Frontiers in VaR forecasting and backtesting

Abstract

The interest on forecasting Value at Risk (VaR) has been growing over the last two decades due to the practical relevance of this risk measure for financial and insurance institutions. Furthermore, VaR forecasts are often used as a battleground when alternative models are fitted to represent the dynamic evolution of time series of financial returns. There is a vast amount of alternative methods for constructing and evaluating VaR forecasts. In this paper, we survey the new benchmarks proposed in the recent literature.

Value‐at‐risk under market shifts through highly flexible models

“…The asymmetric power ARCH (APARCH) model developed by Ding, Granger, and Engle (1993) is considered as highly flexible, since it can nest a large variety of other GARCH-type models. Some authors (see Diamandis, Drakos, Kouretas, & Zarangas, 2011;Giot & Laurent, 2003;Nieto & Ruiz, 2016;Rodríguez & Ruiz, 2012) suggest measuring the VaR using asymmetric models, such as APARCH to cope with different responses of the volatility to negative and positive shocks. The fractionally integrated version of this model (FIAPARCH) is not recommended in this context, because incorporating a long-memory effect in the volatility while computing the VaR is against the Basel accords, which requires short-run forecasts (Nieto & Ruiz, 2016).…”

“…Some authors (see Diamandis, Drakos, Kouretas, & Zarangas, 2011;Giot & Laurent, 2003;Nieto & Ruiz, 2016;Rodríguez & Ruiz, 2012) suggest measuring the VaR using asymmetric models, such as APARCH to cope with different responses of the volatility to negative and positive shocks. The fractionally integrated version of this model (FIAPARCH) is not recommended in this context, because incorporating a long-memory effect in the volatility while computing the VaR is against the Basel accords, which requires short-run forecasts (Nieto & Ruiz, 2016). These fractionally integrated models provide, however, a good fit compared to their normal versions (Gencer & Demiralay, 2016;Slim, Koubaa, & BenSaïda, 2017).…”

“…The Basel committee further requires daily forecasts of the VaR for returns over a holding period of 10 days (Basel Committee on Banking Supervision, 2006). However, most researchers often predict the 1-day-ahead VaR that corresponds to returns over a holding period of 1 day, since it provides the most reliable measure for model comparison (see, e.g., Ardia & Hoogerheide, 2014;Berger & Missong, 2014;Cheng & Hung, 2011;Dendramis et al, 2014;Nieto & Ruiz, 2016;Takahashi, Watanabe, & Omori, 2016), and because the Basel accords allow the 10-day-ahead VaR to be obtained from shorter period forecasts by using the square-root-of-time rule (Nieto & Ruiz, 2016). 7 7 The square-root-of-time rule, however, can lead to overestimating the VaR under a "realistic" data-generating process for financial returns featuring serial dependence, mean reversion, and heavy tails (Daníelsson & Zigrand, 2006).…”

“…A large literature has been devoted to the VaR estimation and forecasting using various methodologies (e.g., Billio & Pelizzon, 2000;Giot & Laurent, 2003;Nieto & Ruiz, 2016;Rodríguez & Ruiz, 2012;Salhi, Deaconu, Lejay, Champagnat, & Navet, 2016) to the extent that VaR estimates are central to ass et allocation and capital adequacy decisions of banking and financial institutions. For example, Giot and Laurent (2003) use several univariate and multivariate GARCH-based models with the skewed-t distribution to model the VaR for traders that have both short and long trading positions.…”

Modeling the conditional distribution of financial returns with asymmetric tails

“…It is based on the asymmetric Student t-distribution (hereafter AST 2 See Nelson (1991, p. 352) for a discussion of the problems of the EGARCH model under Student t errors. 3 A recent review by Nieto and Ruiz (2016) suggested that this was the most popular parametric skewed distribution, though it is not the only alternative. I refer the reader to section 3.3.3 of their paper for a detailed discussion of these alternatives and references to applied work.…”