Backtesting Value-at-Risk Based on Tail Losses
32 Pages Posted: 5 Dec 2007 Last revised: 10 Nov 2008
Date Written: November 2, 2008
Extreme losses caused by leverage and financial derivatives highlight the need to backtest Value-at-Risk (VaR) based on sizes of tail losses, for the risk measure disregards losses beyond the VaR boundary and there is no formal statistical analysis required for stress testing. While Basel II backtests VaR by counting the number of exceptions, this paper proposes to use saddlepoint technique to backtest VaR by summing the tail losses. Monte Carlo simulations show that the technique is very accurate and powerful even for small samples. The proposed backtest finds substantial downside tail risks in S&P 500, and that risk models which account for jumps, skewed and fat-tailed distributions fail to capture the tail risk during the 1987 stock market crash. Finally, the saddlepoint technique is used to derive a multiplication factor for risk capital requirement that is responsive to sizes of tail losses.
Keywords: Value-at-Risk, tail risk, backtesting, risk management, risk capital
JEL Classification: G10, G18, G32
Suggested Citation: Suggested Citation