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Review of Quantitative Finance and Accounting

Erschienen in:

01.02.2007

A robust VaR model under different time periods and weighting schemes

verfasst von: Timotheos Angelidis, Alexandros Benos, Stavros Degiannakis

Erschienen in: Review of Quantitative Finance and Accounting | Ausgabe 2/2007

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Abstract

This paper analyses several volatility models by examining their ability to forecast Value-at-Risk (VaR) for two different time periods and two capitalization weighting schemes. Specifically, VaR is calculated for large and small capitalization stocks, based on Dow Jones (DJ) Euro Stoxx indices and is modeled for long and short trading positions by using non parametric, semi parametric and parametric methods. In order to choose one model among the various forecasting methods, a two-stage backtesting procedure is implemented. In the first stage the unconditional coverage test is used to examine the statistical accuracy of the models. In the second stage a loss function is applied to investigate whether the differences between the models, that calculated accurately the VaR, are statistically significant. Under this framework, the combination of a parametric model with the historical simulation produced robust results across the sample periods, market capitalization schemes, trading positions and confidence levels and therefore there is a risk measure that is reliable.

Vorheriger Artikel Relationship between Treasury bills and Eurodollars: Theoretical and Empirical Analyses

Nächster Artikel Oil convenience yields estimated under demand/supply shock

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For more information on Historical Simulation, see Hendricks (1996), and Vlaar (2000) among others.

For more information on EVT techniques on VaR modelling see Jondeau and Rockinger (1999), Ho et al. (2000), MacNeil and Frey (2000), Rozario (2002), Bali (2003), Jondeau and Rockinger (2003), Seymour and Polakov (2003), Byström (2004) and Gençay and Selçuk (2004).

Under the assumption that the portfolio returns are normally distributed, the calculation of VaR is simplified as both \( \sigma _{t + 1|t} \) and \( F_a (z_t ;\theta ) \) have tractable expressions, while this method will be referred as Variance-Covariance. This method is used as benchmark.

A special case of the GARCH model is the exponentially weighted moving average (EWMA) model, \( \sigma _t^2 = 0.06\varepsilon _{t - 1}^2 + 0.94\sigma _{t - 1}^2 \), that was used by RiskMetrics^TM, when they introduced their analytic VaR methodology.

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The volatility models for the FHS and the EVT are based on quasi-maximum likelihood method assuming a normal distribution, as in Diebold et al. (1998) and McNeil and Frey (2000).

For more information see Balkema and de Hann (1974), Pickands (1975), McNeil and Frey (2000), and Christoffersen (2003) among others.

A failure occurs if the predicted VaR is not able to cover the realized loss.

Christoffersen's (1998) conditional coverage test was also implemented, but the results were qualitatively similar and therefore are not reported. They are available upon request.

If the numerical maximization of the log-likelihood function failed to converge more than six times, we excluded the models from our results. This number of failures (six) is almost the 1% of the out-of-sample.

A similar ranking was also made by Brooks and Persand (2003b).

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Titel: A robust VaR model under different time periods and weighting schemes
verfasst von: Timotheos Angelidis
Alexandros Benos
Stavros Degiannakis
Publikationsdatum: 01.02.2007
Verlag: Kluwer Academic Publishers-Plenum Publishers
Erschienen in: Review of Quantitative Finance and Accounting / Ausgabe 2/2007
Print ISSN: 0924-865X
Elektronische ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-006-0010-y

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