# Measuring contagion risk in high volatility state among Taiwanese major banks

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## Abstract

This paper studies the structural tail dependence and contagion risk especially in high volatility state between domestic (Taiwanese) and foreign banks. Aptly the two-state threshold copula GARCH provides the threshold regression and copulas to classify the actual volatility index into a high or in a low state and estimate the structural tail dependences using Kendall taus to probe the co-movement among banks. In high volatility state, the average Kendall taus and value at risk as well as expected shortfall are about two times larger than in low volatility state. The asymmetric jumps of Kendall taus appear more frequent in the subprime crisis whereas the symmetric trends of Kendall taus appear higher in Greek debt crisis. Among three copula models in low volatility state, Gaussian and Student-t copula models have established a more significant estimate than the Clayton copula model. However, in high volatility state, Clayton copula model could still produce an acceptable estimate. Empirically, using Clayton copula in high volatility state has demonstrated clearly intensive tail jumps capable to distinguish the contagion risk.

## Keywords

Contagion risk Threshold GARCH Copula Tail dependence## Notes

### Acknowledgements

The author wants to express great appreciation to Dr. Thomas W. Knowles (Emeritus Professor of IIT Stuart School of Business in Chicago), Dr. Arch G. Woodside (Professor of Marketing of Wallace E. Carroll School of Management at Boston College), and Dr. Sheng-Jung Li (Assistant Professor of Finance Department at Shu-Te University in Kaohsiung) for their constructive comments and insights and deeply thankful to the support of The Ministry of Science and Technology of the Republic of China for the grant of research funding.

## References

- Aloui, R., and M.S. Ben Aïssa. 2016. Relationship between oil, stock prices and exchange rates: A vine copula based GARCH method.
*The North American Journal of Economics and Finance*37: 458–471.CrossRefGoogle Scholar - Ang, A. and Bekaert, G. (1999). International asset allocation with time-varying correlations. NBER Working Paper 7056.Google Scholar
- Ang, A., and J. Chen. 2002. Asymmetric correlations of equity portfolios.
*Journal of Financial Economics*63 (3): 443–494.CrossRefGoogle Scholar - Bezdek, J.C., R. Ehrlich, and W.E. Full. 1984. FCM: the fuzzy c-means clustering algorithm.
*Computers and Geosciences*10 (2–3): 191–203.CrossRefGoogle Scholar - Betz, F., S. Oprică, T.A. Peltonen, and P. Sarlin. 2014. Predicting distress in European banks.
*Journal of Banking and Finance*45: 225–241.CrossRefGoogle Scholar - Boetel, B., R. Hoffmann, and D. Liu. 2007. Estimating investment rigidity within a threshold regression framework: the case of U.S. hog production sector.
*American Journal of Agricultural Economics*89 (1): 36–51.CrossRefGoogle Scholar - Brandt, M.W., J.H. Cochrane, and P. Santa-Clara. 2006. International risk sharing is better than you think, or exchange rates are too smooth.
*Journal of Monetary Economics*53 (4): 671–698.CrossRefGoogle Scholar - Brooks, C., O.T. Henry, and G. Persand. 2002. The effect of asymmetries on optimal hedge ratios.
*Journal of Business*75 (2): 333–352.CrossRefGoogle Scholar - Cao, C.Q., and R.S. Tsay. 1992. Nonlinear time series analysis of stock volatilities.
*Journal of Applied Econometrics*7: 165–185.CrossRefGoogle Scholar - Chan, K.S., and H. Tong. 1986. On estimating thresholds in autoregressive models.
*Journal of Time Series Analysis*7 (3): 179–190.CrossRefGoogle Scholar - Chang, K.L. 2012. The time-varying and asymmetric dependence between crude oil spot and futures markets: Evidence from the Mixture copula-based ARJI-GARCH model.
*Economic Modelling*29 (6): 2298–2309.CrossRefGoogle Scholar - Clayton, D.G. 1978. A model for association in bi-variate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence.
*Biometrika*65: 141–151.CrossRefGoogle Scholar - Conrad, J., B. Cornell, and W.R. Landsman. 2002. When is bad news really bad news?
*Journal of Finance*57 (6): 2507–2532.CrossRefGoogle Scholar - Das, S.R., and R. Uppal. 2004. Systemic risk and international portfolio choice.
*The Journal of Finance*59 (6): 2809–2834.CrossRefGoogle Scholar - Dias, A., and P. Embrechts. 2010. Modeling exchange rate dependence dynamics at different time horizons.
*Journal of International Money and Finance*29 (8): 1687–1705.CrossRefGoogle Scholar - Embrechts, P., Lindskog, F., and McNeil, A. 2001. Modelling dependence with copulas and applications to risk management. ETHZ, Working Paper.Google Scholar
- Embrechts, P., A. McNeil, and D. Strauman. 2002. Correlation and dependence properties in risk management: properties and pitfalls. In
*Risk management: Value at Risk and beyond*, ed. M. Dempster. Cambridge: Cambridge University Press.Google Scholar - Engle, R.F. 1983. Estimates of the variance of U.S. inflation based upon the ARCH model.
*Journal of Money, Credit, and Banking*15 (3): 286–301.CrossRefGoogle Scholar - Frahm, G., M. Junker, and A. Szimayer. 2003. Elliptical copulas: applicability and limitations.
*Statistics and Probability Letters*63 (3): 275–286.CrossRefGoogle Scholar - Frank, M.J. 1979. On the simultaneous associativity of F(x, y) and x + y−F(x, y).
*Aequationes Mathamaticae*19 (1): 194–226.CrossRefGoogle Scholar - Gagliardini, P., and C. Gouriéroux. 2013. Correlated risks versus contagion in stochastic transition models.
*Journal of Economic Dynamics and Control*37 (11): 2241–2269.CrossRefGoogle Scholar - Garcia, R., and G. Tsafack. 2011. Dependence structure and extreme co-movements in international equity and bond markets.
*Journal of Banking and Finance*35 (8): 1954–1970.CrossRefGoogle Scholar - Gijbels, I., N. Veraverbeke, and M. Omelka. 2011. Conditional copulas, association measures and their applications.
*Computational Statistics and Data Analysis*55 (5): 1919–1932.CrossRefGoogle Scholar - Glosten, L., R. Jagannathan, and D. Runkle. 1993. Relationship between the expected value and the volatility of the nominal excess return on stocks.
*The Journal of Finance*48 (5): 1779–1801.CrossRefGoogle Scholar - Gumbel, E.J. 1960. Bi-variate exponential distributions.
*Journal of the American Statistical Association*55 (292): 698–707.CrossRefGoogle Scholar - Hansen, B.E. 1996. Inference when a nuisance parameter is not identified under the null hypothesis.
*Econometrica*64: 413–430.CrossRefGoogle Scholar - Huang, J., K. Lee, L. Hueimei, and W. Lin. 2009. Estimating value at risk of portfolio by conditional copula-GARCH method.
*Insurance: Mathematics and Economics*45 (3): 315–324.Google Scholar - Jamaleh, A., and G. Venezia. 2001. Threshold model for Italian stock market volatility.
*Revista Politica Economia*91 (2): 79–132.Google Scholar - Jawadi, F., and U.R. Loredana. 2013. Threshold linkages between volatility and trading volume: evidence from developed and emerging markets.
*Studies in Nonlinear Dynamics and Econometrics*17 (3): 313–333.Google Scholar - Joe, H. 1997.
*Multivariate models and dependence concepts*. London: Chapman and Hall.CrossRefGoogle Scholar - Jondeau, E. and Rockinger, M. 2002. Conditional dependency of financial series: The copula GARCH model. FAME Research Paper Series rp69.Google Scholar
- Jondeau, E., and M. Rockinger. 2006. The copula GARCH model of conditional dependencies: an international stock market application.
*Journal of International Money and Finance*25 (5): 827–853.CrossRefGoogle Scholar - Kendall, M., and A. Stuart. 1979.
*The advanced theory of statistics*, 4th ed. London: Charles Griffin.Google Scholar - Laih, Y.W. 2014. Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm.
*European Journal of Operational Research*232 (2): 375–382.CrossRefGoogle Scholar - Longin, F., and B. Solnik. 2001. Extreme correlations in international equity markets.
*Journal of Finance*56 (2): 649–676.CrossRefGoogle Scholar - Nelsen, R.B. (1999). An introduction to copulas. In
*Lectures notes in statistics*, 139. New York: Springer.Google Scholar - Patton, A.J. 2001. Modelling time-varying exchange rate dependence using the conditional copula, Working Paper, U.C. San Diego.Google Scholar
- Patton, A.J. 2006. Modelling asymmetric exchange rate dependence.
*International Economic Review*47 (2): 527–556.CrossRefGoogle Scholar - Rungcharoenkitkul, P. 2012. Risk sharing versus financial contagion in Asia: An asset price perspective.
*Review of Development Finance*2 (3): 101–117.CrossRefGoogle Scholar - Schweizer, B., and E. Wolff. 1981. On nonparametric measures of dependence for random variables.
*The Annals of Statistics*9: 879–885.CrossRefGoogle Scholar - Sklar, M. 1959. Fonctions de repartition an dimensions et leurs marges.
*Publ. inst. Statist. Univ. Paris*8: 229–231.Google Scholar - Tong, H. 1990.
*Non-linear time series: a dynamical system approach*. Oxford: Oxford University Press.Google Scholar - Tong, H., and K. Lim. 1980. Threshold autoregression, limit cycles, and cyclical data.
*Journal of the Royal Statistical Society*42: 245–292.Google Scholar - Tsay, R.S. 1989. Testing and modeling threshold autoregressive processes.
*Journal of the American Statistical Association*84 (405): 231–240.CrossRefGoogle Scholar - Tse, Y.K., and K.C. Tsui. 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations.
*Journal of Business and Economic Statistics*20 (3): 351–362.CrossRefGoogle Scholar - Veronesi, P. 1999. Stock market overreaction to bad news in good times: a rational expectations equilibrium model.
*Review of Financial Studies*12 (5): 975–1007.CrossRefGoogle Scholar - Wu, C.C., H. Chung, and Y.H. Chang. 2012. The economic value of co-movement between oil price and exchange rate using copula-based GARCH models.
*Energy Economics*34: 270–282.CrossRefGoogle Scholar