الگوسازی و مقایسه مدل‌های توزیع شاخص کل بورس اوراق بهادار تهران

نوع مقاله : علمی - پژوهشی

نویسندگان

1 دانشجوی دکتری مدیریت مالی، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران

2 دانشیار دانشکده مدیریت و اقتصاد, واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران .

3 استادیار دانشکده مدیریت و اقتصاد، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران.

4 استاد دانشکده مدیریت و اقتصاد، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران.

چکیده

     بررسی رفتار حدی بازار سهام و الگوسازی صحیح شکل توزیع بازده کل بازار نقش مهمی در مدیریت ریسک بازار دارد. در پژوهش حاضر، الگوی توزیع بازده‌های حدی بورس اوراق بهادار تهران بر اساس رویکرد ماکزیمم بلوک‌ها و در فواصل متفاوت زمانی مورد بررسی قرار گرفت. جهت انتخاب مدل مناسب در سری‌های زمانی متفاوت از نمودار نسبت ال-مومنت(شاخص گشتاوری) استفاده گردید و سپس با استفاده از محاسبه پارامترهای مدل‌های انتخاب شده بر اساس روش حداکثر درست نمایی، نسبت به مطابقت و انتخاب مدل مناسب در هر فاصله زمانی بر اساس آزمون اندرسون دارلینگ اقدام گردید. به منظور الگوسازی توزیع بازده کل بازار از داده‌های شاخص کل بورس از سال 1384 تا 1395 استفاده شده و پایه محاسبات انجام شده نیز لگاریتم بازده روزانه بورس تهران بوده است. نتایج پژوهش نشان می‌دهد که از بین مدل‌های مورد بررسی، مدل GL در فواصل زمانی سالانه سری‌های حداقل و مدل GEV در سایر فواصل زمانی سری‌های حداقل و حداکثر عملکرد بهتری دارد.

کلیدواژه‌ها

عنوان مقاله [English]

Modeling and Comparison of the Distribution Models of Tehran Stock Exchange Index

نویسندگان [English]

  • Ali Rezaian 1
  • Hamidreza Vakilifard 2
  • Maryam Khalili Araghi 3
  • Freydon Rahnamay Roodposhti 4
1 PhD. Candidate in Financial Management, Faculty of Management and Economic, Science and Research Branch, Islamic Azad university, Tehran, Iran.
2 Associate Prof, Faculty of Management and Economic, Science and Research Branch, Islamic Azad university, Tehran, Iran.
3 Assistant Prof, Faculty of Management and Economic, Science and Research Branch, Islamic Azad university, Tehran, Iran,
4 Professor, Faculty of Management and Economic, Science and Research Branch, Islamic Azad university, Tehran, Iran.
چکیده [English]

Study of the Extreme behavior of the Stock Market and the correct pattern of the distribution of returns has an important role in the management of market risk. The current study, based on BMM approach, examines the distribution pattern of return in Tehran Stock Exchange in different time intervals. In order to choose the appropriate model in different time series, L-Moment ratio diagram was used. Then, by using the calculation of parameters of the selected models based on the approach of Maximum likelihood, the conformity and selection of appropriate model in each time interval was performed based on AD test. To model the distribution of patterns of total market returns, the total stock index data of 2004-2016 was used and the basis of the performed calculation has the log of daily return of Tehran stock exchange. The results indicated that among the examined model, GL model in annual time interval and in minimum series, and GEV model in other time intervals of minimum and maximum series had a better performance.

کلیدواژه‌ها [English]

  • Extreme value theory
  • management of market risk
  • daily Extreme returns

مراجع

  1. Arshad, M., & Rasool, M. T, (2003). Anderson Darling and modified Anderson Darling tests for generalized Pareto distribution. Journal of applied sciences, 3 (2), 85-88.
  2. Assaf, A, (2009). Extreme observations and risk assessment in the equity markets of MENA region: tail measures and Value-at-Risk. Journal of international review of financial analysis, 18 (3), 109-116.
  3. Black. F., Scholes, M., (1973). The Pricing of Options and Corporate Liabilities. Journal of political economy, 81(3), 637-654.
  4. Christoffersen, P., Errunza, V., Jacobs, K., & Longlois, H. (2012). Is the potential for international diversification disappearing? A dynamic copula approach. The Review of financial studies, 25(12), 3711-3751.
  5. Dominicy Y., Ilmonen, P., & Veredas, D. (2015). Multivariate Hill estimators. International statistical Review banner, 85(1), 108-142.
  6. Falahpoor, S., & Fezolah, S. (2016). Choosing stock portfolios using the low sequence affinities and the theoretical amount of the margin. Quarterly Journal of Financial Knowledge of Analysis Securities, 30:33-54. (In Persian)
  7. Fallahshams, M., & Ghazanfari, S. (2016). Evaluation of downside risk and stock returns in tehran stock Exchange via extreme value theory. financial engineering and portfolio management, 7(27), 137-157. (In Persian)
  8. Fallah Talab, H., & Azizi M. R. (2014). The application of the theory of Extreme value in the prediction of value at risk. Quarterly journal of Investment Knowledge, 12, 159-180. (In Persian)
  9. Gencay, R., Selcuk, F., (2004). Extreme Value Theory and Value-at-risk: relative performance in emerging markets. International Journal of Forecasting, 20(2), 284-303.
  10. Gettinby, G., Sinclair, C., Power, D., Brown, R., (2006). An analysis of the distribution of extreme share returns in the UK from 1952 to 2000. Journal of Business Finance and Accounting, 31(5-6), 607-646.
  11. Hasan, H. Ahmad Radi, N. F., & Kassim, S. (2012). Modeling the distribution of extreme share return in Malaysia using generalized extreme value (GEV) distribution. The 5th international conference on research and education in mathematics, 1450, 82-89.
  12. Heikkila, M., Dominicy, Y., Ilmonen, P. (2017). Multivariate moment based extreme value index estimators .Computational statistics, 32(4), 1481-1513.
  13. Hosking, J. R., (1990). L-moments: analysis and estimation of distributions using linear combinations of order statistics. Journal of Royal statistical society, 52(1), 105-124.
  14. Jansen, D. W., & De Vries, C. G., (1991). On the frequency of large stock returns: putting booms and busts into perspective. The review of economics and statistics, 73(1), 18-24.
  15. Kelvin, A.K, & Mung’atu, J.K., (2016). Extreme Values Modelling of Nairobi Securities Exchange Index. American Journal of Theoretical and Applied Statistics. 5(4), 234-241.
  16. Lee C.F, Su J.B, (2012). Alternative statistical distributions for estimating value-at-risk: theory and evidence. Review of quantitative finance and accounting, 39(3), 309-331.
  17. Longin, F. M. (1996). The asymptotic distribution of extreme stock market returns. Journal of Business, 69(3), 383-408.
  18. Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 7(1), 77-91.
  19. Merton, R. C. (1973). An intertemporal capital asset pricing model. Econometric, 41(5), 867-887.
  20. McNeil A, Frey R. (2000). Estimation of Tail-Related Risk Measures for heteroscedastic financial time series: an extreme value Approach. Journal of Empirical finance, 7(3-4), 271-300.
  21. Mora – Valencia, A., Niguez, T. M., Perote, J., (2017). Multivariate approximations to portfolio return distribution. Journal of computational and mathematical organization theory, 23(3), 347-361.
  22. Niguez T.M, Perote J, (2016). The multivariate moments Expansion density: an application of the dynamic equicorrelation model. Journal of Banking and finance, 72(10), 216-232.
  23. Noroozizadeh, P. (2006). Modeling the Tail of Tehran Stock Exchange Index Distribution. 1stConference of Future Research, Tehran Amir Kabir Industrial University. (In Persian)
  24. Onour, E. (2010). Extreme risk and fat-tails distribution model: empirical analysis. Journal of money, investment and banking, Issue 13, 27-34.
  25. Polanski A., & Stoja E. (2010). Incorporating higher moments into value at risk forecasting. Journal of forecasting banner, 29(6), 523-535.
  26. Raee, R., & nabizadeh, A. (2013). The distribution of return on equity in Tehran Stock Exchange. Financial Management Strategy Quarterly, 10(1), 1-15. (In Persian)
  27. Rostami, M. R. & Haghighi, F. (2013). Comparison of Multivariate GARCH Models in Determining the Risk of a Portfolio. Journal of Financial Research, 15(2), 215-228. (In Persian)
  28. Saiful, IH, Li, S, (2015). Modeling the distribution of extreme returns in the Chinese stock market. Journal of international Financial Markets, institutions and money. 34(2015) 263-276.
  29. Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425-442.
  30. Schmdt R, Stadtmuller U. (2006). Non-parametric estimation of tail dependence. Scandinavian Journal of statistics banner, 33(2), 307-335.
  31. Tasi M, Chen L. (2011). The calculation of capital requirement using extreme value theory. Economic Modelling, 28(1-2), 390-395.
  32. Tolikas, K., Gettinby, G. D., (2009). Modelling the distribution of the extreme share returns in Singapore. Journal of Empirical Finance, 16(2), 254-263.
  33. Yarahmadi, M., & Fallahpour, S. (2012). Estimation of Value at Risk Using the Extreme Theory in Tehran Stock Exchange.Journal of Financial Engineering and Management of Securities, 13, 103-120. (In Persian).

فایل ها

هم رسانی

ارجاع به این مقاله

آمار