Estimating Value at Risk of Portfolio of Oil and Gold by Copula-GARCH Method

Document Type : Research Paper

Authors

1 Assistant Prof., Faculty of Management, University of Tehran, Iran

2 MSc in Financial Management, Faculty of Management, University of Tehran, Iran

Abstract

Copula functions are powerful tools that describe dependence structure of multi- dimension random variables and are considered as one of the newest tools for risk management. One application of copula functions in risk management is calculating Value at Risk that can assert is the most widely used risk measures in financial institutions. In this article which primary goal is estimating more accurate risk of portfolio, by combining copula functions and GARCH models we used a method called copula-GARCH model for calculating VaR of a portfolio composed of crude oil and gold with data from 2007 to 2012. We will then compare the results with the results of traditional VaR calculation methods. Empirical results indicate that copula-GARCH method measures portfolio risk more accurately in comparison with traditional methods

Keywords

Main Subjects

References

Clayton, D. (1978). A model for association in bivariate life tables and its application to a uranium exploration data set. Technometrics, 28 (2): 123-131.
Deng, L. Ma, C. & Yang, W. (2011). Portfolio Optimization via Pair Copula-GARCH-EVT-CVaR Model. Systems Engineering Procedia, 2 (1): 171-181.
Embrechts, P. McNeil, A. & Straumann, D. (2002). Risk Management Value at Risk and Beyond. Cambridge University Press.
Engle, R. (1982). Auto-regressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50 (4): 987-1007.
Frank, M. (1987). Best-poss bounds for the distribution of a sum – a problem of Kolmogorov. Probability Theory and Related Fields, 74 (1): 199-211.
Genest, C. (1987). Frank's family of bivariate distribution. Biometrika, 74 (3): 549-555.
Goorbergh, R. Genest, W. & Werker, B. (2005). Bivariate option pricing using dynamic copula models. Insurance, Mathematics and Economics, 37 (1): 101-114.
Gumbel, E. (1960). Bivariate exponential distributions. Journal of American Statistical Association, 55 (292): 698-707.
Hamerle, A. & Rosch, D. (2005). Misspecified Copulas in Credit Risk Models: How Good is Gaussian?. Journal of Risk, 8 (1): 35-47.
Hotta, L. Lucas, E. & Palaro H. (2008). Estimation of VaR using copula and extreme value theory. Multinational Finance Journal, 12 (3/4): 205-221.
Huang, J. Lee, H. Liang, H. & Fu, W. (2009). Estimating value at risk of portfolio by conditional copula-GARCH method. Insurance: Mathematics and Economics, 45 (3): 315-324.
Kupiec, P. (1998). Stress testing in a value at risk framework. The Journal of Derivatives, 6 (1): 7–24.
Ling, C. (1965). Represention of associative functions. Publicationes Mathematicae Debrecen, 12 (1): 189-212.
Meneguzzo, D. & Vecchiato, W. (2004). Copula Sensitivity in Collateralized Debt Obligations and Basket Default Swaps. The Journal of Future Markets,24 (1): 37-70.
National Bureau of Economic Research. (1927). The Behaviour of Prices. [Brochure].  New York : Mills, C.
Neslehova, J. Embrechts, P. & Demoulin, C. (2006). Infinite-mean Models and the LDA for Operational Risk. Journal of Operational Risk, 1 (1): 3-25.
Palaro, H. & Hotta, L. (2006). Using conditional copulas to estimate value at risk. Journal of Data Science, 4 (1): 93-115.
Patton, A. (2001). Applications of Copula Theory in Financial Econometrics. (Unpublished Ph.D. dissertation). University of California, San Diego, USA.
Schweizer, B. & Sklar, A. (1961). Associative functions and statistical triangle inequalities. Publicationes Mathematicae Debrecen, 8 (1): 169-186.
Sklar, A. (1959). Fonctions de repartition a n dimensions et leurs marges. Publicationsde l'Institut Statistique de l'Universite de Paris, 8 (1): 229-231.
Financial Research Journal
Volume 16, Issue 2 - Serial Number 2
Autumn & Winter
October 2015
Pages 309-326

Files

Share

How to cite

Statistics