Cheng, Gang; Li, Ping; Shi, Peng A new algorithm based on copulas for VaR valuation with empirical calculations. (English) Zbl 1121.91044 Theor. Comput. Sci. 378, No. 2, 190-197 (2007). Summary: This paper concerns the application of copula functions in VaR valuation. The copula function is used to model the dependence structure of multivariate assets. After the introduction of the traditional Monte Carlo simulation method and the pure copula method we present a new algorithm based on mixture copula functions and the dependence measure, Spearman’s rho. This new method is used to simulate daily returns of two stock market indices in China, Shanghai Stock Composite Index and Shenzhen Stock Composite Index, and then empirically calculate six risk measures including VaR and conditional VaR. The results are compared with those derived from the traditional Monte Carlo method and the pure copula method. From the comparison we show that the dependence structure between asset returns plays a more important role in valuating risk measures comparing with the form of marginal distributions. Cited in 3 Documents MSC: 91B28 Finance etc. (MSC2000) Keywords:value-at-risk; copulas; Spearman’s rho; Monte Carlo simulation PDFBibTeX XMLCite \textit{G. Cheng} et al., Theor. Comput. Sci. 378, No. 2, 190--197 (2007; Zbl 1121.91044) Full Text: DOI References: [1] Acerbi, C.; Tasche, D., On the coherence of expected shortfall, Journal of Banking and Finance, 26, 1487-1503 (2002) [2] Cossette, H.; Gaillardetz, P., On two dependent individual risk models, Insurance: Mathematics and Economics, 30, 153-166 (2002) · Zbl 1055.91044 [3] Embrechts, P.; McNeil, A.; Straumann, D., Correlation and dependence in risk management: properties and pitfalls, (Dempster, M., Risk Management: Value-at-Risk and Beyond (2002), Cambridge University Press: Cambridge University Press Cambridge), 176-223 [4] Fréchet, M., Les tableaux de corrélations dont les marges sont sonnées, Annales de l’Université de Lyon, Sciences Mathématiques at Astronomie Série A, 4, 13-31 (1957) [5] Genest, C.; Rivest, L. P., On the multivariate probability integral transformation, Statistics and Probability Letters, 53, 391-399 (2001) · Zbl 0982.62056 [6] Hürlimann, W., Hutchinson-Lai’s conjecture for bivariate extreme value copulas, Statistics and Probability Letters, 61, 191-198 (2003) · Zbl 1101.62340 [7] Hürlimann, W., Fitting bivariate cumulative returns with copulas, Computational Statistics and Data Analysis, 45, 355-372 (2004) · Zbl 1429.62471 [8] B.V.M. Mendes, R.P.C. Leal, Robust statistical modeling of portfolios, in: Proceedings of the 9th Annual Conference of the Multinational Finance Society, Paphos, Cyprus, June 30-July 3, 2002; B.V.M. Mendes, R.P.C. Leal, Robust statistical modeling of portfolios, in: Proceedings of the 9th Annual Conference of the Multinational Finance Society, Paphos, Cyprus, June 30-July 3, 2002 [9] Mendes, B. V.M.; Moretti, A., Improving financial risk assessment through dependency, Statistical Modeling, 2, 103-122 (2002) · Zbl 0999.62086 [10] Mendes, B. V.M.; Souza, M. R., Measuring financial risks with copulas, International Review of Financial Analysis, 13, 27-45 (2004) [11] Nelsen, R. B., Dependence and order in families of Archimedean copulas, Journal of Multivariate Analysis, 60, 111-122 (1997) · Zbl 0883.62049 [12] Nelsen, R. B., An Introduction to Copulas [M] (1998), Springer: Springer New York [13] Nelsen, R. B.; Quesada-Molina, J. J.; Rodríguez-Lallena, J. A., Distribution functions of copulas: a class of bivariate probability integral transforms, Statistics and Probability Letters, 54, 277-282 (2001) · Zbl 0992.60020 [14] Rodríguez-Lallena, J. A.; Úbeda-Flores, M., Distribution functions of multivariate copulas, Statistics and Probability Letters, 64, 41-50 (2003) · Zbl 1113.62330 [15] Sklar, A., Functions de repartition à n dimensions et leurs marges, Publications de l’Institut de Statistique de l’Université de Paris, 8, 229-231 (1959) · Zbl 0100.14202 [16] Vandenhende, F.; Lambert, P., Improved rank-based dependence measures for categorical data, Statistics and Probability Letters, 63, 157-163 (2003) · Zbl 1116.62362 [17] Wei, G.; Hu, T. Z., Supermodular dependence ordering on a class of multivariate copulas, Statistics and Probability Letters, 57, 375-385 (2002) · Zbl 1005.60037 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.