Empirical study of value‐at‐risk and expected shortfall models with heavy tails

Abstract

Purpose -This paper aims to test empirically the performance of different models in measuring VaR and ES in the presence of heavy tails in returns using historical data. Design/methodology/approach -Daily returns of popular indices (S&P500, DAX, CAC, Nikkei, TSE, and FTSE) and currencies (US dollar vs Euro, Yen, Pound, and Canadian dollar) for over ten years are modeled with empirical (or historical), Gaussian, Generalized Pareto (peak over threshold (POT) technique of extreme value theory (EVT)) and Stable Paretian distribution (both symmetric and non-symmetric). Experimentation on different factors that affect modeling, e.g. rolling window size and confidence level, has been conducted. Findings -In estimating VaR, the results show that models that capture rare events can predict risk more accurately than non-fat-tailed models. For ES estimation, the historical model (as expected) and POT method are proved to give more accurate estimations. Gaussian model underestimates ES, while Stable Paretian framework overestimates ES. Practical implications -Research findings are useful to investors and the way they perceive market risk, risk managers and the way they measure risk and calibrate their models, e.g. shortcomings of VaR, and regulators in central banks. Originality/value -A comparative, thorough empirical study on a number of financial time series (currencies, indices) that aims to reveal the pros and cons of Gaussian versus fat-tailed models and Stable Paretian versus EVT, in estimating two popular risk measures (VaR and ES), in the presence of extreme events. The effects of model assumptions on different parameters have also been studied in the paper.

Quantifying extreme market risk in the selected Western Balkan countries

“…In the contrary to these models, as the confidence level increases, the VaR estimates obtained by EVT models are getting better and better. Similar results were presented by Neftci (2000), Harmantzis et al (2006), as well as Marinelli (2007). They have shown that VaR EVT models provide better performance compared to parametric models and HS models.…”

Scaling laws: a viable alternative to value at risk?

“…895 VaR based on the GPD has received much empirical support, for example Harmantzis et al (2006), Bali (2003) and Gençay and Selçuk (2004). Fernandez (2003) finds that it tends to predict losses much more accurately than a VaR model based on the normal distribution, even when the variance of the normal-based VaR follows a GARCH model.…”

Measuring Extreme Market Risk: The Sri Lankan Context

“…In order to compare unconditional models, a moving window approach -such as that used in Harmantzis, Miao, and Chien (2006) -will be employed. The length of each moving window will be 1,000 observations.…”

“…Both studies showed that the POT method shows relatively better performance for modelling VaR, especially at higher quantiles. Harmantzis, Miao, and Chien (2006) found that the historical simulation method and POT estimate ES accurately.…”

“…Studies have been carried out to ascertain which static model is most appropriate for various indices (Harmantzis, Miao, and Chien 2006;Gencay and Selcuk 2004). These studies compared the performance of the POT method against other methods such as the historical simulation method and variancecovariance method with student's t distribution.…”