An Extensive Comparison of Some Well‐Established Value at Risk Methods

Abstract

Summary In the last two decades, several methods for estimating Value at Risk have been proposed in the literature. Four of the most successful approaches are conditional autoregressive Value at Risk, extreme value theory, filtered historical simulation and time‐varying higher order conditional moments. In this paper, we compare their performances under both an empirical investigation using 80 assets and a large Monte Carlo simulation. From our analysis, we conclude that most of the methods seem not to imply huge numerical difficulties and, according to usual backtests and performance measurements, extreme value theory presents the best results most of the times, followed by filtered historical simulation.

A comparison of methods for forecasting value at risk and expected shortfall of cryptocurrencies

“…Although there are several methods to forecast the VaR and ES in the literature (see Bayer & Dimitriadis, 2020; Calmon et al, 2020, Nieto & Ruiz, 2016; Righi & Ceretta, 2015, for interesting reviews), only a few procedures have shown good performance in cryptocurrency markets. Those procedures are briefly described next.…”

Sparse estimation within Pearson's system, with an application to financial market risk

“…When applied to the S&P 500 in a period of turmoil, the proposed approach gave VaR limits that were only exceeded four times; accurate estimates of the shortfall incurred on these days were also provided. When applied to the S&P 500 in a less turbulent period, the proposed approach showed an improved performance compared to GARCH-EVT, which Calmon et al (2020) identified as the leading approach for estimating VaR. The proposed approach is the only one that consistently quantified the market risk in both periods.…”

“…The S&P 500 exhibits conditional heteroscedasticity, which needs to be filtered via generalized autoregressive conditional heteroscedastic (GARCH) modelling before one can focus on the distribution of the innovations. This type of modelling was used by Calmon et al (2020) in an extensive comparison of existing VaR forecasting methods. Their empirical analysis was based on S&P 500 returns from May 30, 2013 to May 1, 2017, which was a period of relatively standard market behaviour.…”

“…In Section 5.2, these data are revisited to assess the accuracy of VaR and ES forecasts produced by Data2Density and to make direct comparisons with the findings of Calmon et al (2020) in the case of VaR. Section 5.3 then looks at how the different methods perform between May 1, 2008 and May 1, 2009, which was a period of market turmoil.…”

“…To assess the performance of the proposed approach, daily 99% VaR estimates based on the proposed approach, historical VaR, the Cornish-Fisher, and various GARCH methods were computed using S&P 500 values for the period of standard market behaviour already considered by Calmon et al (2020), namely May 30, 2013 to May 1, 2017.…”