Markets liquidity risk under extremal dependence: Analysis with VaRs methods

Value-at-Risk (VaR) is a widely used tool for assessing financial market risk. In practice, the estimation of liquidity extreme risk by VaR generally uses models assuming independence of bid–ask spreads. However, bid–ask spreads tend to occur in clusters with time dependency, particularly during crisis period. Our paper attempts to fill this gap by studying the impact of negligence of dependency in liquidity extreme risk assessment of Tunisian stock market. The main methods which take into account returns dependency to assess market risk is Time series–Extreme Value Theory combination. Therefore we compare VaRs estimated under independency (Variance–Covariance Approach, Historical Simulation and the VaR adjusted to extreme values) relatively to the VaR when dependence is considered. The efficiency of those methods was tested and compared using the backtesting tests. The results confirm the adequacy of the recent extensions of liquidity risk in the VaR estimation. Therefore, we prove a performance improvement of VaR estimates under the assumption of dependency across a significant reduction of the estimation error, particularly with AR (1)-GARCH (1,1)-GPD model.