Value-at-Risk estimates

Abstract

This thesis consists of three empirical essays on the Value-at-Risk (VaR) estimates. The first empirical study (Chapter 2) evaluates the performance of bank VaRs. The second empirical study (Chapter 3) investigates the predictive power of various VaR models using bank data. The third empirical study (Chapter 4) explores VaR estimates with high-frequency data. The first study examines the performance of VaR estimates at seven international banks from 2001 to 2012. Using statistical tests, we find that bank VaRs were conservatively estimated in pre-crisis and post-crisis periods. During financial crisis, while some banks continued to overstate their VaRs, the others significantly underestimated their risk. The potential causes of the poor performance of bank VaRs are also discussed. The second study investigates the predictive power of various VaR models using bank data. We find that the GARCH-based models are superior in estimating bank VaRs in both normal and crisis periods. We conclude that good VaR estimates at banks can be obtained using simple, accessible models rather than the complicated approach or banks’ internal model. Thus, we argue that VaR should not be blamed for misleading risk estimates during financial crisis. The third study evaluates VaR estimates using 5-minute sampling data of WTI Futures. First, we acknowledge the value of high-frequency data on the measure of volatility to characterize the quantile forecast of asset returns. Second, we find that quantile combination can improve the forecast accuracy. With the VaR implication, we show that VaR combination provides more accurate and robust results than individual VaR estimates.