Modeling Price Dynamics and Risk Forecasting in Tehran Stock Exchange Market: Nonlinear and Non-gaussian Models of Stochastic Volatility

Document Type : Research Paper

Authors

1 Ph.D. Candidate, Department of Financial Engineering, Yazd University, Yazd, Iran.

2 Associate Prof., Department of Accounting and Finance, Yazd University, Yazd, Iran.

Abstract

Objective: The daily observations of the total index of the Tehran Stock Exchange show that in the last few years, stock prices have been very volatile. This volatility can harm the economic environment of Iran. Modeling and predicting price volatility in this market can provide important information about uncertainty and risk to actors and thus help with managing possible unwanted changes in the field of financial investments. This, along with the rise in the value of the stock market in recent years, has caused the investigation of the issue of volatility to become increasingly popular among academicians and financial policymakers. Volatility and risk measurements are essential parameters in risk management programs and can affect a country’s economic activity and public confidence. These are also key parameters in studies that examine the relationship between the stock market, economic growth, and other financial variables. Tehran Stock Exchange markets have been volatile in recent years. Controlling the negative effects caused by stock price volatility has made it necessary to predict and model price dynamics for participants in this market.
Methods: In this paper, the class of Parameter-Driven volatility models (stochastic volatility models) is used to predict the price volatility and calculate the risk of the price index in the Tehran stock market. Therefore, four stochastic volatility models were used. To make a comprehensive review, the asymmetry in the volatility (leverage effect) and the heavy tail of the stock price return distribution (with t- student distribution and Skew normal) have been included in the models. To estimate the models, the Gibbs sampling method was used, and to accurately compare the models, the test based on the posterior distribution of the models and the Bayesian factor was used.
Results: The results indicated that the canonical stochastic volatility model with Skew normal distribution (SNSV) is more effective than other stochastic volatility models in predicting the price of stock market volatility based on the Bayesian factor. Therefore, to analyze stock market risks using stochastic volatility models, there is no need to include the leverage effect in the state space of the Volatility equation.
Conclusion: The SNSV model makes it possible to observe volatility and make predictions related to it, thereby improving market transparency and ultimately making diversification and risk management easier to implement. Also, the backtests of VaR and CVaR market risk assessment using Kupiec and DQ tests do not show evidence that the estimation is over or under the risk limit. As a result, the calculation of volatility and pricing with this model will lead to more precision risk management for professionals, especially fund managers who intend to include Tehran Stock Exchange stocks for asset allocation.

Keywords

Main Subjects

References

 
Agbeyegbe, T. D. (2022). Modeling JSE Stock Returns Dynamics: GARCH Versus Stochastic Volatility. The Journal of Developing Areas, 56(1), 175-191.
Ardia, D., & Hoogerheide, L. F. (2010). Bayesian estimation of the garch (1, 1) model with student-t innovations. The R Journal, 2(2), 41-47.
Artzner, P., Delbaen, F., Eber, J. M., & Heath, D. (1997). Thinking coherently. Risk, 10. November, 68, 71.
Behzadi, A. (2021). Portfolio Risk Measurement with Asymmetric Tail Dependence in Tehran Stock Exchange. Financial Research Journal, 22(4), 542-567. (in Persian)
Bentes, S. R. (2021). How COVID-19 has affected stock market persistence? Evidence from the G7’s. Physica A: Statistical Mechanics and its Applications, 581, 126210.
Berg, A., Meyer, R., & Yu, J. (2004). Deviance information criterion for comparing stochastic volatility models. Journal of Business & Economic Statistics, 22(1), 107-120.
Berger, J. (2006). The case for objective Bayesian analysis. Bayesian analysis, 1(3), 385-402.
Chan, J. C., & Grant, A. L. (2016). Modeling energy price dynamics: GARCH versus stochastic volatility. Energy Economics, 54, 182-189.
Chen, L., Zerilli, P., & Baum, C. F. (2019). Leverage effects and stochastic volatility in spot oil returns: A Bayesian approach with VaR and CVaR applications. Energy Economics, 79, 111-129.
Chib, S., Nardari, F., & Shephard, N. (2002). Markov chain Monte Carlo methods for stochastic volatility models. Journal of Econometrics, 108(2), 281-316.
Choy, B., Wan, W. Y., & Chan, C. M. (2009). Bayesian student-t stochastic volatility models via scale mixtures. Wai Yin and Chan, Chun Man, Bayesian Student-T Stochastic Volatility Models Via Scale Mixtures (August 18, 2009).
Cox, D. R., Gudmundsson, G., Lindgren, G., Bondesson, L., Harsaae, E., Laake, P., ... & Lauritzen, S. L. (1981). Statistical analysis of time series: Some recent developments [with discussion and reply]. Scandinavian Journal of Statistics, 93-115.
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the econometric society, 987-1007.
Engle, R. F., & Manganelli, S. (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of business & economic statistics, 22(4), 367-381.
Evgenidis, A. (2018). Do all oil price shocks have the same impact? Evidence from the euro area. Finance Research Letters, 26, 150-155.
Farhadian, A., Rostami, M., & Nilchi, M. (2020). Compare Canonical stochastic volatility model of focal MSGJR-GARCH to measure the volatility of stock returns and calculating VaR. Journal of Financial Management Perspective, 10(32), 131-158. (in Persian)
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). third. Bayesian data analysis.
Hansen, P. R., Huang, Z., & Shek, H. H. (2012). Realized GARCH: a joint model for returns and realized measures of volatility, Journal of Applied Econometrics, 27(6), 877-906.
Harvey, A.C., Ruiz, E. and Shephard, N. (1994). Multivariate stochastic variance models. Review of Economic Studies, 61, 247–264.
Hull, J., and White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281–300.
Koop, G. (2003). Bayesian Econometrics. Wiley & Sons, New York.
Koopman, S. J., Lucas, A., & Scharth, M. (2016). Predicting time-varying parameters with parameter-driven and observation-driven models. Review of Economics and Statistics, 98(1), 97-110.
Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models (Vol. 95, No. 24). Division of Research and Statistics, Division of Monetary Affairs, Federal Reserve Board.
Lenk, P. J., & DeSarbo, W. S. (2000). Bayesian inference for finite mixtures of generalized linear models with random effects. Psychometrika, 65(1), 93-119.
Li, Y., & Yu, J. (2012). Bayesian hypothesis testing in latent variable models. Journal of Econometrics, 166(2), 237-246.
Markowitz, H. (1952). The utility of wealth. Journal of political Economy, 60(2), 151-158.
Meyer, R. and Yu, J. (2000). BUGS for a Bayesian analysis of stochastic volatility models. Econometrics Journal, 3, 198–215.
Najafi, A. A., Nopour, K., & Ghatarani, A. (2017). Interval Optimization In Portfolio Selection with Conditional Value At Risk. Financial Research Journal, 19(1), 157-172.
(in Persian) doi: 10.22059/jfr.2017.132312.1006053
Nakajima, J., & Omori, Y. (2009). Leverage, heavy-tails and correlated jumps in stochastic volatility models. Computational Statistics & Data Analysis, 53(6), 2335-2353.
Oyuna, D., & Yaobin, L. (2021). Forecasting the Crude oil Prices Volatility with Stochastic Volatility Models. Sage Open, 11(3), 21582440211026269.
Phelan, M. J. (1997). Probability and statistics applied to the practice of financial risk management: The case of JP Morgan's RiskMetrics™. Journal of Financial Services Research, 12(2), 175-200.
Poon, S. H. (2005). A practical guide to forecasting financial market volatility. John Wiley & Sons.
Poterba, J. M., & Summers, L. H. (1988). Mean reversion in stock prices: Evidence and implications. Journal of financial economics, 22(1), 27-59.
Raei, R., Basakha, H., & Mahdikhah, H. (2020). Equity Portfolio Optimization Using Mean-CVaR Method Considering Symmetric and Asymmetric Autoregressive Conditional Heteroscedasticity. Financial Research Journal, 22(2), 149-159. (in Persian)
Rastegar, M. A., & Hemati, M. (2022). Sensitivity Analysis of Two-Step Multinomial Backtests for Evaluating Value-at-Risk. Financial Research Journal, 23(4), 523-544. (in Persian)
Saranj, A., & Nourahmadii, M. (2016). Estimating of value at risk and expected shortfall by using conditional extreme value approach in Tehran Securities Exchange. Financial Research Journal, 18(3), 437-460. doi: 10.22059/jfr.2016.62450 (in Persian)
Sharpe, W. F. (1966). Mutual fund performance. The Journal of business, 39(1), 119-138.
Shephard, N. (Ed.). (2005). Stochastic volatility: selected readings. Oxford University Press on Demand.
Tanner, M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation. Journal of the American statistical Association, 82(398), 528-540.
Taylor, S.J (1986). Modelling Financial Time Series. John Wiley, New York.
Tiwari, A. K., Kumar, S., & Pathak, R. (2019). Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models. Applied Economics, 51(37), 4073-4082.
Tobin, J. (1958). Liquidity preference as behavior towards risk. The review of economic studies, 25(2), 65-86.
Tsay, R. S. (2012). An introduction to analysis of financial data with R. John Wiley & Sons.
Yong, L., & Zhang, J. (2014). Bayesian testing for jumps in stochastic volatility models with correlated jumps. Quantitative Finance, 14(10), 1693-1700.
Financial Research Journal
Volume 25, Issue 2
2023
Pages 275-299

Files

Share

How to cite

Statistics