Using Conditional Extreme Value Theory to Estimate Value-at-Risk for Daily Currency Exchange Rates

Abstract

This paper implements different approaches used to compute the one-day Value-at-Risk (VaR) forecast for a portfolio of four currency exchange rates. The concepts and techniques of the conventional methods considered in the study are first reviewed. These approaches have shortcomings and therefore fail to capture the stylized characteristics of financial time series returns such as; non-normality, the phenomenon of volatility clustering and the fat tails exhibited by the return distribution. The GARCH models and its extensions have been widely used in financial econometrics to model the conditional volatility dynamics of financial returns. The paper utilizes a conditional extreme value theory (EVT) based model that combines the GJR-GARCH model that takes into account the asymmetric shocks in time-varying volatility observed in financial return series and EVT focuses on modeling the tail distribution to estimate extreme currency tail risk. The relative out-of-sample forecasting performance of the conditional-EVT model compared to the conventional models in estimating extreme risk is evaluated using the dynamic backtesting procedures. Comparing each of the methods based on the backtesting results, the conditional EVT-based model overwhelmingly outperforms all the conventional models. The overall results demonstrate that the conditional EVT-based model provides more accurate out-of-sample VaR forecasts in estimating the currency tail risk and captures the stylized facts of financial returns.

Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models

“…To this day, many researchers have investigated the estimation of VaR and CVaR, with the help of Extreme Value Theory (Bee and Trapin 2018). A look at past studies in finance literature shows that, as opposed to other models, Value at Risk can be calculated much more accurately, using the EVT (Gencay and Selcuk 2004;Omari et al 2017). However, VaR is not only incoherent but also fails to precisely estimate the risk of loss when the loss distributions show "fat tails" (Rockafellar and Uryasev 2002), and this significantly hurts the accuracy of this risk measure (Chen 2018).…”

Conditional Var Using Garch-Evt Approach With Optimal Tail Selection

“…An often used procedure is the analysis of a mean residual life plot which represents the mean of the excesses of the threshold u. This method is used by Aboura (2014), Omari, Mwita and Waititu (2017) to estimate VaR based on GARCH-EVT approach. Another very popular procedure to threshold selection is graphical representation of Hill (Hill, 1975), Pickands (Pickands, 1975) or Dekkers-Einmahl-de Haan estimators (Dekkers, Einmahl and Haan, 1989).…”

An Optimal Tail Selection in Risk Measurement

“…A frequently used procedure relies on the analysis of a mean excess plot, which represents the mean of the excesses of the threshold u. This method was applied in Aboura (2014), Cifter (2011), Gilli and Këllezi (2006), Łuczak and Just (2020) and Omari et al (2017). The change in the pattern for a very high threshold is observed in this plot; therefore, the choice of a threshold is ambiguous.…”