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The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study

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  • Fantazzini, Dean

Abstract

The effect on the estimation of the Value at Risk when dealing with multivariate portfolios when there is a misspecification both in the marginals and in the copulas is investigated. It is first shown that, when there is skewness in the data and symmetric marginals are used, the estimated elliptical (normal or t) copula correlations are negatively biased, reaching values as high as 70% of the true values. Besides, the bias almost doubles if negative correlations are considered, compared to positive correlations. As for the t copula degrees of freedom parameter, the use of wrong marginals delivers large positive biases, instead. If the dependence structure is represented by a copula which is not elliptical, e.g.the Clayton copula, the effects of marginal misspecifications on the copula parameter estimation can be rather different, depending on the sign of marginal skewness. Extensive Monte Carlo studies then show that the misspecifications in the marginal volatility equation more than offset the biases in copula parameters when VaR forecasting is of concern, small samples are considered and the data are leptokurtic. The biases in the volatility parameters are much smaller, whereas those ones in the copula parameters remain almost unchanged or even increase when the sample dimension increases. In this case, copula misspecifications do play a role for VaR estimation. However, these effects depend heavily on the sign of the dependence.

Suggested Citation

  • Fantazzini, Dean, 2009. "The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2168-2188, April.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2168-2188
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    Cited by:

    1. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 22(2), pages 98-134.
    2. Penikas, Henry, 2010. "Copula-Models in Foreign Exchange Risk-Management of a Bank," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 17(1), pages 62-87.
    3. Rossi, Eduardo & Santucci de Magistris, Paolo, 2013. "Long memory and tail dependence in trading volume and volatility," Journal of Empirical Finance, Elsevier, vol. 22(C), pages 94-112.
    4. Fantazzini, Dean, 2008. "Econometric Analysis of Financial Data in Risk Management (continuation). Section III: Managing Operational Risk," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 11(3), pages 87-122.
    5. Berger, Theo, 2016. "On the isolated impact of copulas on risk measurement: Asimulation study," Economic Modelling, Elsevier, vol. 58(C), pages 475-481.
    6. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(3), pages 457-493, June.
    7. Fantazzini, Dean & Nigmatullin, Erik & Sukhanovskaya, Vera & Ivliev, Sergey, 2017. "Everything you always wanted to know about bitcoin modelling but were afraid to ask. Part 2," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 45, pages 5-28.
    8. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    9. Fantazzini, Dean & Nigmatullin, Erik & Sukhanovskaya, Vera & Ivliev, Sergey, 2016. "Everything you always wanted to know about bitcoin modelling but were afraid to ask. I," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 44, pages 5-24.
    10. repec:eee:eneeco:v:68:y:2017:i:c:p:89-108 is not listed on IDEAS
    11. Weiß, Gregor N.F. & Scheffer, Marcus, 2015. "Mixture pair-copula-constructions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 175-191.
    12. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.
    13. Gregor Weiß, 2013. "Copula-GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 179-202, August.
    14. Penikas, H., 2010. "Financial Applications of Copula-Models," Journal of the New Economic Association, New Economic Association, issue 7, pages 24-44.
    15. Weiß, Gregor N.F., 2011. "Are Copula-GoF-tests of any practical use? Empirical evidence for stocks, commodities and FX futures," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(2), pages 173-188, May.
    16. Fantazzini, Dean, 2008. "An Econometric Analysis of Financial Data in Risk Management," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 10(2), pages 91-137.
    17. Siburg, Karl Friedrich & Stoimenov, Pavel & Weiß, Gregor N.F., 2015. "Forecasting portfolio-Value-at-Risk with nonparametric lower tail dependence estimates," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 129-140.
    18. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2012. "Global Risk Evolution and Diversification: a Copula-DCC-GARCH Model Approach," Brazilian Review of Finance, Brazilian Society of Finance, vol. 10(4), pages 529-550.
    19. Ausin, M. Concepcion & Lopes, Hedibert F., 2010. "Time-varying joint distribution through copulas," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2383-2399, November.

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