Latent Volatility Modeling and Bayesian Analysis of stochastic Volatility of Intraday Data of Tehran Stock Exchange Index Based on Markov Monte Carlo Chain

Subject Areas : Journal of Investment Knowledge

Saeed Shahriyari ¹ , Peyman Iman zadeh ² , Mehdi Khoshnood ³

1 - Department of Financial Engineering, Rasht Branch, Islamic Azad University, Rasht, Iran
2 - Department of Accounting, Talesh Branch, Islamic Azad University, Talesh, Iran
3 - Department of Accounting, Rudsar and Amlash Branch, Islamic Azad University, Rudsar, Iran

Received: 2023-07-08 Accepted : 2023-07-30 Published : 2024-09-22

Keywords: Copula Functions, realized returns, Stochastic Volatility,

Abstract :

In this study, latent volatility modeling and Bayesian analysis of stochastic Volatility of intraday data of Tehran Stock Exchange index based on Markov Monte Carlo chain in uncertainty conditions (downward crisis of stock market index) have been developed. The method of the current research is a correlational description. For this purpose, at first, the distribution of the logarithm of the squared return as a measure of the realized volatilities was simulated using the stochastic Volatility model to obtain the latent volatilities, and then by using the hybrid MCMC-Copula model, the parameters affecting the stochastic Volatilities were identified and estimated in the training phase. Finally, using the results obtained from the training phase, in the test phase, the comparison of Copula and GARCH models was done. The results showed that the Copula Gumble, Galambos, Joe, Clayton and Frank provide similar and lower MSE and RMSE indices than the GARCH base model, and therefore the model based on copula provides the possibility of serial dependence in the latent volatility process. The findings of the current research can be useful for financial and investment companies for portfolio management and portfolio management in different conditions of market volatilities in order to achieve the investor's goals and increase the value of the portfolio.

References:

• بناکار، مهسا، قالیباف اصل، حسن، مینویی، مهرزاد (1400)، تبیین و آزمون مدل‌ تلاطم و سرریز در بورس اوراق بهادار تهران (مبتنی بر مدل‌های خانواده کاپولا)، مهندسی مالی و مدیریت اوراق بهادار، شماره 47، صص 534-563


• سعیدی، حسین، محمدی، شاپور (1390)، پیش‌بینی نوسانات بازده بازار با استفاده از مدل‌های ترکیبی گارچ-شبکه عصبی، فصلنامه بورس اوراق بهادار، شماره 16، ص 153-174


• فراهانی برز آبادی، مریم، قلی زاده، محمدحسن، چیرانی، ابراهیم (1399)، مدل‌سازی متغیر زمانی نسبت بهینه پوشش ریسک با استفاده از قراردادهای آتی: رهیافت ترکیبی توابع کاپولای زوجی و تجزیه موجک، چشم‌انداز مدیریت مالی، دوره 10، شماره 30


• فرهادیان، علی و نیلچی، مسلم (1401). سرریز تلاطمی بازار نفت در بازار سهام با الگوی نوسانات تصادفی چند متغیره بیزی، دانش سرمایه‌گذاری،11(43)،129-148.


• مرادی، مهدی، صدوقی یزدی،‌هادی، عبدالهیان، جواد (1394)، رویکرد مهندسی جدید برای پیش‌بینی نوسان شاخص‌های بورس اوراق بهادار تهران، مجله پیشرفت‌های حسابداری دانشگاه شیراز، دوره هفتم، شماره دوم


• Billio, M., Casarin, R., & Osuntuyi, A. (2016). Efficient Gibbs sampling for Markov switching GARCH models. Computational Statistics & Data Analysis, 100, 37-57.


• Bladt, Martin., McNeil, Alexander.j (2021), Time series copula models using d-vines and v-transforms, Econometrics and Statistics, In Press, Corrected Proof


• Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327.


• Brix, A., Lunde, A., & Wei, W. (2018). A generalized Schwartz model for energy spot prices — Estimation using a particle MCMC method. Energy Economics, 72, 560-582.


• Chan, J. (2015). The stochastic volatility in mean model with time-varying parameters: an application to inflation modeling. Journal of Business & Economic Statistics, 35(1), 17-28.


• Chan, J., & Grant, A. (2016). Modeling energy price dynamics: GARCH versus stochastic volatility. Energy Economics, 54, 182-189.


• Chen, X., Fan, Y., 2006. Estimation of copula-based semiparametric time series models. Econ. 130 (2), 307–335.


• Diebold, F., Schorfheide, F., & Shin, M. (2017). Real-time forecast evaluation of DSGE models with stochastic volatility. NBER Working Paper Series, working paper 22615.


• Doucet, A., Pitt, M., Deligianndis, G., & Kohn, R. (2015). Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator. Biometrika, 102(2), 295-313.


• Engle, R., Ito, T. and Lin, W., (1990). Meteor showers or heat waves? het- eroscedasticity intra-daily volatility in the foreign exchange markets. Econo- metrica, 58, 525-542.


• Figlewski, S. (1997). Forecasting volatility. Financial Markets, Institutions and Instruments, 6, 1-88.


• Gatheral, J., Jaisson, T., & Rosenbaum, M. (2018). Volatility is rough. Quantitative Finance, 18(6), 933-949.


• Glosten, L., Jagannathan, R., & Runkle, D. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779-1801.


• Jacquier, E., Polson, N., & Rossi, P. (1994). Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics, 12, 371-417.


• Kastner, G., Fruhwirth-Schnatter, S., & Lopes, H. (2017). Efficient Bayesian inference for multivariate factor stochastic volatility models. Journal of Computational and Graphical Statistics, 26(4), 905- 917.


• Kim, J., Jung, H., & Qin, L. (2016). Linear time-varying regression with a DCC-GARCH model for volatility. Applied Economics, 48(17), 1573-1582.


• Kim, J., Park, Y., & Ryu, D. (2017). Stochastic volatility of the futures prices of emission allowances: A Bayesian approach. Physica A: Statistical Mechanics and its Applications, 465, 714-724.


• Kim, S., Shephard, N., & Chib, S. (1998). Stochastic volatility: likelihood inference and comparison with ARCH models. The Review of Economic Studies, 65(3), 361-393.


• Klein, T., & Walther, T. (2016). Oil price volatility forecast with mixture memory GARCH. Energy Economics, 58, 46-58.


• Kristjanpoller, W., & Minutolo, M. (2016). Forecasting volatility of oil price using an Artificial Neural Network-GARCH model. Expert Systems With Applications, 65, 233-241.


• Lin, L., Liu, K., & Sloan, A. (2000). A noisy Monte Carlo algorithm. Physical Review D, 61. https://doi.org/10.1103/PhysRevD.61.074505


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


• Patton, A., & Sheppard, K. (2015). Good volatility, bad volatility: signed jumps and the persistence of volatility. Review of Economics and Statistics, 97(3), 683-697.


• Pinho, F., & Couto, R. (2017). Comparing volatility forecasting models during the global financial crisis. Communications in Statistics - Simulation and Computation, 46(7), 5257-5270.


• Pinho, F., Franco, G., & Silva, R. (2016). Modeling volatility using state space models with heavy tailed distributions. Mathematics and Computers in Simulation, 119, 108-127.


• Pitt, M. K., Shephard, N. (1999). Filtering via simulation: Auxiliary particle filters. Journal of the American statistical Association, 94(446), 590-599.


• Ravenzwaaij, D., Cassey, P., & Brown, S. (2018). A simple introduction to Markov Chain Monte–Carlo sampling. Download PDF Psychonomic Bulletin & Review, 25(1), 143-154.


• Roberts, G., & Rosenthal, S. (2009). Examples of Adaptive MCMC. Journal of Computational and Graphical Statistics, 18(2), 349-367.


• Salimans, T., Kingma, D., & Welling, M. (2015). Markov Chain Monte Carlo and variational inference: bridging the gap. JMLR Workshop and Conference Proceedings, 37, 1218-1226.


• Sentana, E. (1995). Quadratic ARCH models: A potential reinterpretation of ARCH models as second-order Taylor approximations. Unpublished paper (London School of Economics).


• Mitra (2020), Downside risk measurement in regime switching stochastic volatility, Journal of Computational and Applied Mathematics (2020), doi: https://doi.org/10.1016/j.cam.2020.112845


• Takaishi T. (2009) An Adaptive Markov Chain Monte Carlo Method for GARCH Model. In: Zhou J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02469-6_22


• Taylor, S. J., (1982). Financial returns modelled by the product of two stochastic. Processes a study of daily sugar prices 1961-75, In Anderson, O. O., Time series Analysis: Theory and practice (1, 203-226, North-Holland: Amsterdom).


• Trucios, C., & Hotta, L. (2016). Bootstrap prediction in univariate volatility models with leverage effect. Mathematics and Computers in Simulation, 120, 91-103.


• Virbickaite, A., Ausín, M.C., & Galeano, P. (2020). Copula stochastic volatility in oil returns: Approximate Bayesian computation with volatility prediction. Energy Economics, 92, 104961.


• Yao, Y., Zhai, J., Cao, Y., Ding, X., Liu, Y., & Luo, Y. (2017). Data analytics enhanced component volatility model. Expert Systems With Applications, 84, 232-241.