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

摘要

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.