Evaluating Value-at-Risk in BIST Using Copula Approach

Emre Yildirim, Mehmet Ali Cengiz

Abstract


Modelling dependence structure between variables is commonly investigated in literature. A large variety of methods have been improved in recent times. One of the methods is the copula which models accurately dependency regardless of marginal distributions. In this paper Value-at-Risk (VaR) is computed using the copulas. It is assumed that the dependency does not vary through time since small time interval is used. The study composes of two steps. In the first step the best fitted copula is determined by ML (Maximum likelihood). In the second step equal-weighted portfolio analysis is performed by joint distribution function obtained from the copula and maximum possible losses of the portfolio are evaluated. The main challenge in portfolio analysis is that joint distribution function for stocks cannot be correctly constructed by considering dependence structure among them. We obtain joint distribution function for stocks using the copula approach that has been commonly used in recent times. After the best fitted copula is determined using the criterions such as AIC (Akaike information criterion) and SBC (Schwarzs Bayesian Criterion), next-day maximum possible losses for the portfolio are evaluated by means of equal weighted portfolio technique.


Keywords


Copula; Dependence Structure; Stock Exchange; Value-at-Risk.

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References


Sklar A. Fonctions de Rpartion n Dimensions et Leur Marges. Publications de lInstitu de Statistique de lUniversit de Paris, 8: 229-231, 1959.

Dimitrova D.S., Kaishev V.K., Panev S.I. GeD spline estimation of multivariate Archimedean copulas. Computational Statistics & Data Analysis, 52.7: 3570-3582, 2008.

Genest C., Ne?lehov J., Ben Gharbal N. Estimators based on Kendalls tau in multivariate copula models. Australian & New Zealand Journal of Statistics, 53.2: 157-177, 2011.

McNeil A., Ne?lehov J. Multivariate Archimedean Copulas, d-Monotone Functions and l_i-Norm Symmetric Distributions. The Annals of Statistics, 3059-3097, 2009.

Taylor M.D. Multivariate measures of concordance for copulas and their marginals. arXiv,1004.5023, 2010.

Berger T., Jammazi R. On the dependence structure between US stocks: A time varying wavelet-copula-evt approach, 2015.

Wang X., Cai J., He K. EMD Copula Based Value at Risk Estimates for Electricity Markets. Procedia Computer Science, 55:1318-1324, 2015.

Righi M.B., Ceretta P.S. Forecasting Value at Risk and expected shortfall based on serial pair-copula constructions. Expert Systems with Applications, 42.17:6380-6390, 2015.

de Mello Junior H. D., Marti L., da Cruz A.V.A., Vellesco M.M.R. Evolutionary algorithms and elliptical copulas applied to continuous optimization problems. Informaiton Sciences, 369:419-440, 2016.

Joe H. Multivariate models and dependence concepts. London and New York: Chapman & Hall/CRC monographs on statistics & applied probability, 1997.

Roger B.N. An Introduction to Copulas. New York: Springer series in statistics, 2006.


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