Journal of Economic Research (Tahghighat- E- Eghtesadi)

Journal of Economic Research (Tahghighat- E- Eghtesadi)

Estimation of Value at Risk in the Presence of Dependence Structure in Financial Returns: A Copula Based Approach

Document Type : Research Paper

Authors
GholamReza keshavarz Haddad 1
Mehrdad Heyrani 2
1 Associate Professor Sharif University of Technology
2 Master of Economic Sciences, Sharif University of Technology
10.22059/jte.2014.53191
Abstract
Modeling dependence structure in financial economics is of paramount importance when estimating portfolio’s value at risk, since risk of an asset in addition to its own behavior is also dependent on the behavior of other assets in the portfolio. Application of joint distribution Copula is one of the methods for incorporation dependence at lower and upper tail of returns’ distribution in financial economics. Copulas are functions that connect multivariate distribution function to their marginal distribution. In the current study, the dependence structure among two price indexes for chemical and pharmaceutical products of TEPIX between 3/1/2005 – 18/3/2013 was evaluated by combining different types of Copula functions and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. In addition, the effect of dependence structure on estimation of comprised portfolio’s value at risk is investigated. Empirical results of this study demonstrate that there is asymmetric dependence structure between chemical and pharmaceutical products of TEPIX indexes. Furthermore, the results indicate that Copula-GARCH approach is more accurate and efficient compared to commonly used models such as M-GARCH, DCC-GARCH, EWMA, and historical simulation methods in estimation of portfolio’s value at risk
Keywords
Value at Risk
Dependence Structure
Copula function
GARCH
Back Testing
  1. سایت رسمی بورس اوراق بهادار تهران http://www.irbourse.com/
  2. مفتخر دریایی‌نژاد، کبری و کشاورز حداد، غلامرضا (1391). اثر سرایت بازده و تلاطم در برآورد ارزش در معرض ریسک سبد دارایی متشکل از طلا، ارز و سهام. پایان‎نامة کارشناسی ارشد، دانشکدة مدیریت و اقتصاد دانشگاه صنعتی شریف.
    1. Aloui, A., Ben Aıssa, M.S., Nguyen, D.K., (2011). Global financial crisis, extreme interdependences, and contagion effects: the role of economic structure? Journal of Banking and Finance 35 (1), 130–141.
    2. Ang, A. and Bekaert, G. (2002). International asset allocation with regime shifts, Review of Financial Studies, 15 (4), 1137–1187.
    3. Ang, A., Chen, J., and Xing, Y. (2006). Downside risk, Review of Financial Studies, 19 (4), 1191–1239.
    4. Boubaker, H. and Sghaier, N. (2013). Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach, Journal of Banking and Finance, 37 (2), 361-377.
    5. Canela, M.A. and Collazo, E.P. (2006). Modelling dependence in latin american markets using copula functions, Working paper, Universitat de Barcelona.
    6. Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Copulas methods in Finance J. Wiley.
    7. Chollete, L., de la Pena, V., Lu, C-C., (2011). International diversification: a copula approach. Journal of Banking and Finance 35 (2), 403–417.
    8. Clayton, D.G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika, 65 (1), 141–151.
    9. Costinot, A. and, Thierry, R and Teiletche, J.(2000). Revisiting the Dependence between Financial Markets with Copulas, Working paper.
    10. Das, S.R. and Uppal, R. (2004). Systemic risk and international portfolio choice, Journal ofFinance, 59 (6), 2809–2834.
    11. de Melo Mendes, B.V., Kolev, N., (2008). How long memory in volatility affects true dependence structure. International Review of Financial Analysis 17 (5),  1070– 1086.
    12. Di Clemente. A. and Romano, C. (2004). Measuring and optimizing portfolio credit risk: acopula-based approach, Economic Notes, 33 (3), 325–357.
    13. Dias, A. and Embrechts, P.(2003). Dynamiccopulamodelsformultivariatehigh-frequency data in finance, Working Paper, ETH Zurich: Department of Mathematics.
    14. Embrechts, P., McNeil, A.J. and Straumann, D. (1999). “Correlation: pitfalls and alternatives a short, RISK Magazine, 69–71.
    15. Embrechts, P., McNeil, A.J. and Straumann, D. (2002). Correlation and dependence in risk management: properties and pitfalls, In: Dempster, M.A.H. (Ed.), RiskManagement: Value at Risk and Beyond, Cambridge University Press, Cambridge.
    16. Engle, R.F. (2002). Dynamic conditional correlation: a simple class of multivariate generalized autoregressive conditional heteroskedasticity models, Journal ofBusiness and Economic Statistics, 20 (3), 339–350
    17. Engle, R.F., (1982). Auto-regressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50 (4), 987_1007.
    18. Fantazzini, D. (2008). Copula’s conditional dependence measures for portfoliomanagement and Value at Risk, Working paper, SFB 649, University of Konstanz (Germany): Chair of Economics and Econometrics.
    19. Garcia, R., Tsafack, G., (2011). Dependence structure and extreme comovements in international equity and bond markets. Journal of Banking and Finance 35 (8), 1954–1970.
    20. Giacomini, E. and Hardle, W. (2005). Value-at-Risk calculations with time varying copulae, Discussion paper, Humboldt University of Berlin: Institute Statistics and Econometrics.
    21. Glosten, L.R., R. Jagannathan and D. Runkle (1993), On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance, 48, 1779-1801.
    22. Hartmann, P., Straetmans, S. and de Vries, C.G. (2004). Asset market linkages in crisis periods, Review of Economics and Statistics, 86 (1), 313–326.
    23. He, X. and Gong, P. (2009). Measuring the coupled risks: a copula-based CVaR model, Journal of Computational and Applied Mathematics, 223 (2), 1066–1080.
    24. Hotta, L.K. and Palaro, H.P. (2006). Using conditional copula to estimate Value at Risk, Journal of Data Science, 4 (1), 93-115.
    25. Hotta, L.K., Lucas, E.C. and Palaro, H.P. (2008). Estimation of VaR using copula and extreme value theory, Multinational Financial Journal, 12 (3/4), 205-218.
    26. Hu, L., (2006). Dependence patterns across financial markets: a mixed copula approach. Applied Financial Economics 16 (10), 717–729.
    27. Hung, J.J., Kuo, L., Liang, H. and Lin, W.F. (2009). Estimating value at risk of portfolio by conditional copula-GARCH method, Insurance: Mathematics and Economics, 45 (2009) 315_324
    28. Hurlimann, W. (2004). Fitting bivariate cumulative returns with copulas, Computational Statistics & Data Analysis, 45 (2), 355-372.
    29. Ignatievay, K., Platen, E., (2010). Modelling co-movements and tail dependency in the international stock market via copulae. Asia-Pacific Financial Markets 17 (3), 261–302.
    30. Jondeau, E., Rockinger, M., (2003). Conditional volatility, skewness and kurtosis: existence, persistence, and comovements. Journal of Economic Dynamics and Control 27 (10), 1699–1737.
    31. Kole, E., Koedijk, K., Verbeek, M., (2005). Testing Copulas to Model Financial Dependence. Working paper, RSM Erasmus University
    32. Martinelli, L. and Meyfredi, J.C. (2007). A copula approach to Value-at-Risk estimation for fixed-income portfolios, The Journal of fixed income, summer, 17, 1.
    33. McNeil, A.J., Frey, R., and Embrechts, P. (2005). Quantitative Risk Management: Concepts, techniques and tools, Princeton University Press, New Jersey.
    34. Micocci, M., and masala.G, )2005). Pricing pension funds guarantees using a copula approach. Available online at www.  ctuaries.org/AFIR/colloguia/Maastricht/Micocci_Masala.pdf
    35. Necula, C. (2010). Modeling the dependency structure of stock index returns using a copula function approach, Romanian Journal of Economic Forecasting, 13 (3).
    36. Nelsen, R., (1999). An Introduction to Copulas. Springer, New York.
    37. Ozun, A. and Cifter, A. (2007). Portfolio value-at-risk with time-varying copula: Evidence from the Americans, Marmara University, MPRA Paper, No. 2711.
    38. Palaro, H.P. and Hotta, L.K. (2006). Using conditional copula to estimate Value at Risk, Journal of Data Science, 4 (2006), 93-115.
    39. Patton, A. (2004). On the out-of-sample importance of skewness and asymmetric dependence for asset allocation, Journal of Financial Econometrics, 2 (1), 130–168.
    40. Poon, S-H., Rockinger, M. and Tawn, J. (2004). Modeling extreme-value dependence in international stock markets, Statistica Sinica, 13, 929–953.
    41. Rockinger, M., Jondeau, E., (2001). Conditional dependency of financial series: An application of copulas. Working paper NER # 82. Banque de France. Paris.
    42. Rodriguez, J.C., (2007). Measuring financial contagion: a copula approach. Journal of Empirical Finance 14 (3), 401–423.
    43. Sklar, A., (1959). Fonctions de repartition a n dimensions et leurs marges. Publications de l'Institut Statistique de l'Universite de Paris 8, pp. 229_231.
    44. Song, P. X.-K.(2000) ,Multivariate dispersion models generated from gaussian copula. Scandinavian Journal of Statistics, 27(2):305–320
    45. Sun, W., Rachev, S., Fabozzi, F.J., Kalev, P., (2009). A new approach to modeling comovement of international equity markets: evidence of unconditional copulabased simulation of tail dependence. Empirical Economics 36 (1), 201–229.
    46. Susmel, R. (2001). Extreme observations and diversification in Latin American emerging equity markets, Journal of International Money and Finance, 20 (7), 971–986.
    47. Tsafack, G. (2009). Asymmetric dependence implications for extreme risk management, Journal of Derivatives, 17 (1), 7–20.
    48. Wang, K., Chen, Y.H., and Huang, S.W. (2011). The dynamic dependence between the Chinese market and other international stock markets: A time-varying copula approach, International Review of Economics and Finance, 20 (4), 654-664.
    49. Wang, Y.C., Wu, J.L., and Lai, Y.H. (2013). A revisit to the dependence structure between the stock and foreign exchange markets: A dependence-switching copula approach, Journal of Banking and Finance, 37 (5), 1706-1719.
Journal of Economic Research (Tahghighat- E- Eghtesadi)
Volume 49, Issue 4 - Serial Number 4
Winter 2015
Pages 869-902

  • Receive Date 26 May 2014
  • Revise Date 19 August 2014
  • Accept Date 30 September 2014