Evaluating Value-at-Risk Models with Desk-Level Data

Abstract

We present new evidence on disaggregated profit and loss and VaR forecasts obtained from a large international commercial bank. Our dataset includes daily P/L generated by four separate business lines within the bank. All four business lines are involved in securities trading and each is observed daily for a period of at least two years. We also collected the corresponding daily, 1-day ahead VaR forecasts for each business line. Given this rich dataset, we provide an integrated, unifying framework for assessing the accuracy of VaR forecasts. Our approach includes many existing backtesting techniques as special cases. In addition, we describe some new tests which are suggested by our framework. A thorough Monte Carlo comparison of the various methods is conducted to provide guidance as to which of these many tests have the best finite-sample size and power properties.

Managing risk with a realized copula parameter

“…We find that the RCop models perform very well at any quantile. Among all models, their hitting ratios are close to the target levels, and the p-values of the Kupiec test, the t-test, and the Berkowitz et al (2011) test are among the highest. Moreover, we cannot distinguish between the two copulae (Clayton versus rotated Gumbel).…”

“…Computing risk measures for portfolios of stocks followed by a backtesting analysis are standard procedures in applied risk management; see, e.g., Berkowitz and O'Brien (2002), Audrino and Barone-Adesi (2005), Giacomini et al (2009), Jin (2010, Berkowitz et al (2011), among others. Closest to our research is Giot and Laurent (2004), who appear to be among the first to include both low and high-frequency data for such an analysis.…”

“…This test is due to Kupiec (1995). We also consider a simple t-test based on the normal approximation for the binomial distribution and independence testing based on Ljung-Box statistics as suggested by Berkowitz et al (2011).…”

A systematic design for coping with model risk

“…However, most discussions in literatures of risk management (Pennings & Smidts, 2000;Iversen, Mathiassen, & Nielson, 2004;Benaroch, Lichtenstein, & Robinson, 2006;Dewan & Ren, 2007;Gefen, Wyss, & Lichtenstein, 2008;Berkowits, Christoffersen, & Pelletier, 2009;Lin & Ko, 2009;Roisenberg, Schoeninger, & da Silva, 2009) do not seem to generalize to present a systematical way of designing such a SSS.…”

Risk management in portfolio applications of non-convex stochastic programming

“…Therefore how to control the risk of portfolio seems to be very important. There are many ways to measure risk, among these VaR ( [1,7,18,21], etc.) and CVaR ( [2,8,10,13,16,19], etc.)…”