The Predictive Performance of Asymmetric Normal Mixture GARCH in Risk Management: Evidence from Turkey

Bu çalışmanın amacı, Türk hisse senedi piyasası için Asimetrik Normal Karma GARCH (NMAGARCH) ve diğer GARCH modellerinin öngörü performansını Kupiec ve Christoffersen geriye dönük testleri ile test etmektir. Ampirik bulgular %99 güven aralığı için örneklem dışı Christoffersen testine göre NMAGARCH modelinin, %95 güven aralığı için örneklem dışı Christoffersen ve Kupiec testlerine göre normal ve student-t dağılımlı GARCH modelinin diğer modellerden daha iyi sonuç verdiğini göstermektedir. Bu sonuçlar, NMAGARCH modeli de dâhil olmak üzere hiçbir modelin diğer modellere göre tüm posizyon ve güven aralıklarında daha iyi sonuç vermediğini göstermektedir ve Riske Maruz Değer hesaplamasında bu bulgunun sonucu volatilite modelinin ticaret posizyonu ve güven aralığına göre seçilmesi gerektiğidir. Ayrı ca, NMAGARCH modeli Basel’ında gerektirdiği şekilde yüksek güven aralığında öngörü performansını arttırmaktadır.

Risk Yönetiminde Asimetrik Normal Karma GARCH Modelinin Öngörü Performansı: Türkiye Uygulaması

Abstract The purpose of this study is to test predictive performance of Asymmetric Normal Mixture GARCH (NMAGARCH) and other GARCH models based on Kupiec and Christoffersen tests for Turkish equity market. The empirical results show that the NMAGARCH perform better based on %99 CI out-of-sample forecasting Christoffersen test where GARCH with normal and student-t distribution perform better based on %95 Cl out-of-sample forecasting Christoffersen test and Kupiec test. These results show that none of the model including NMAGARCH outperforms other models in all cases as trading position or confidence intervals and the real implications of these results for Value-at-Risk estimation is that volatility model should be chosen according to confidence interval and trading positions. Besides, NMAGARCH increases predictive performance for higher confidence internal as Basel requires.

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1. Ackert, L. F., and Racine, M. D. (1999). Time Varying Volatility in Canadian and US Stock Index and Index Futures Markets: A Multivariate Analysis, Federal Reserve Bank of Atlanta Working Paper Series, No: 98-14.
2. Alexander, C. and Lazar, E. (2003). Symmetric Normal Mixture GARCH, ISMA Center Discussion Paper in Finance, No:9.
3. Alexander, C. and Lazar, E. (2005). The Equity Index Skew, Market Crashes and Asymmetric Normal Mixture GARCH, ISMA Center, Mimeo
4. Alexander, C. and Lazar, E. (2006). Normal Mixture GARCH(1,1):Applications to Exchange Rate Modeling, Journal of Applied Econometrics, 21(3): 307-336.
5. Andersen, T.G. and Bollerslev, T. (1998). DM-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer-Run Dependencies, Journal of Finance, 53(1):.219-265.
6. Baillie, R. T., Bollerslev, T., and Mikkelsen, H.O. (1996). Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 74: 3-30.
7. Baillie, R. T. and Bollerslev, T. (1989). The Message in Daily Exchange Rates: A Conditional-Variance Tale, Journal of Business and Economic Statistics, 7:297-305.
8. Basle Committee on Banking Supervision. (1996a). Amendment to the Capital Accord to Incorporate Market Risks, Basle, Switzerland: BIS.
9. Basle Committee on Banking Supervision. (1996b). Supervisory Framework for the Use of ‘Backtesting’ in Conjunction with the Internal Models Approach to Market Risk Capital Requirements. Manuscript, Basle, Switzerland: BIS.
10. Bates, D. S. (2003). Empirical Options Pricing: A Retrospection, The Journal of Econometrics, 116: 387-404.
11. Bates, D. S. (1991). The Crash of ’87: Was It Expected? The Evidence from Options Markets, Journal of Finance, 46: 1009-1044.
12. Bekaert, G., and Wu, G. (2000). Asymmetric Volatility and Risk Equity Markets, The Review of Financial Studies, 13(1): 1-42.
13. Bollerslev, T. and Woolridge, J. M. (1992). Quasi-maximum Likelihood Estmation Inference in Dynamic Models with Time-varying Covariances, Econometric Theory, 11: 143-172.
14. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31: 307–327.
15. Bollerslev, T., and Ghysels, E. (1996). Periodic Autoregressive Conditional Heteroskedasticity, Journal of Business and Economics Statistics, 14: 139–152.
16. Bollerslev, T., Chou, R. Y. and Kroner, K. F. (1992). ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence, Journal of Economics and Statistics, 69: 542-547.
17. Bollerslev, T. (1987). A Conditional Heteroskedasticity Time Series Model for Speculative Prices and Rates of Return, Review of Economic and Statistics. 69:542-547.
18. Bollerslev, T., and Mikkelsen, H. O. (1996). Modelling and pricing long memory in stock market volatility, Journal of Econometrics, 73: 151-84.
19. Çifter, A. (2004). Asymmetric and Fractionally Integrated GARCH Models with (Skewed) Student-t and Ged Distribution in Risk Management: An Application on Eurobond, Presented in VIII. National Finance Symposium, Istanbul Technical University (in Turkish).
20. Christoffersen, P. F. (1998). Evaluating Interval Forecasts, International Economic Review, (39): 841-862.
21. Christoffersen, P. F., and Jacobs, Kris. (2004). Which GARCH Model for Option Valuation?, Management Science, 50: 1204-1221.
22. Christoffersen, P. F., Heston, S., and Jacobs, K. (2004). Option Valuation with Conditional Skewness. Fortcoming in The Journal of Econometrics.
23. Cung, C.-F. (1999). Estimating the Fractionally Integrated GARCH Model, National Taiwan University, Working Paper.
24. Darrat, A., and Benkato, O. (2003). Interdependence and Volatility Spillovers under Market Liberalization: The case of Istanbul Stock Exchange, Journal of Business, Finance & Accounting, 30:1089-1114.
25. Ding, Z., Granger, C. W. J. and Engle, R. F. (1993). A Long Memory Property of Stock Market Returns and a New Model, Journal of Empirical Finance, 1:83–106.
26. Dickey, D. A., and Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root, Econometrica, 49: 1057–1072.
27. Davidson, J. (2001). Moment and Memory Properties of Linear Conditional Heteroskedasticity Models, Manuscript, Cardiff University.
28. Davidson, J. (2002). Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, Working Paper, http://www.cf.ac.uk/carbs/econ/davidsonje.
29. Doornik, J.A. (1999). An Object Oriented Programming Language, UK: Timberlake Consultant, Third Ed.
30. Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimate of the Variance of United Kingdom Inflation, Econometrica, 50: 987-1007.
31. Engle, R. F. and Tim, B. (1986). Modeling the Persistence of Conditional Variances, Econometric Reviews, 5: 1-50.
32. Engle, R. F. and Ng, V. K. (1993). Measuring and Testing the Impact of News on Volatility, Journal of Finance, 48: 1749-1778.
33. Fernandez, C., and Stell, M. (1998). On Bayesian Modeling of fat tails and skewness, Journal of the American Statistical Association, 93: 359-371.
34. Glosten, L. R., Jagahannathan, R., and Runkle, D. E. (1993). On the Relationship between the Expected Value and The Volatility of the Nominal Excess Return on Stocks, Journal of Finance, 48: 1779-1801.
35. Hamilton, J. D., and Susmel R. (1994). Autoregressive Conditional Heteroskedasticity and Changes in Regime, Journal of Econometrics, 64: 307-333.
36. Harris, R. and Sollis, R. (2003). Applied Time Series Modeling and Forecasting,UK: Wiley Press.
37. Hsieh, D. A. (1989). Modeling Heteroskedasticity in Daily Foreign Exchange Rates, Journal of Business and Economic Statistics, 7: 307-317.
38. Kupiec, P. H. (1995). Techniques for Verifying the Accuracy of Risk Measurement Models, Journal of Derivatives, winter, 73-84.
39. Lambert, P., and Laurent, S. (2001). Modelling Financial Time Series Using GARCH-type Models with a Skewed Student Distribution for the Iinnovations, Univ. Li`ege, Belgium, Working paper.
40. Laurent, S. and Peters, J.-P. (2002). G@rch 2.2: An Ox Package for Estimating and Forecasting Various ARCH Models, Journal of Economic Surveys, 16(3):447-485.
41. Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59(2): 347-370.
42. Nyblom, J. (1989). Testing for the Constancy of Parameters Over Time, Journal of the American Statistical Association, 84: 223-230.
43. Palm, F. (1996). GARCH Models of Volatility, in Handbook of Statistics, ed. By G.Maddala, and C.Rao, Amsterdam: Elsevier Science. 209-240.
44. Palm, F., and Vlaar, P. JG. (1997). Simple Diagnostics Procedures for Modeling Financial Time Series, Allgemeines Statistisches Archiv, 81: 85-101.
45. Pagan, A. (1996). The Econometrics of Financial Markets, Journal of Empirical Finance, 3: 15-102.
46. Peters, J.-P. (2001). Estimating and Forecasting Volatility of Stock Indices Using Asymmetric GARCH Models and (Skewed) Student-t Densities, Mimeo, Ecole d’Admin. des Affaires, Unv.of Li`ege
47. Puttonen, V. (1995). International Transmission of Volatility between Stock and Stock Index Future Markets, Journal of International Financial Markets, Institutions & Money, 5.(2/3).
48. Saltoğlu, B. (2003). A High Frequency Analysis of Financial Risk and Crisis: An Empirical Study on Turkish Financial Market, Istanbul: Yaylım Publishing.
49. Sarma, M., Thomas, S. and Shah, A. (2001). Selection of Value-at-Risk Models,Mimeo
50. Tang, T.-L., and Shieh, S.-J. (2006). Long-Memory in Stock Index Futures Markets: A Value-at-Risk Approach, Phsica A, 366: 437-448.
51. Tsay, R. S. (2005). Analysis of Financial Time Series, New York: John Wiley &Sons.
52. Tse, Y. (1998). The Conditional Heteroscedasticity of the Yen-Dollar Exchange Rate, Journal of Applied Econometrics, 193: 49-55.
53. Taylor, S. (1986). Modeling Financial Time Series, New York : John Wiley & Sons.
54. Wu, G. (2001). The Determinants of Asymmetric Volatility, The Review of Financial Studies, 14(3): 837-859.
55. Zakoian, J.-M. (1994). Threshold heteroskedascity Models, Journal of Economic Dynamics and Control, 15: 931-955.