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The optimal portfolio under VaR and ES

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An analysis of the dependence structure among certain European indices (FTSE100, CAC40, DAX30, ATX20, PX, BUX and BIST) has been conducted. The main features of the financial data were studied: asymmetry, fat-tailedness (leptokurtosis), variability and mutual dependence. We have fitted a regime switching copula based model including asymmetric and fat-tailed copulas. All the indices are left-skewed and fat-tailed. Large indices are more skewed and less fail-tailed. The findings suggest that size of a market has an influence on its properties. A particular behaviour of the Turkish market suggests the importance of geographical factors. It is also suggested that the maturity of a market is insignificant in the analysis. Another important conclusion drawn from our empirical investigation is that VaR is a less exact risk measure than ES. However, the dynamics of the temporal and statistical properties of both measures are similar.
Rocznik
Strony
59--79
Opis fizyczny
Bibliogr. 27 poz., rys.
Twórcy
autor
  • AGH University of Science and Technology in Cracow, Department of Applications of Mathematics in Economics
autor
  • AGH University of Science and Technology in Cracow, Department of Applications of Mathematics in Economics
Bibliografia
  • [1] AAS K., CZADO C., FRIGESSI A., BAKKEN H., Pair-copula construction of multiple dependence, Insurance: Mathematics, Economics, 2009, 44, 182–198.
  • [2] BEDFORD T., COOKE R., Probability density decomposition for conditionally dependent random variables modeled by vines, Annals of Mathematics, Artificial Intelligence, 2001, 32, 245–68.
  • [3] BEDFORD T., COOKE R., Vines – a new graphical model for dependent random variables, Annals of Statistics, 2002, 30, 1031–1068.
  • [4] BERG D., Copula goodness-of-fit testing: an overview, power comparison, The European Journal of Finance, 2009, 15, 1466–4364.
  • [5] BILLIO N., PELIZZON L., Value at risk: a multivariate switching regime approach, Journal of Empirical Finance, 2000, 7, 531–554.
  • [6] CHAN N.-H., CHEN J., CHEN X., FAN Y., PENG L., Statistical inference for multivariate residual copula of GARCH models, Statistica Sinica, 2009, 19, 53–70.
  • [7] CHOLLETE L., HEINEN A., VALDESOGO A., Modeling international financial returns with a multivariate regime-switching copula, Journal of Financial Econometrics, 2009, 7 (4), 437–480.
  • [8] CHOLLETE L., PEÑA V., LUC C.-C., International diversification. A copula approach, Journal of Banking and Finance, 2011, 35 (2), 403–417.
  • [9] CZADO C., Pair-copula constructions of multivariate copulas, [in:] P.E.A. Jaworski (Ed.), Copula theory, its applications, Lecture Notes in Statistics, 198, Springer-Verlag, Berlin 2010, 93–109.
  • [10] CZADO C., SCHEPSMEIER U., MIN A., Maximum likelihood estimation of mixed C-vines with application to exchange rates, Statistical Modelling, 2012, 12 (3), 229–255.
  • [11] HAMILTON J.D., A new approach to the economic analysis of nonstationary time series, the business cycle, Econometrica, 1989, 57, 357–384.
  • [12] HAMILTON J.D., Analysis of time series subject to changes in regime, Journal of Econometrics, 1990, 45, 39–70.
  • [13] JOE H., Families of m-variate distributions with given margins, m(m – 1)/2 bivariate dependence parameters, [in:] L. Riischendorf, B. Schweizer, M.D. Taylor (Eds.), Distributions with fixed marginals, related topics, Hayward, CA, Inst. Math. Statist., 1996, 28, 120–141.
  • [14] JOE H., Multivariate models, dependence concepts, Chapman & Hall, London 1997.
  • [15] JOE H., Asymptotic efficiency of the two-stage estimation method for copula-based models, Journal of Multivariate Analysis, 2005, 94, 401–19.
  • [16] JONDEAU E., ROCKINGER M., The copula-GARCH model of conditional dependencies: an international stock market application, Journal of International Money, Finance, 2006, 25, 827–853.
  • [17] KAWATA R., KIJIMA M., Value at risk in a market subject to regime switching, Quant. Finan., 2007, 7, 609–619.
  • [18] KUESTER K., MITTNIK S., PAOLELLA M., Value at risk prediction: a comparison of alternative strategies, Journal of Financial Econometrics, 2006, 4 (1), 53–89.
  • [19] KUROWICKA D., COOKE R.M., Uncertainty analysis with high dimensional dependence modelling, Wiley, Chichester 2006.
  • [20] MASHAL R., ZEEVI A., Beyond correlation. Extreme co-movements between financial assets, Technical Report, Columbia University, New York 2002.
  • [21] NEFTCI S.N., Value at risk calculations, extreme events, fat tail estimation, Journal of Derivatives, 2000, 7 (3), 23–37.
  • [22] NELSEN R.B., An introduction to copulas, 2nd Ed., Springer-Verlag, Berlin 2006.
  • [23] NING C., Extreme dependence of international stock market, Technical Report, Ryerson University, Toronto 2008.
  • [24] OKIMOTO T., New evidence on asymmetric dependence structures in international equity markets, Journal of Financial, Quantitative Analysis, 2008, 48 (3), 787–815.
  • [25] PATTON A., On the out-of-sample importance of skewness, asymmetric dependence for asset allocation, Journal of Financial Econometrics, 2004, 2 (1), 1301–1368.
  • [26] RODRIGUEZ J., Measuring financial contagion: a copula approach, Journal of Empirical Finance, 2007, 14, 401–423.
  • [27] ROSENBERG J., SCHUERMANN T., A general approach to integrated risk management with skewed, fat-tailed risks, Journal of Financial Economics, 2006, 79, 569–614.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6bebf047-15f4-4ee2-925d-34638c3b090c
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