Modeling the Daily Volatility of Oil, Gold, Dollar, Bitcoin and Iranian Stock Markets: An Empirical Application of a Nonlinear Space State Model

Document Type : Research Paper


Faculty of Economics, Allameh Tabataba’i University, Tehran, Iran.


Using the daily data of returns of 9 assets during the period from 04/29/2013 to 09/20/2021, the volatilities of different asset markets were modeled in this paper. The multivariate factor stochastic volatility model (MFSV) under the nonlinear space-state approach provides the basis for decomposing asset return volatility into two components, “volatility rooted in latent factors” and “idiosyncratic volatility”, and for estimating the time-varying pairwise correlation of time series. The results show: First, there are three latent factors so that the volatility of returns of five Iranian stock markets is affected by the first and third hidden factors, while the volatility of the other four international markets is mainly affected by the second latent factor. Second, the idiosyncratic volatility of the different Iranian stock returns exhibits clustering behavior, and there is a relatively strong correlation among them. Third, the volatility of oil returns is explained by the hidden factors, and consequently their idiosyncratic volatility is almost smooth. Fourth, the correlations between the return volatility of bitcoin and the volatilities of other conventional assets are negligible. The results of this paper may be useful for future research on investment opportunities and risk-return characteristics of portfolios.


Main Subjects

Abounoori, E., Noferesti, M., & Tour, M. (2020). Asymmetric Effects of Volatility in Iran and UAE Stock Market. Financial Engineering and Securities Management, 11(43), 57-75 (In Persian).
Abounoori, E., & Moutameni, M. (2008). Analysis of Volatility Feedback in Tehran Stock Exchange. Economic Research Review, 7(27), 247-261 (In Persian).
---------- (2007). Simultaneous Effects of Leverage and Volatility Feedback in Tehran Stock Exchange. Economic Research, 76, 101-117 (In Persian).
Al-Yahyaee, K., Rehman, M., Mensi, W., & Al-Jarrah, I. (2019). Can Uncertainty Indices Predict Bitcoin Prices? A Revisited Analysis Using Partial and Multivariate Wavelet Approaches. The North American Journal of Economics and Finance, 49, 47-56.
Aguilar, O., & West, M. (2000). Bayesian Dynamic Factor Models and Portfolio Allocation. Journal of Business and Economic Statistics, 18(3), 338-357.
Arbabi, F. (2018). A Prediction of Gold Coin Returns Volatility on Financial Market (ANN GARCH Approach). Financial Economics, 12(43), 179-192 (In Persian).
Aslanidis, N., Bariviera, A. F., & Martinez-Ibanez, O. (2019). An Analysis of Cryptocurrencies Conditional Cross Correlations. Financial Research Letters, 31(3), 130-137.
Baumohl, E. (2019). Are Cryptocurrencies Connected to Forex? A Quantile Cross-Spectral Approach. Financial Research Letters, 29, 363-372.
Bollerslev, T. (1986). Generalized Autoregressive Conditional Hetroskedasticity. Journal of Econometrics, 31(3), 307-327.
Boss, C. S. (2012). Relating Stochastic Volatility Estimation Methods. In Bauweans, L., Hafner, C., & Laurent, S. (Eds.), Handbook of Volatility Model and Their Applications. New Jersey: John Wiley & Sons.
Botshekan, M. H., & Mohseni, H. (2018). Investigation Volatility Spillovers between Oil Market and Stock Index Return. Investment Knowledge, 7(25), 267-284 (In Persian).
Bouri, E., Azzi, G., & Dyhrberg, A. H. (2017). On the Return-Volatility Relationship in the Bitcoin Market around the Price Crash of 2013. Economics: The Open-Access, Open Assessment E-Journal, 11, 1-16.
Calvo, S., & Reinhart, C. M. (1996). Capital Flows to Latin America: Is There Evidence of Contagion Effects? In A. Guillermo, S. Calvo, M. Goldstein, and E. Hochreiter (Eds.), Private Capital Flow to Emerging Markets after the Mexican Crisis. Washington, DC: Institute for International Economics.
Caporale, G. M., & Zekokh, T. (2019). Modelling Volatility of Cryptocurrencies Using Markov-Switching GARCH Models. Research in International Business and Finance, 48, 143155.
Catania, L., & Grassi, S. (2017). Modeling Cryptocurrencies Financial Time-Series. CEIS Working Paper, 417, 1-28.
Catania, L., Grassi, S., & Ravazzolo, F. (2018). Predicting the Volatility of Cryptocurrency Time-Series. CAMP Working Paper Series, 3, 1-20.
Charle, A., & Darne-Lemna, O. (2018). Volatility Estimation for Bitcoin: Replication and Robustness. International Economics, 157, 23-32.
Charfeddine, L., & Maouchi, Y. (2018). Are Shocks on the Returns and Volatility of Cryptocurrencies Really Persistent? Finance Research Letters, 28, 423-430.
Cheong, C. W., Lai, N. S., Isa, Z., & Nor, A. H. (2012). Asymmetry Dynamic Volatility Forecast Evaluations Using Interday and Intraday Data. Sains Malaysiana, 14(10), 128-135.
Chib, S., Nardari, F., & Shephard, N. (2006). Analysis of High Dimensional Multivariate Stochastic Volatility Models. Journal of Econometrics, 134(2), 341–371.
Chu, J., Chan, S., Nadarajah, S., & Osterrieder, J. (2017). GARCH Modeling of Cryptocurrencies. Journal of Risk and Financial Management, 10(4), 1-15.
Classens, S., & Forbes, K. (2004). International Financial Contagion: The Theory, Evidence and Policy Implications. The IMF’s Role in Emerging Market Economies: Reassessing the Adequacy of its Resources, U.S. Council of Economic Advisors.
Conard, C., Custovic, A., & Ghysels, E. (2018). Long- and Short-Term Cryptocurrency Volatility Components: A GARCH-MIDAS Analysis. Journal of Risk and Financial Management, 11(2), 1-12.
Corbet, S., Meegan, A., Larkin, C., Lucey, B., & Yarovaya, L. (2018). Exploring the Dynamic Relationships between Cryptocurrencies and Other Financial Assets. Economics Letters, 165, 28 34.
Dornbusch, R., Park, Y., & Claessens, S. (2000). Contagion Understanding How It Spreads. The World Bank Research Observer, 15, 177-197.
Engle, R. F. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007.
Esposti, R. (2021). On the Long-Term Common Movement of Resource and Commodity Price, a Methodological Proposal. Resource Policy, 72, 102-110.
Fakhfekh, M., & Jeribi, A. (2020). Volatility Dynamics of Cryptocurrencies’ Returns: Evidence from Asymmetric and Long Memory GARCH Models. Research in International Business and Finance, 51, 101-175.
Fallahi, F., Haghighat, J., Sanoubar, N., & Jahangiri, Kh. (2014). Study of Correlation between Volatility of Stock, Exchange and Gold Coin Markets in Iran with DCC-GARCH Model. Journal of Economic Research, 14(1), 123-147 (In Persian).
Fattahi, Sh., Khanzadi, A., & Nafisi Moghadam, M. (2017). Forecasting Stock Return Volatility for the Tehran Stock Exchange by Algorithm MCMC and Metropolis-Hasting Approach. Financial Knowledge of Security Analysis, 9(32), 79-94 (In Persian).
Ghazi Fini, S. R., & Panahian, H. (2019). Forecasting and Modeling Stock Returns Volatility in Tehran Stock Exchange Using GARCH Models. Journal of Accounting and Auditing Researches, 11(43), 55-70 (In Persian).
Han, Y. (2006). Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model. Review of Financial Studies, 19(1), 237-271.
Harvey, A. C., Ruiz, E., & Shephard, N. (1994). Multivariate Stochastic Variance Models. The Review of Economic Studies, 61(2), 247–264.
Heidari, H., Sanginabadi, B., Almasi, S., & Nassirzadeh, F. (2012). The Effects of Anticipated and Unanticipated Stock Return Volatility on Stock Return of Automobile Manufacturing Industries in Tehran Stock Market. Financial Knowledge of Securities Analysis, 19(4), 163-190 (In Persian).
Hosseini Nasab, E., Khezri, M., & Rasoli, A. (2011). Assessing the Effects of Oil Price Shocks Exchange Stock Returns: Using Wavelet Decomposition and Markov Switching. Energy Economics Review, 8(29), 30-60 (In Persian).
Hosseinioun, N., Behnami, M., & Ebrahimi Salari, T. (2016). Volatility Transmission of the Rate of Returns in Iranian Stock, Gold and Foreign Currency Markets. Iranian Economic Research, 21(66), 123-150 (In Persian).
Hosszenjni, D., & Kastner, G. (2021). Modeling Univariate and Multivariate Stochastic Volatility in R with Stochvol and Factorstochvol. Journal of Statistical Software, 100(12), 1-34.
Jahangiri, Kh., & Hekmati Fard, S. (2015). The Study of Volatility Spillover Effects between Stock, Gold, Oil and Currency Markets. Economic Research Review, 15(56), 159-192 (In Persian).
Jaroenwlryakul, S., & Tanomchat, W. (2020). Exploring the Dynamic Relationships between Cryptocurrencies and Stock Markets in the Asean-5. Journal of Economics and Management Strategy, 7(1), 129-144.
Karimi, M., Sarraf, F., Emam Verdi, Gh., & Baghani, A. (2020). Dynamic Conditional Correlation of Oil Prices and Stock Markets Volatilities in Persian Gulf Countries, Focusing on Effect of Financial Crisis Contagion. Journal of Financial Economics, 13, 101-130 (In Persian).
Kashanitabar, Sh., Rahnamaroodposhti, F., Fallah, M., Chirani, E., & Zmorodian, Gh. (2020). Prediction of Stock Price Bubble in Tehran Stock Exchange (Conditional Volatility Approach). Financial Engineering and Portfolio Management, 11(4), 328-349 (In Persian).
Kastner, G. (2016). Dealing with Stochastic Volatility in Time Series Using the R Package Stochvol. Journal of Statistical Software, 69(5), 1-30.
Kastner, G., Fruhwirth-Schnatter, S., & Lopes, H. F. (2017). Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Model. Journal of Computational and Graphical Statistics, 26(4), 905-917.
Kastner, G. (2019). Spare Bayesian Time-Varying Covariance Estimation in Many Dimensions. Journal of Econometrics, 210, 98-115.
Kastner, G., & Huber, F. (2020). Sparse Bayesian Vector Autoregressions in Huge Dimensions. Journal of Forecasting, 39(7), 1142-1165.
Katsiampa, P. (2017). Volatility Estimation for Bitcoin: A Comparison of GARCH Models. Economics Letters, 158, 3-6.
Keshavarz Hadded, Gh., & Moftakhar Daryaee, K. (2018). Returns and Volatility Spillover Effects on the Estimated VaR of Gold and Exchange Ratio Portfolio. Journal of Economic Research, 53(1), 117-152 (In Persian).
Keshavarz Hadded, Gh., & Mohammadi, E.. (2016). Does Diversification Reduce Risk in Tehran Stock Market when It Is Volatile? Journal of Economic Research, 53(2), 493-515 (In Persian).
Keshavarz Hadded, Gh., & Heidari, H. (2011).The Impact of Political News on Tehran Stock Exchange (AFIGARCH and MSM) Approach. Journal of Economic Research, 46(1), 111-135 (In Persian).
Keshavarz Hadded, Gh., & Esmaeilzadeh, M. (2010). Time Series Modeling of Volatility Forecasting in the Return of Tehran Cement Share Price. Journal of Economic Research, 45(2), 219-255 (In Persian).
Keshavarz Hadded, Gh., & Samadi, B. (2009). An Appraisal on the Performance of FIGARCH Models in the Estimation of VaR: the Case Study of Tehran Stock Exchange. Journal of Economic Research, 44(1), 193-235 (In Persian).
Khodayari, M. A., Yaghobnejad, A., & Lkalili Araghi, M. (2020). Comparison of the Forecasting of Financial Markets Volatility Using the Regression Model and Neural Network Model. Journal of Financial Economics, 14(52), 223-240 (In Persian).
Kim J. M., Kim S. T., & Kim, S. (2020). On The Relationship of Cryptocurrency Price with US Stock and Gold Price Using Copula Models. Mathematics, 8, 1-15.
Kurka, J. (2019). Do Cryptocurrencies and Traditional Assets Classes Influence Each Other? Finance Research Letters, 31, 38-46.
Lee, D. K. C., Guo, L., & Wang, Y. (2018). Cryptocurrency: A New Investment Opportunity? The Journal of Alternative Investments, 20(3), 16-40.
Liu, W., & Yu, Y. (2019). Comparison of Price Fluctuation Among Domestic and Oversea Oil Shipping Stocks Based on DC-MSV Model. Tongi Daxue Xubao, 47(10), 1528-1532.
Lopes, H. F., & Carvalho, C.M. (2007). Factor Stochastic Volatility with Time Varying Loadings and Markov Switching Regimes. Journal of Statistical Planning and Inference, 137(10), 3082-3091.
Liu, R., Shao, Z., Wei, G., & Wang, W. (2017). GARCH Model with Fat-Tailed Distributions and Bitcoin Exchange Rate Returns. Journal of Accounting, Business and Finance Research, 1(1), 71-75.
Mamalipour, S., & Feli, A. (2016). The Impact of Oil Price Volatility on Tehran Stock Market at Sector-Level: A Variance Decomposition Approach. Monetary and Financial Economics, 24(13), 205-236 (In Persian)
Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.
Moghaddasi, M., Shirinbakhsh, Sh., & Mohammadi, T. (2018). Analyzing Volatility of Tehran Stock Exchange Using MSBVAR-DCC Model. Journal of Financial Management Perspective, 8(22), 97-112 (In Persian).
Nademi, Y., Abounoori, E., & Elmi, Z. (2016). Introducing an Early Warning System for High Volatility in Tehran Stock Exchange: Markov Switching GARCH Approach. Financial Knowledge of Security Analysis, 8(28), 27-40 (In Persian).
Nabavi Chashmi, S.A., & Mokhtarinejad, M. (2017). Comparison Models of Brownian Motion and Fractional Brownian Motion and GARCH in Volatility Estimation of Stock Return. Financial Engineering and Securities Management, 7(29), 25-44 (In Persian).
Naimy, V. Y., & Hayek, M. R. (2018). Modelling and Predicting the Bitcoin Volatility Using GARCH Models. International Journal of Mathematical Modelling and Numerical Optimization, 8(3), 197-215.
Nakajima, J., & West, M. (2013). Dynamic Factor Volatility Modeling: A Bayesian Latent Threshold Approach. Journal of Financial Econometrics, 11(1), 116-153.
Nakajima, J., & Omori, Y. (2009). Leverage, Heavy-Tails and Correlated Jumps in Stochastic Volatility Models. Computational Statistics and Data Analysis, 53(6), 2335-2353.
Nazifi Naeenim M., Fatahi, Sh., & Samadi, S. (2012). Estimating and Forecasting the Volatility of Tehran Stock Market, Using Markov Regime Switching GARCH Models. Journal of Economic Modeling Research, 3(9), 117-141 (In Persian).
Peng, Y., Albuquerque, P. H. M., de Sa, J. M. C., Padula, A. J. A., & Montenegro, M. R. (2018). The Best of Two Worlds: Forecasting High Frequency Volatility for Cryptocurrencies and Traditional Currencies with Support Vector Regression. Expert Systems with Applications, 97, 177-192.
Philipov, A., & Glickman, M. E. (2006). Factor Multivariate Stochastic Volatility via Wishart Processes. Econometric Review, 25(2-3), 311-334.
Poon, S. H., & Granger, W. J. (2003). Forecasting Volatility in Financial Markets: A Review. Journal of Economic Literature, 41(2), 478-539.
Rahim, M. A. A., Zahari, S. M., & Shariff, S. R. (2018). Variance Targeting Estimator for GJR-GARCH under Model’s Misspecification. Sains Malaysiana, 47(9), 2195-2204.
Ranaei Kordsholi, H., Abbasi, A., & Pashootanizadeh, H. (2018). Simulated the Model of the Effects of Alternative Assets Volatility on Overall Index of Tehran Stock Exchange and Housing Prices with Using System Dynamics. Financial Engineering and Securities Management, 8(33), 25-50 (In Persian).
Rasekhy, S., & Khanalipour, A. (2009). Investigation of the an Empirical Analysis of Stock Market’s Fluctuations and Information Efficiency; A Case Study for Tehran Stock Market Demand for Subsidized Food in Urban Areas of Iran, Using AIDS Model for Priority Subsidy Allocation. Iranian Economic Research, 13(40), 29-57 (In Persian).
Rastinfar, A., & Hematfar, M. (2020). Modeling and Predicting Stock Market Volatility using Neural Network and Conditional Variance Patterns. Financial Engineering and Securities Management, 11(43), 451-473 (In Persian).
Rehman, M. M., & Apergis, N. (2019). Determining the Predictive Power between Cryptocurrencies and Real Time Commodity Futures: Evidence from Quantile Causality Tests. Resource Policy, 61, 603-616.
Rezazadeh, R., & Falah, M. (2020). Examining the Overflow of Financial Stress Index Fluctuations of Inflation, Interest Rate, Liquidity and Industry Index Using GARCH-BEKK and VAR Models and Granger Causality. Financial Engineering and Securities Management, 11(42), 272-301 (In Persian).
Sefidbakht, E., & Ranjbar, M. H. (2017). Volatility Spillover between Oil Price, Exchange Rates, Gold Price and Stock Market Indexes with Structural Breaks. Financial Engineering and Securities Management, 8(33), 51-87 (In Persian).
Shi, Y., Tiwari, A. K., Gozgor, G., & Lu, Z. (2020). Correlations among Cryptocurrencies: Evidence from Multivariate Factor Stochastic Volatility Model. Research in International Business and Finance, 53, 101-131.
Shirazian, Z., Nikoomaram, H., Rahnamay Roodposhti, F., & Torabi, T. (2018). Volatility Clustering In Financial Markets with Factor-Based Simulation Model. Financial Engineering and Securities Management, 9(36), 201-224 (In Persian)
Stavroyiannis, S., & Babalos, V. (2017). Dynamic Properties of the Bitcoin and the US Market. SSRN Electronic Journal, 2966998, 1-11.
Tiemoori, B., Emamverdi, Gh., Esmaeeliniya Ketabi, A., & Nessabian, Sh. (2021). The Investigation of Contagion Unanticipated Stocks in Iranian Financial Markets by DFGM Approach. Financial Engineering and Securities Management, 43, 30-56 (In Persian).
Tsay, R. S. (2002). Analysis of Financial Time Series. New Jersey: John Wiley & Sons.
Taylor, J. W. (2001). Smooth Transition Exponential Smoothing. Journal of Forecasting, 23(6), 385-404.
Urquhart, A. (2017). The Volatility of Bitcoin. SSRN Electronic Journal, 2921082, 1-20.
Yamauchi, Y., & Omori, Y. (2020). Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations. Journal of Business and Economic Statistics, 38(4), 839-855.
Zaharieva, M. D., Trade, M., & Wilfling, B. (2020). Bayesian Semiparametric Multivariate Stochastic Volatility with Application. Econometric Review, 39(9), 947-970.
Zhang, J., & Zhuang, Y. M. (2021). Cross-Market Infection Research on Stock Herding Behavior Based on DGC-MSV Models and Bayesian Network. Complexity, 2021, 1-8.
Zhang, J., & Zhuang, Y. M. (2017). Volatility Spillover among USA and Major East Asian Stock Indices Based on Multivariate Stochastic Volatility with Regime-Switching Model. International Conference on Control, Automation and Systems, Jeju: IEEE.
Zhou, X., Nakajima, J., & West, M. (2014). Bayesian Forecasting and Portfolio Decisions Using Dynamic Dependent Sparse Factor Models. International Journal of Forecasting, 30(4), 963-980.