Title: Backtesting expected shortfall via multi-quantile regression
Authors: Jeremy Leymarie - LEO - CNRS - University of Orleans (France)
Ophelie Couperier - LEO CNRS - ENSAE - CREST (France) [presenting]
Abstract: A new approach to backtest Expected Shortfall (ES) exploiting the definition of ES as a function of Value-at-Risk (VaR) is proposed. The strategy aims at assessing the quality of multiple VaRs jointly along the tail distribution of the risk model, and encompasses the Basel Committee recommendation of verifying two given quantiles. Building on multi-quantile theory, we propose four backtests that focus on parameter estimates of an auxiliary regression model. Monte-Carlo simulations show that our tests are powerful to detect misspecified ES models. We provide an empirical application on S\&P500 returns over the period 2007-2012 and demonstrate the good capability of our methodology to identify misleading ES forecasts. Our empirical results show that the detection abilities are higher with more than two quantiles, and should accordingly be taken into account in the current regulatory guidelines.