EML-Estimation of Multivariate t Copulas with Heuristic Optimization

In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structure and joint tail events. In this study, we employ two optimization heuristics, namely Differential Evolution and Threshold Accepting to tackle the parameter estimation of multivariate t distribution models in the EML approach. Since the evolutionary optimizer does not rely on gradient search, the EML approach can be applied to estimation of more complicated copula models such as high-dimensional copulas. Our experimental study shows that the proposed method provides more robust and more accurate estimates as compared to the IFM approach.

Authors:

• Jin Zhang
• Wing Lon Ng

Keywords:

• Copula Models
• Student t Copula
• Parameter Inference
• Differential Evolution
• Threshold Accepting.

References:

[1] T. Bollerslev. A conditional heteroskedastic time series
model for speculative prices and rates of return. Review
of Economics and Statistics, 69:542-547, 1987.
[2] G. Dueck and T. Scheuer. Threshold Accepting: a general
purpose optimization algorithm appearing superior to
Simulated annealing. Journal of Computational Physics,
90:161-175, 1990.
[3] Harry Joe. Multivariate Models and Dependence Concepts.
Chapman & Hall/CRC, 1997.
[4] S. Kirkpatrick, C. Gelatt, and M. Vecchi. Optimization
by simulated annealing. Science, 220:671-680, 1983.
[5] Dietmar Maringer and Olufemi Oyewumi. Index tracking
with constrained portfolios. Intelligent Systems in Accounting
and Finance Management, 15(1):51-71, 2007.
[6] A. J. McNeil, R. Frey, and P. Embrechts. Quantitative
Risk Management. Princeton Series in Finance. Princeton
University Press, 2005.
[7] Attilio Meucci. Risk and Asset Allocation. Springer,
2005.
[8] Roger B Nelsen. An Introduction to Copulas. Springer,
1998.
[9] Kenneth V. Price, Rainer M. Storn, and Jouni A.
Lampinen. Differential Evolution: A Practical Approach
to Global Optimization. Springer, 1998.
[10] A. Sklar. Fonctions de r'epartition `a n dimensions et
leurs marges. Publications de 1-institut de statistique
de 1-Universit'e de Paris, 8:229-231, 1959.
[11] Rainer Storn and Kenneth Price. Differential Evolution
- a simple and efficient heuristic for global optimization
over continuous spaces. Journal of Global Optimization,
11(4):341-359, 1997.
[12] Peter Winker. Optimization Heuristics In Econometrics:
Applications of Threshold Accepting. JohnWiley & Sons,
2001.