Abstract
Tail dependence is an important property of a joint distribution function that has a huge impact on the determination of risky quantities associated to a stochastic model (Value-at-Risk, for instance). Here we aim at presenting some investigations about tail dependence including the following aspects: the determination of suitable stochastic models to be used in extreme scenarios; the notion of threshold copula, that helps in describing the tail of a joint distribution. Possible applications of the introduced concepts to the analysis of financial time series are presented with particular emphasis on cluster methods and determination of possible contagion effects among markets.
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Bonanno, G., Caldarelli, G., Lillo, F., Miccichè, S., Vandewalle, N., Mantegna, R.: Networks of equities in financial markets. Eur. Phys. J. B 38(2), 363–371 (2004)
Bradley, B., Taqqu, M.: Framework for analyzing spatial contagion between financial markets. Financ. Lett. 2(6), 8–16 (2004)
Charpentier, A., Juri, A.: Limiting dependence structures for tail events, with applications to credit derivatives. J. Appl. Probab. 43(2), 563–586 (2006)
Chavez-Demoulin, V., Embrechts, P.: An EVT primer for credit risk. In: Lipton, A., Rennie, A. (eds.) Handbook of Credit Derivatives. Oxford University Press (2010)
Cherubini, U., Mulinacci, S., Gobbi, F., Romagnoli, S.: Dynamic Copula methods in finance. Wiley Finance Series. John Wiley & Sons Ltd., Chichester (2012)
de Amo, E., DÃaz-Carrillo, M., Fernández-Sánchez, J.: Absolutely continuous copulas and sub–diagonal sections. Fuzzy Sets and Systems (in press, 2013)
De Baets, B., De Meyer, H., Mesiar, R.: Asymmetric semilinear copulas. Kybernetika (Prague) 43(2), 221–233 (2007)
De Luca, G., Zuccolotto, P.: A tail dependence-based dissimilarity measure for financial time series clustering. Adv. Data Anal. Classif. 5(4), 323–340 (2011)
Durante, F.: A new class of symmetric bivariate copulas. J. Nonparametr. Stat. 18(7-8), 499–510 (2006, 2007)
Durante, F., Fernández-Sánchez, J.: On the classes of copulas and quasi-copulas with a given diagonal section. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 19(1), 1–10 (2011)
Durante, F., Foschi, R., Spizzichino, F.: Threshold copulas and positive dependence. Statist. Probab. Lett. 78(17), 2902–2909 (2008)
Durante, F., Foscolo, E.: An analysis of the dependence among financial markets by spatial contagion. Int. J. Intell. Syst. 28(4), 319–331 (2013)
Durante, F., Foscolo, E., Sabo, M.: A spatial contagion test for financial markets. In: Kruse, R., Berthold, M., Moewes, C., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Synergies of Soft Computing and Statistics. AISC, vol. 190, pp. 313–320. Springer, Heidelberg (2013)
Durante, F., Hofert, M., Scherer, M.: Multivariate hierarchical copulas with shocks. Methodol. Comput. Appl. Probab. 12(4), 681–694 (2010)
Durante, F., Jaworski, P.: Spatial contagion between financial markets: a copula-based approach. Appl. Stoch. Models Bus. Ind. 26(5), 551–564 (2010)
Durante, F., Kolesárová, A., Mesiar, R., Sempi, C.: Semilinear copulas. Fuzzy Sets and Systems 159(1), 63–76 (2008)
Durante, F., Pappadà , R., Torelli, N.: Clustering of financial time series in risky scenarios (2012) (submitted)
Durante, F., RodrÃguez-Lallena, J., Úbeda-Flores, M.: New constructions of diagonal patchwork copulas. Inform. Sci. 179(19), 3383–3391 (2009)
Durante, F., Salvadori, G.: On the construction of multivariate extreme value models via copulas. Environmetrics 21(2), 143–161 (2010)
D’Urso, P., Maharaj, E.: Autocorrelation-based fuzzy clustering of time series. Fuzzy Sets and Systems 160(24), 3565–3589 (2009)
Forbes, K.J., Rigobon, R.: No contagion, only interdependence: measuring stock market comovements. J. Financ. 57(5), 2223–2261 (2002)
Fredricks, G.A., Nelsen, R.B.: The Bertino family of copulas. In: Cuadras, C.M., Fortiana, J., RodrÃguez-Lallena, J. (eds.) Distributions with given Marginals and Statistical Modelling, pp. 81–91. Kluwer, Dordrecht (2003)
Jaworski, P., Durante, F., Härdle, W. (eds.): Copulae in Mathematical and Quantitative Finance. Lecture Notes in Statistics - Proceedings. Springer, Heidelberg (2013)
Jaworski, P., Durante, F., Härdle, W., Rychlik, T. (eds.): Copula Theory and its Applications. Lecture Notes in Statistics - Proceedings, vol. 198. Springer, Heidelberg (2010)
Joe, H.: Parametric families of multivariate distributions with given margins. J. Multivariate Anal. 46(2), 262–282 (1993)
Jones, S.: Of couples and copulas. Financial Times (2009) (Published on April 24, 2009)
Jwaid, T., De Baets, B., De Meyer, H.: Orbital semilinear copulas. Kybernetika (Prague) 45(6), 1012–1029 (2009)
Klement, E.P., Kolesárová, A.: Intervals of 1-Lipschitz aggregation operators, quasi-copulas, and copulas with given affine section. Monatsh. Math. 152(2), 151–167 (2007)
Li, D.: On default correlation: a copula function approach. J. Fixed Income 9, 43–54 (2001)
Marshall, A.W.: Copulas, marginals, and joint distributions. In: Distributions with Fixed Marginals and Related Topics (Seattle, WA, 1993). IMS Lecture Notes Monogr. Ser., vol. 28, pp. 213–222. Inst. Math. Statist., Hayward (1996)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative risk management. Concepts, Techniques and Tools. Princeton Series in Finance. Princeton University Press, Princeton (2005)
Nelsen, R.B., Quesada-Molina, J.J., RodrÃguez-Lallena, J.A., Úbeda-Flores, M.: On the construction of copulas and quasi-copulas with given diagonal sections. Insurance Math. Econom. 42(2), 473–483 (2008)
Otranto, E.: Clustering heteroskedastic time series by model–based procedures. Comput. Statist. Data Anal. 52(10), 4685–4698 (2008)
Salvadori, G., De Michele, C., Durante, F.: On the return period and design in a multivariate framework. Hydrol. Earth Syst. Sci. 15, 3293–3305 (2011)
Salvadori, G., De Michele, C., Kottegoda, N.T., Rosso, R.: Extremes in Nature. An Approach Using Copulas. Water Science and Technology Library, vol. 56. Springer, Dordrecht (2007)
Whitehouse, M.: How a formula ignited market that burned some big investors. The Wall Street Journal (2005) (Published on September 12, 2005)
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Durante, F. (2013). Copulas, Tail Dependence and Applications to the Analysis of Financial Time Series. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_3
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DOI: https://doi.org/10.1007/978-3-642-39165-1_3
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