Old-fashioned parametric models are still the best: a comparison of value-at-risk approaches in several volatility states

Mateusz Buczyński and Marcin Chlebus

Abstract

Numerous advances in the modeling techniques of value-at-risk (VaR) have provided financial institutions with a wide range of market risk approaches. However, which model to use depends on the state of volatility. We present backtesting results for 1% and 2.5% VaR of six indexes from emerging and developed countries using several of the best-known VaR models, including generalized autoregressive conditional heteroscedasticity (GARCH), extreme value theory (EVT), conditional autoregressive VaR (CAViaR) and filtered historical simulation (FHS) with multiple sets of parameters. The backtesting procedure is based on the excess ratio, Kupiec and Christoffersen tests for multiple thresholds and cost functions. The main contribution of this paper is that we compared the models in four different scenarios, with different states of volatility in the training and testing samples. The results indicate that the best of the models, ie, the least affected by changes in the volatility, is GARCH(1,1) with a standardized Student t distribution. Nonparametric techniques (eg, CAViaR with GARCH setup or FHS with a skewed normal distribution) have very prominent results in testing periods with low volatility, but they are worse in turbulent periods. We also discuss an automatic method to set an extreme distribution threshold for EVT models as well as several ensembling methods for VaR, of which the minimum VaR estimate from the best models – in particular, a minimum of GARCH(1,1) with a standardized Student t distribution and either the EVT or the CAViaR model – has been proven to give very good results.