Backtesting value-at-risk tail losses on a dynamic portfolio

Alasdair Graham and János Pál

Abstract

ABSTRACT

Backtesting is an essential component of the implementation and operation of any risk model. As perhaps the most well-known market risk metric, value at-risk (VaR) has received regulatory, industry and academic backtesting scrutiny. In particular, the Basel II mandated VaR violation counting backtest is well-known. One specific focus within recent work has been the quantification of the tail risk inherent in VaR models, as such quantitative analysis is complementary to the Basel II mandated counting backtest. This paper expands upon and generalizes a recent tail-loss backtest using a small-sample asymptotic saddle-point technique, rendering it analytically tractable and operationally feasible, as well as demonstrating its clear usefulness within industry applications.