Backtesting the Tail Risk of VaR in Holding US Dollars
27 Pages Posted: 5 Dec 2007 Last revised: 27 May 2008
The US dollar is the most widely held currency in the world. In recent years, however, it suffered huge depreciation. In this paper, various risk models are used to forecast the Value-at-Risk (VaR) in holding the currency. Being a quantile measure, VaR disregards valuable information conveyed by the sizes of tail losses. As a result, there is tail risk in the use of VaR in practice. Saddlepoint technique is used to backtest tail risk of VaR by summing all the tail losses. Substantial downside tail risks are detected in the US currency, and Asymmetric Power ARCH with normal inverse Gaussian innovation is found capable of capturing such risks.
Keywords: Value-at-Risk, tail risk, foreign exchange, backtesting, saddlepoint technique
JEL Classification: C53, G32
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