مقایسه مدل‌ تلاطم تصادفی کانونی و MSGJR-GARCH در اندازه‌گیری تلاطم بازده سهام و محاسبه ارزش در معرض ریسک

نوع مقاله : علمی - پژوهشی

نویسندگان

1 استادیار گروه مدیریت و کارافرینی، دانشکده علوم انسانی، دانشگاه کاشان، اصفهان، ایران

2 پژوهشگر پسادکتری اقتصاد، تهران، ایران.

3 دانشجوی دکتری مهندسی مالی، دانشگاه یزد، یزد، ایران

چکیده

یکی از مهمترین چالش‌ها در بررسی رفتار سرمایه‌گذاران در بازارهای مالی اندازه‌گیری تلاطم دارایی‌های مالی است. علت این موضوع آن است که تلاطم بازده سهام یک متغیر غیرقابل مشاهده می‌باشد. دو رویکرد اساسی برای مدل‌سازی تلاطم در اقتصاد مالی وجود دارد که تفاوت آنها در ساختار احتمالاتی آنهاست. در رویکرد اول تلاطم با استفاده از شوک‌های وارد آمده بر بازده سهام مدل‌سازی می‌شود و در رویکرد دوم تلاطم براساس یک فرآیند تصادفی که می‌تواند مستقل از دینامیک بازده سهام در طول زمان باشد تحول یابد. مدل‌های ارائه شده در رویکرد اول کلاس GARCH و در رویکرد دوم کلاس تلاطم تصادفی و تغییر وضعیت مارکفی را تشکیل می‌دهند. با وجود برتری ساختار احتمالاتی این دسته از مدل‌ها محاسبه پارامترهای مدل و پیش‌بینی تلاطم بسیار پیچیده می‌باشد که استفاده از روش‌های بیزی و شبیه‌سازی MCMC را ناگزیر می‌سازد. نتایج این پژوهش حاکی از این است که در بازه زمانی پژوهش، وجود اثر اهرمی با استفاده از الگوی CSV در بازار سهام تهران تایید نمی‌شود و روش MSGJR-GARCH با توزیع t در پیش‌بینی تلاطم بازده پنجاه شرکت فعال بورس اوراق بهادار براساس معیار انحراف اطلاعاتی بیزی کاراتر عمل می‌کند. در نهایت برمبنای مدل کاراتر ارزش در معرض ریسک هفت روز اول خارج از داده‌ها محاسبه گردید.

کلیدواژه‌ها

عنوان مقاله [English]

Compare Canonical stochastic volatility model of focal MSGJR-GARCH to measure the volatility of stock returns and calculating VaR

نویسندگان [English]

  • Ali Farhadian 1
  • Mojtaba Rostami 2
  • Moslem Nilchi 3
1 Assistant Prof., Dep of Management and entrepreneur, Faculty of Human Science, University of Kashan, Isfahan, Iran
2 Postdoctoral researcher in Economics, Tehran, Iran.
3 Ph.D. Candidate in Financial Engineering, Yazd Universtity, Yazd, Iran
چکیده [English]

One of the most important challenges in examining the behavior of investors in financial markets is measuring the volatility of financial assets. This is because stock price volatility is a latent variable. There are two basic approaches to modeling volatility in financial economics that differ in their probabilistic structure. In the first approach, volatility is modeled using shocks to stock returns, and in the second approach, volatility is transformed based on a stochastic process that can be independent of stock return dynamics over time. The models presented in the first approach of the GARCH class and in the second approach of the class constitute random volatility and Markov regime change. Despite the superiority of the probabilistic structure of these models, the calculation of model parameters and volatility prediction is very complex, which makes it necessary to use Bayesian methods and MCMC simulations. The results of this study indicate that in the period of this study, the existence of a leverage effect in the Tehran stock market is not confirmed and the MSGJR-GARCH method is more efficient in predicting fifty more active companies of Stock Exchange return volatility based on Bayesian information deviation criteria. Finally, based on the more efficient model, the out-of-sample VaR was calculated for the first seven days.

کلیدواژه‌ها [English]

  • : Volatility
  • Simulation
  • Bayesian methods
  • Value at Risk

مراجع

1.Andersen, T. G., & Benzoni, L. (2009). Realized volatility. In T. G. Andersen, R. A. Davis, J.-P. Kreiss, & T. V. Mikosch (Eds.), Handbook of financial time series (pp. 555–576). Berlin, Heidelberg: Springer.
2.Ardia, D., & Hoogerheide, L. F. (2010). Bayesian Estimation of the GARCH (1,1) Model with Student-t Innovations. In R. the R Journal, 2(2), 41–47.
3.Ari, Y. & Papadopoulos, S. A. (2016). Bayesian Estimation of the Parameters of the ARCH Model with Normal Innovations Using Lindley’s Approximation. Journal of Economic Computation and Economic Cybernetics Studies and Research, 50(4), 217–234
4.Asai, M. (2006). Comparison of MCMC Methods for Estimating GARCH Models. Journal of the Japan Statistical Society, 36, 199–212.
5.Ausin MC, Galeano P (2007). "Bayesian Estimation of the Gaussian Mixture GARCH Model." Computational Statistics and Data Analysis, 51(5), 2636-2652. DOI: 10.  1016/j.csda.01/2006.006.
6.Baghjari, M., Nilchi, M., Rasoolian, A. (2016). Examining the Return and the Return Volatility of Investment Industry in the Months of Ramadan and Muharram. Journal of Financial Management Perspective, 6(15), 25-41.
7.Baillie, R.T., Bollerslev, T. and Mikkelsen, H.O. (1996). Fractionally Integrated Generalized AutoregressiveConditional Heteroskedasticity, Journal of Econometrics, 74, 3–30.
8.Bernardo, J. M., & Smith, A. F. M. (2000). Bayesian Theory. Chichester: John Wiley.
9.Bodie, Z., Kane, A., & Marcus, A. J. (2018). Investments management. Taipei: McGraw-Hill/Irwin.‏
10.Bollerslev, T. (1986). Generalised Autoregressive Conditional Heteroscedasticity. Journal of Econometrics
11.Bollerslev, T., Engle, R.F. and Nelson, D.B. (1994). ARCH Models, in R.F. Engle and D. Mc­Fadden (Eds.), Handbook of Econometrics Vol. IV, Amsterdam: North-Holland, PP. 2959–3038.
12.Broto, C., Ruiz, E. (2004). Estimation methods for stochastic volatility models: a survey. Journal of Economic Surveys 18:613–649.
13.Bühlmann, P. and McNeil, A. J. (2002). An Algorithm for Nonparametric GARCH Modelling. Computnl Statist.  Data Anal., 40, 665–683
14.Cao, C.Q., and R.S. Tsay (1992) Nonlinear time-series analysis of stock volatilities, Journal of Applied Econometrics, December, Supplement, 1, S165–S185.
15.Chou, R.Y. (1988). Volatility Persistence and Stock Valuations: Some Empirical Evidence Using GARCH, Journalof Applied Econometrics, 3, 279–294.
16.Danielsson, J. (2011). Financial risk forecasting: the theory and practice of forecasting market risk with implementation in R and Matlab (Vol. 588). John Wiley & Sons.‏
17.Engle RF (2004). Risk and Volatility: Econometric Models and Financial Practice.The American Economic Review, 94(3), and 405-420. Doi: 1257/10/0002828041464597.
18.Engle, R. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987–1007
19.Engle, R. F., & Patton, A. J. (2006). What good is a volatility model? In Forecasting volatility in the financial markets (pp. 47-63). Butterworth-Heinemann.‏
20.Engle, R.F. and Ng, V. (1993). Measuring and Testing the Impact of News on Volatility, Journal of Finance, 48, 1749–1778.
21.Engle, R.F., Ng, V.K. and Rothschild, M. (1990). Asset Pricing with a Factor-ARCH Covariance Structure, Journal of Econometrics, 45, 235–237.
22.Fama, E.F. (1965). The Behavior of Stock-Market Prices, Journal of Business, 38, 34–105.
23.Geweke, J. (1989), "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, 57, 1317-1339.
24.Glosten LR, Jaganathan R, Runkle DE (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 48(5), 1779-1801.
25.Hoeting, J. A., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999). Bayesian Model Averaging: A Tutorial.  Statistical Science, 14 (4), 382–417.
26.Hull, J., and White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42:281–300.
27.Jacquier, E., Polson, N., and Rossi, P. (2004). Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics, (122):185–212.
28.Jeffreys, H. (1939). Theory of Probability. Oxford: Oxford University Press.
29.Kim, S., N. Shephard, and S. Chib (1998). Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361–393.
30.Li, Y., Zeng, T., & Yu, J. (2014). A new approach to Bayesian hypothesis testing. Journal of Econometrics, 178, 602-612.
31.Lopez, J.A. (2001) Evaluating the predictive accuracy of volatility models, Journal of Forecasting, 20, 2, 87–109.
32.Malkiel, B. G. (2003). The efficient market hypothesis and its critics. Journal of economic perspectives, 17(1), 59-82.
33.Mandelbrot, B. (1963). The Variation of Certain Speculative Prices, Journal of Business, 36, 394–419. Nelson, D.B. (1991). Conditional Heteroscedasticity in Asset Returns: A New Approach, Econometrica, 59, 347–370.
34.Marcucci, J. (2005). Forecasting Stock Market Volatility with Regime-Switching GARCH models.” Working Paper, University of California at San Diego.
35.Melino, Angelo and Stuart Turnbull, 1989, Pricing foreign currency options with stochastic volatility, Journal of Econometrics 45, 239-266
36.Meyer, R. and Yu, J. (2000). BUGS for a Bayesian analysis of stochastic volatility models. Econometrics Journal, 3, 198–215.
37.Pesaran, M. H. (2015). Time series and panel data econometrics. Oxford University Press.
38.Rostami M, Makiyan S N. (2020). Modeling Stock Return Volatility Using Symmetric and Asymmetric Nonlinear State Space Models: Case of Tehran Stock Market. Jemr,11 (41) :197-229
39.Sadorsky, P. (1999). Oil price shocks and stock market activity. Energy economics, 21(5), 449-469.
40.Schwert, G.W. (1989). Why Does Stock Market Volatility Change Over Time? Journal of Finance, 44, 1115–1153.
41.Sims, C.A. (1988), Bayesian Skepticism on Unit Root Econometrics, Journal of Economic Dynamics and Control, 12, 463-474.
42.Stock, J. H. (1991). Bayesian Approaches to the Unit Root' Problem: A Comment. Journal of Applied Econometrics, 403-411.
43.Taylor, J.W. (2004) Volatility forecasting with smooth transition exponential smoothing, International Journal of Forecasting, 20, 273–286.
44.Taylor, S.J (1986). Modelling Financial Time Series. John Wiley, New York.
45.Taylor, Stephen J., 1984, estimating the variances of auto correlations calculated from financial time series, Journal of the Royal Statistical Association, Series C (Applied Statistics) 33, 300-308.
46.Withers, S. D. (2002). Quantitative Methods: Bayesian Inference, Bayesian Thinking, Progress in Human Geography, 26 (4), 553–566.
47.Y Omori, S Chib, N Shephard, J Nakajima (2007). Stochastic volatility with leverage: Fast and efficient likelihood inference. Journal of Econometrics 140 (2), 425-449, 2007. 295, 2007.
48.Yu, J. (2005). On leverage in a stochastic volatility model. Journal of Econometrics, 127(2), 165-178.‏
49.Zakoian, J.-M. (1994). Threshold Heteroskedastic Models, Journal of Economic Dynamics Control, 18, 931–955.
50.Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. New York: John Wiley.
51.Haas, M., Mittnik, S., & Paolella, M. S. (2004). A new approach to Markov-switching GARCH models. Journal of financial econometrics, 2(4), 493-530.

فایل ها

هم رسانی

ارجاع به این مقاله

آمار