Extreme-quantile tracking for financial time series

Time series of financial asset values exhibit well known statistical features such as heavy tails and volatility clustering. Strongly present in some series, nonstationarity is a feature that has been somewhat overlooked. This may however be a highly relevant feature when estimating extreme quantiles (VaR) for such series. We propose a nonparametric extension of the classical Peaks-Over-Threshold method to fit the time varying volatility in situations where the stationarity assumption is strongly violated by erratic changes of regime. A back testing study for the UBS share price over the subprime crisis reveals that our approach provides better extreme-quantile (VaR) estimates than methods that ignore nonstationarity.