Assessing Efficiency of D-Vine Copula ARMA-GARCH Method in Value at Risk Forecasting: Evidence from PSE Listed Companies

Abstract

The article points out the possibilities of using static D-Vine copula ARMA-GARCH model for estimation of 1 day ahead market Value at Risk. For the illustration we use data of the four companies listed on Prague Stock Exchange in range from 2010 to 2014. Vine copula approach allows us to construct high-dimensional copula from both elliptical and Archimedean bivariate copulas, i.e. multivariate probability distribution, created from process innovations. Due to a deeper shortage of existing domestic results or comparison studies with advanced volatility governed VaR forecasts we backtested D-Vine copula ARMA-GARCH model against the VaR rolling out of sample forecast from October 2012 to April 2014 of chosen benchmark models, e.g. multivariate VAR-GO-GARCH, VAR-DCC-GARCH and univariate ARMA-GARCH type models. Common backtesting via Kupiec and Christoff ersen procedures off er generalization that technological superiority of model supports accuracy only in case of an univariate modeling -working with non-basic GARCH models and innovations with leptokurtic distributions. Multivariate VAR governed type models and static Copula Vines performed in stated backtesting comparison worse than selected univariate ARMA-GARCH, i.e. it have overestimated the level of actual market risk, probably due to hardly tractable time-varying dependence structure.

Using HMM Approach for Assessing Quality of Value at Risk Estimation: Evidence from PSE Listed Company

“…But so far from the actual results (i. e. Klepáč and Hampel 2015) we in general propose ARMA-GARCH-GJR with Student-t, GED or NIG distribution as appropriate way to forecast portfolio VaR when we won't work with dependence between return streams. After the testing we can take that as possible fact.…”

“…The aim of this paper is to test the ability in VaR estimation, as it is important metric in financial industry, with HMM model in comparison to selected univariate ARMA(1,1)-GARCH(1,1)-GJR 1 models in similar way to Khaled et al (2016) Klepáč & Hampel (2015) this paper uses the conditional and unconditional coverage framework for VaR testing. The results supply literature with at least two specific contributions: we tell if there exists significant difference in VaR estimates between static univariate volatility based model and HMM approach.…”

“…We used data of ČEZ, a.s. company, when other authors (see Khaled et al (2016) mostly used data of more traded companies -from our previous knowledge (like in Klepáč & Hampel (2015) or in Kresta (2011) …”

Default Probability Prediction with Static Merton-D-Vine Copula Model

“…This specific model setting performed best from in in-sample testing in our previous work, e.g. see Klepáč and Hampel (2015) for more details about techniques for models selections. The estimation of time-varying equity volatility and solving of simultaneous system (to get asset volatility and its market value) of equations were performed in software (SW) package R 3.1.1.…”

The Probability of Default Under IFRS 9: Multi-period Estimation and Macroeconomic Forecast

“…Jakubík (2007) uses the approach of Merton for credit risk modelling and for stress testing of banks in the Czech Republic. This approach was also elaborated in Klepáč (2015) and Klepáč, Hampel (2015), where copulas were used to include information from financial markets for corporate PDs estimation, and in Pesaran et al (2006), where the effects of macroeconomic shocks are investigated (among others). In Simons, Rolwes (2009) and Bruce, González-Aguado (2010) relations among macroeconomic indicators and default rates are explored with some applications in credit risk management.…”