Estimation of dynamic asymmetric tail dependences: an empirical study on Asian developed futures markets

Abstract

In this research, we employ three two-parameter Archimedean copulas (BB1, BB4 and BB7) to investigate the dynamic asymmetric tail dependences between two of three Asian developed futures markets, Hong Kong, Japan and Singapore, during the post-Asian financial crisis period. We first model the marginal distribution by conditional skewed-t distribution and find that higher moments of each filtered index futures return are time dependent. We then extend the two-parameter copulas incorporating time-varying tail dependences to capture the dynamic asymmetries. The estimated results provide strong evidence of asymmetric dependence across the three futures markets. Moreover, to take account of data snooping, we implement Hansen's (2005) superior predictive ability test to evaluate the model fitting. We found that the BB7 copula for the Hang Seng–MSCI SIN (Morgan Stanley Capital International index) pair and the BB1 copula for the Nikkei 225–MSCI SIN pair outperform the simple symmetric Gaussian copula. These best model fittings also demonstrate that the probability of dependence in bear markets is higher than in bull markets further exposing downside dependent risk in these markets. Finally, based on the model evaluation result, we estimate the copula-based portfolio Value at Risks (VaRs) and the diversification benefits at both lower and higher confidence levels. The results clearly show that the conditional copula-based portfolio VaR models can provide higher degree of diversification benefit at higher confidence level. Therefore, these sophisticated copula models are adequate and considerable for the financial risk management.

Acknowledgements

We are indebted to Mark Taylor (the editor) and an anonymous referee for their helpful comments and suggestions; and also to the participants at the 13th Conference on the Theories and Practices of Securities and Financial Markets and the 14th Annual Symposium of the Society for Nonlinear Dynamics and Econometrics. All errors and omissions remain our own.

Notes

¹ For instance, Erb et al. (1994), King et al. (1994), De Santis and Gerard (1997), Longin and Solnik (1995, 2001), Ang and Bekaert (2002) and Ang and Chen (2002).

² See Hong and Stein (2003) and Levy (2008).

³ For example, Chen et al. (1999, 2000), Kim et al. (2002) and So and Tse (2004), among others.

⁴ The BB7 copula is also called Joe–Clayton copula in Patton (2006a).

⁵ The functions of densities for the three two-parameter Archimedean copulas are very long. Matlab codes are available from the author upon request.