سنجش ارزش در معرض ریسک شرطی با استفاده از ترکیب مدل FIGARCH و نظریه ارزش فرین

نوع مقاله: مقاله پژوهشی

نویسندگان

1 استادیار دکتری مدیریت مالی، دانشگاه تهران، تهران، ایران

2 استاد دانشگاه تهران، دکتری مدیریت مالی، تهران، ایران

3 استادیار گروه سیستم‌های اقتصادی و اجتماعی دانشگاه علم و صنعت ایران، تهران، ایران

4 دانشجوی دکتری مدیریت مالی دانشگاه تهران، تهران، ایران (نویسنده مسئول)

چکیده

تلاش در جهت شناسایی مدل مناسب و بالا بردن دقت اندازه‏گیری با استفاده از سنجه ارزش در معرض ریسک از اهمیت ویژه ای برخوردار است. ارزش در معرض ریسک شرطی (CVaR) با نداشتن برخی نواقص ارزش در معرض ریسک، سنجه قابل اعتماد‏تری می‏باشد. در این پژوهش با مطالعه در خصوص ویژگی‏های داده‏های شاخص کل بورس اوراق بهادار تهران وکاربرد مدل FIGARCH-EVT در محاسبه ارزش در معرض ریسک شرطی، تصریح دقیق‏تری حاصل شده است. ابتدا مدل ترکیبی GARCH-EVT پیاده‏سازی شد و با توسعه آن، به مدل FIGARCH-EVT رسیدیم که خاصیت خوشه‏ای بودن، پویا بودن و حافظه بلندمدت را در مدل‏سازی لحاظ نموده است. استفاده از مدل FIGARCH برای داده‏های بازده لگاریتمی شاخص کل، موجب لحاظ‏کردن خواص فوق در مدل‏سازی خواهد شد. بعلاوه، خاصیت دنباله پهن بودن داده‏های بازده شاخص با استفاده از تئوری مقدار فرین (EVT) برای پسماندهای مدل FIGARCH بکار برده می‏شود. برای مقایسه نتایج، مدل‏های NORMAL-GARCH و t-Student-GARCH، شبیه‏سازی تاریخی و GARCH-EVT نیز برای داده‏ها بازده شاخص بکار برده شده است. نتایج حاصل از مدل‏‏ها با استفاده از آزمون‏های پس‌آزمون مورد بررسی و مقایسه قرار گرفته‏اند. نتایج حاصل از این پژوهش نشان می‏دهد که توزیع داده‏ها بازدهی شاخص نامتقارن دارای چولگی بوده و از توزیع نرمال تبعیت نمی‏کند. بر اساس چهار آزمون جزء اخلال مازاد استاندارد شده، فرآیند نقض تجمعی، پس آزمایی ریزش مورد انتظار و تابع زیان لوپز مدل FIGARCH-EVT نسبت به سایر مدل‏ها از دقت بالاتری برخوردار می‏باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Modeling volatility and conditional VaR measure using GARCH models and theoretical EVT in Tehran Stock Exchange

نویسندگان [English]

  • Saeed Fallahpoor 1
  • Reza Raee 2
  • Saeed Mirzamohammadi 3
  • seyed mohammad hasheminejad 4
1 professor of Tehran University, financial management Ph.D
2 professor of Tehran University, financial management Ph.D
3 Assistant professor of Iran University of Science and Technology, Economic Ph.D
4 Ph.D student of financial management at University of Tehran kish, International Campus,
چکیده [English]

Trying to identify an appropriate model to enhance measurement accuracy by using value at risk measures is of particular importance. Conditional Value at Risk (CVaR) with having some of the shortcomings of VaR, is a more reliable measure. In this study, the characteristics of the Tehran Stock Exchange index data usage FIGARCH-EVT model to calculate value at risk if states have been more accurate. GARCH-EVT hybrid implementation model and its development, FIGARCH-EVT model, we found that the effect of clustering, dynamic and long-term memory has been included in the modeling. FIGARCH model for log data output index, which will be modeled in terms of the above properties. In addition, the wide trail property index return data using extreme value theory (EVT) is used for residual FIGARCH model. To compare the results, NORMAL-GARCH models and t-Student-GARCH, historical simulation and GARCH-EVT indicator is used for data output. The results of the model using retrospective tests were evaluated. The results of this study indicate that the data distribution is skewed and asymmetrical index returns do not follow a normal distribution. The tests Standardized Exceedance Residuals and The Cumulative Violation Process and  Expected shortfall backtesting and loss function Lopez FIGARCH-EVT model over other models is more accurate.

کلیدواژه‌ها [English]

  • Extreme Value Theory
  • function Lopez losses
  • long-term memory
  • FIGARCH
*       Koedijk, K.G., Schafgans, M. and de Vries, C.G. (1990), The tail index of exchange rate returns, Journal of international Economics, 29, 93–108.

*       Jansen, D. and de Vries, C.G. (1991), On the frequency of large stock returns: Putting booms and busts into perspective, Review of Economics and Statistics, 73, 18–24.

*       McNeil, A.J., Frey, R. and Embrechts, P. (2005), Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press.

*       Embrechts, P., Kuppelberg, C. and Mikosch, T. (1997), Modelling Extremal Events for Insurance and Finance: Applications of Mathematics. Springer-Verlag.

*       Danı´elsson, J. and de Vries, C.G. (2003), ‘‘Where do extremes matter?’’ Available at http://www.Risk Research.org

*       Balkema, A. A. and de Haan, L. (1974). Residual life time at great age. Annals of Probability, 2:792-804.

*       Pickands, J. I. (1975). Statistical inference using extreme value order statistics.Annals of Statististics, 3:119-131.

*       Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (minimum) values of meteorological events. Quarterly Journal of the Royal Meteorological Society, 81:158-172.

*       Von Mises, R. (1954). La distribution de la plus grande de n valeurs. In Selected Papers, Volume II, pages 271{294. American Mathematical Society, Providence, RI.

*       Danielsson, J., (2011), Financial Risk Forecasting, John Wiley and Sons.

*       Engle, Robert F., 1982, "Autoregressive Conditional Heteroscedasticity with Estimation of the Variance of United Kingdom Inflation", Econometrica, Vol. 50, No. 4, PP. 987-1007.

*       Bollerslev, T., 1986, "Generalized Autoregressive Conditional Heteroskedasticity", Journal of Econometrics, Vol. 31, No. 3, PP. 307-327.

*       Lopez, J., 1999, "Methods for Evaluating Value-at-Risk estimates, Federal Reserve Bank of San Francisco", Economic Review, Vol. 2, PP. 3-17.

*       Gilli, M., & Këllezi, E. (2006). An Application of Extreme Value Theory for Measuring Financial Risk. Computational Economics, 27(2), 207-228.

*       R. Gencaya, F. Selcukc, 2004, Extreme value theory and Value-at-Risk: Relative performance in emerging markets, International Journal of Forecasting 20 (2004) 287– 303

*       V. Marimoutou, B. Raggad, A. Trabelsi, 2009, Extreme Value Theory and Value at Risk: Application to oil market, Energy Economics.V. O. Andreev, S. E. Tinykov,O. P. Ovchinnikova, G. P. Parahin,2012, Extreme Value Theory and Peaks Over Threshold Model in the Russian Stock Market, Journal of iberian Federal University. Engineering & Technologies 1 (2012 5) 111-121.

*       K. Singh, D.E. Allen, R. J Powell, 2011, Value at Risk Estimation Using Extreme Value Theory, 19th International Congress on Modelling and Simulation, Perth, Australia, 12–16 December 2011.

*       McNeil, A., & Frey, R. (2000). Estimation of Tail Related Risk Measure for Heteroscedastic Financial Time Series: An Extreme Value Approach. Journal of Empirical Finance 7, 271-300.

*       Ben Soltane H., Karaa A., Bellalah M., 2012 Conditional VaR using GARCH-EVT approach:Forecasting Volatility in Tunisian Financial Market, Journal of Computational & modeling, vol.2, no.2.

*       Ling Deng, Chaoqun Ma and Wenyu Yang, Portfolio Optimization via Pair Copula-GARCH-EVT-CVaR Model, Systems Engineering Procedia, 2, (2011), 171-181

*       Campbell, S.D. (2005), A Review of Backtesting and Backtesting Procedures, Technical Report 2005-21, Federal Reserve staff working paper in the Finance and Economics Discussion Series.  

*       Christoffersen, P.F. (1998), ‘‘Evaluating interval forecasts,’’ International Economic Review, 39, 841–862.

*       Kupiec, P. (1995), Techniques for Verifying the Accuracy of Risk Management Models, Journal of Derivatives 3:73-84.

*Baillie, R., Morana, C., 2009. Modeling long memory and structural breaks in conditional variances: an adaptive FIGARCH approach. Journal of Economic Dynamics and Control 33, 1577-1592.

*       Belkhouja, M. and M. Boutahary (2011). Modeling volatility with time-varying figarch models. Economic Modelling 28(3), 1106–1116.

*       Kilic, R., (2009), Long Memory and Nonlinearity in Conditional Variances: A Smooth Transition FIGARCH Model, Journal of Empirical Finance

*       D.B.Nelson, Conditional heteroscedasticity in asset returns: a new approach, Econometrica, 59(2), (1991), 347-370.

*       Glosten, L., R. Jagannathan and D. Runkle (1992), On the Relation between the Expected Value and Volatiltiy and of the Nominal Excess Returns on Stocks, Journal of Finance, 46, 1779-1801.

*       Engle, R.F. and T. Bollerslev (1986), Modeling the persistence of conditional variances,

*       Econometric Reviews, 5, 1-50.

*       Baillie, R., T. Bollerslev and H. Mikkelsen (1996), Fractionally Integrated Generalized

*       Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 73, 5–59.

*       Bollerslev, T. and H. Mikkelsen (1996), Modeling and Pricing Long Memory in Stock

*       Market Volatility, Journal of Econometrics, 73, 151–184.

*       Beine, M., Laurent, S., 2000. Structural Change and Long Memory in Volatility: New Evidence from Daily Exchange Rates, Working Paper, University of Liege.

*       Degiannakis, S. (2004), Volatility Forecasting: Evidence from a Fractional Integrated

*       Asymmetric Power ARCH Skewed-t Model, Applied Financial Economics, 14, 1333-1342.

*       Kang, S. and S. Yoon (2007), Long Memory Properties in Return and Volatility: Evidence from the Korean Stock Market, Physica A, 385, 591-600

*       Jefferis, K. and P. Thupayagale (2008), Long Memory in Southern Africa Stock Markets,

*       South African Journal of Economics, 73, 384-398

*       Ruiz, E. and H. Veiga (2008), Modelling Long-Memory Volatilities with Leverage Effect: ALMSV versus FIEGARCH, Computational Statistics and Data Analysis, 52, 2846- 2862

*       Niguez , T. (2007), Volatility and VaR Forecasting in the Madrid Stock Exchange, Spanish Economic Review, 10, 169-196

*       Pelinecu, E., Acatrinei, M., (2014), Modelling the high frequency exchange rate in Romania with FIGARCH, Procedia Economics and Finance, 15 ( 2014 ) 1724 – 1731.

*       Cevik, P., Emec H., (2013), Long Memory Properties in Return and Volatility: An Application of the Impact of Arab Spring in Turkey Financial Market, Current Research Journal of Social Sciences 5(2): 60-66, 2013

*       Maheshchandra J., P., (2012), Long Memory Property In Return and Volatility: Evidence from the Indian Stock Markets, Asian Journal of Finance & Accounting, Vol. 4, No. 2