Backtest Criteria for the Quantile Correction under Model Risk

Abstract

The fact that financial risks cannot be exactly determined but have to be estimated make Value-at-Risk (VaR) models less reliable. Thus far, VaR-model risk have gained increasing concerns and have been addressed in two general ways. The first way is to evaluate risk models using statistical tests, called backtests. In particular, backtests employ a comparison of VaR series and realized returns in the specified period to examine whether risk estimates are appropriate or not. The second way is adjusting VaR for model risk, which one of the recently proposed frameworks is the quantile correction method via the outcome of backtesting. Set of backtest methods are chosen for being adjustment criteria by considering three desirable properties of VaR models, namely, unconditional coverage, independence, and magnitude of violations (losses that exceed VaR). This thesis extend the general quantile correction framework by applying various backtest methods focusing on their statistical power of backtests shown by authors. Five standard data generating models (DGMs) are used to compute VaR of Stock Exchange of Thailand (SET) index daily returns. The results from ex post validation show that model-risk-adjusted series provide better results than original VaR in many cases. With regards to criteria sets, higher-statistical-power backtest criteria sets outperform their counterparts when static VaR models are used.