (PSO) algorithm is widely used in optimization research due to its high convergence speed. In this study, the MCAViaR model and the Clayton and student’s-t-type hybrid Copula model are used to estimate VaR dynamics in 10 large and active companies of the Tehran Stock Exchange from April 2009 to March 2020. The results showed that the tail dependency coefficients of the MCAViaR model for the studied stocks are zero, and therefore this model can be divided into two independent CAViaR equations. The results of estimating time-varying quantiles, which indicate the dynamics of value at risk, indicate that the time series of quantiles derived from the hybrid Copula model shows the dynamics well due to the higher time-frequency than the MCAViaR model. The results of the Kupiec back-test also confirm the better performance of the hybrid Copula model than the MCAViaR model.