Analysis of asymmetric financial data with directional dependence measures

Yıl 2023, Cilt: 52 Sayı: 4, 1096 - 1119, 15.08.2023

Emel Kızılok Kara Sibel Açık Kemaloğlu Ozan Evkaya

https://doi.org/10.15672/hujms.1141392

Öz

The increase of the product variety in the financial markets requires a clear understanding of the dependence between such instruments for the decision-makers. For a few decades, such dependence structures were often modeled with symmetric copula families. How- ever, financial data may reveal an asymmetric structure, which can be determined via directional dependence measures in the context of copulas. Previously, some asymmetric copula models were proposed in different ways using Khoudraji's device. But they are merely used for financial time series data in a broader sense. In this study, a new set of asymmetric copulas were defined by using one parameter of Archimedean copula families. For this aim, widely used copula families were studied and the corresponding directional dependence measures were analyzed. To illustrate the efficiency of the parameter estimation method, a small simulation scenario consisting of an asymmetric dependence pattern was carried out. Thereafter, the proposed asymmetric bi-variate copulas with directional dependence coefficients were investigated for two different stock market data. The study's primary findings suggested that the newly generated asymmetric models might be useful for directional dependence. Especially, the estimated directional dependence coefficients can serve as an indicator to explain the variability of one stock in terms of the other.

Anahtar Kelimeler

Asymmetric models, directional dependence, Khoudraji copulas, stock indices

Kaynakça

• [1] C. Albulescu, Coronavirus and oil price crash, SSRN: 3553452, Doi: 10.2139/ssrn.3553452, 2020.
• [2] A. Alfonsi and D. Brigo, New families of copulas based on periodic functions, Comm. Statist. Theory Methods 34 (7), 1437-1447, 2005.
• [3] B.N. Ashraf, Stock markets’ reaction to Covid-19: Cases or fatalities?, Res. Int. Bus. Finance 54, 101249, 1-7, 2020.
• [4] S.R. Baker, N. Bloom, S.J. Davis, K. Kost, M. Sammon and T. Viratyosin, The unprecedented stock market reaction to COVID-19, RAPS 10 (4), 742-758, 2020.
• [5] E.C. Brechmann and U. Schepsmeier, Modeling dependence with C- and D-vine copulas: The R package CDVine, J. Stat. Softw. 52 (3), 1-27, 2013.
• [6] Y. Dodge and V. Rousson, On asymmetric properties of the correlation coefficient in the regression setting, Amer. Statist. 55 (1), 51-54, 2001.
• [7] F. Durante, Construction of non-exchangeable bivariate distribution functions, Statist. Papers 50 (2), 383-391, 2009.
• [8] N. Fernandes, Economic effects of coronavirus outbreak (COVID-19) on the world economy, SSRN: 3557504, Doi: 10.2139/ssrn.3557504, 2020.
• [9] C. Genest and A-C. Favre, Everything you always wanted to know about copula modeling but were afraid to ask, J. Hydrol. Eng. 12 (4), 347-368, 2007.
• [10] C. Genest, K. Ghoudi and L.P.A. Rivest, Semiparametric estimation procedure of dependence parameters in multivariate families of distribution, Biometrika 82 (3), 543-552, 1995.
• [11] C. Genest, K. Ghoudi and L.P. Rivest, Understanding relationships using copulas’ by Edward Frees and Emiliano Valdez, N. Am. Actuar. J. 2 (3), 143-149, 1998.
• [12] C. Genest, J. Nelehová and J.F. Quessy, Tests of symmetry for bivariate copulas, Ann. Inst. Statist. Math. 64 (4), 811-834, 2012.
• [13] C. Genest, B. Rèmillard B and D. Beaudoin, Goodness-of-fit tests for copulas: a review and a power study, Insur.: Math. Econ. 44 (2), 199-213, 2009.
• [14] A. Ghalanos, Package: “rugarch: Univariate GARCH models”, R package version: 1.4-2, 2020.
• [15] J.W. Goodell, COVID-19 and finance: Agendas for future research, Finance Res. Lett. 35, 101512, 1-5, 2020.
• [16] M. Hofert, I. Kojadinovic, M. Maechler and J. Yan, Package: “copula: Multivariate Dependence with Copula”, R package version: 1.0-0, 2020.
• [17] H. Joe, Multivariate Models and Dependence Concepts, Chapman and Hall, London, 1997.
• [18] Y.S. Jung, J.M. Kim and J. Kim, New approach of directional dependence in exchange markets using generalized FGM copula function, Comm. Statist. Simulation Comput. 37 (4), 772-788, 2008.
• [19] A. Khoudraji, Contributions a l’etude des copules et a la modelisation de valeurs extremes bivariees, Ph.D. thesis, Universitède Laval, 1995.
• [20] J.M. Kim, Y.S. Jung and T. Soderberg, Directional dependence of genes using survival truncated FGM type modification copulas, Comm. Statist. Simulation Comput. 38 (7), 1470-1484, 2009.
• [21] J.M. Kim, Y.S. Jung and E.A. Sungur, Truncation invariant copulas for modeling directional dependence: application to foreign currency exchange data, Model Assist. Stat. Appl. 9 (4), 309-324, 2014.
• [22] J.M. Kim, Y.S. Jung, E.A. Sungur, K.H. Han, C. Park and I. Sohn, A copula method for modeling directional dependence of genes, BMC Bioinform. 9 (1), 1-12, 2008.
• [23] D. Kim and J.M. Kim, Analysis of directional dependence using asymmetric copulabased regression models, J. Stat. Comput. Simul. 84 (9), 1990-2010, 2014.
• [24] G. Kim, M.J. Silvapulle and P. Silvapulle, Comparison of semiparametric and parametric methods for estimating copulas, Statist. Data Anal. 51 (6), 2836-2850, 2007.
• [25] E.P. Klement and R.Mesiar, How non-symmetric can a copula be?, Comment. Math. Univ. Carol. 47 (1), 141-148, 2006.
• [26] E. Liebscher, Construction of asymmetric multivariate copulas, J. Multivariate Anal. 99 (10), 2234-2250, 2008.
• [27] R. Mesiar and V. Najjari, New families of symmetric/asymmetric copulas, Fuzzy Sets and Systems 252, 99-110, 2014.
• [28] M.V. Muddapur, On directional dependence in a regression line, Comm. Statist. Theory Methods 32 (10), 2053-2057, 2003.
• [29] S. Mukherjee, Y. Lee, J.M. Kim, J. Jang and J.S. Park, Construction of bivariate asymmetric copulas, Commun. Stat. Appl. Methods 25 (2), 217-234, 2018.
• [30] R.B. Nelsen, An Introduction to Copulas, 2nd ed., Springer, New York, 2006.
• [31] R.B. Nelsen, Extremes of nonexchangeability, Statist. Papers 48, 329-336, 2007.
• [32] E. Onali, Covid-19 and stock market volatility, SSRN: 3571453, Doi: 10.2139/ssrn.3571453, 2020.
• [33] L. Quigley and D. Ramsey, Statistical analysis of the log returns of financial assets, BcS thesis, University of Limerick, 2009.
• [34] J.A. Rodriguez-Lallena and M.A. Ùbeda-Flores, A new class of bivariate copulas, Statist. Probab. Lett. 66 (3), 315–325, 2004.
• [35] N.A. Sansa, The impact of the COVID-19 on the financial markets: evidence from China and USA, Electron. Res. J. Soc. Sci. Humanities 2 (2), 29–39, 2020.
• [36] J.H. Shih and T. Emura, On the copula correlation ratio and its generalization, J. Multivariate Anal. 182, 104708, 1-14, 2021.
• [37] K.F. Siburg, K. Stehling, P.A. Stoimenov and G.N. Weiß, An order of asymmetry in copulas, and implications for risk management, Insur.: Math. Econ. 68, 241-247, 2016.
• [38] A. Sklar, Fonctions de repartition a dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8, 229-231, 1959.
• [39] E.A. Sungur, A note on directional dependence in regression setting, Comm. Statist. Theory Methods 34 (9), 1957-1965, 2005.
• [40] E.A. Sungur, Some observations on copula regression functions, Comm. Statist. Theory Methods 34 (9-10), 1967-1978, 2005.
• [41] D. Uhm, J.M. Kim and Y.S. Jung, Large asymmetry and directional dependence by using copula modeling to currency exchange rates, Model Assist. Stat. Appl. 7 (4), 327-340, 2012.
• [42] S. Wu, Construction of asymmetric copulas and its application in two-dimensional reliability modeling, Eur. J. Oper. Res. 238 (2), 476-485, 2014.
• [43] H. Yilmazkuday, Covid-19 effects on the S&P 500 index, Appl. Econ. Lett. 30 (1), 7-13, 2023.