Oil Price estimating Under Dynamic Economic Models Using Markov Chain Monte Carlo Simulation Approach

Document Type : Research Paper


1 Department of Statistics, Islamic Azad University, North branch, Tehran, Iran,

2 Department of Accounting & AMP; Management, Shahriyar Branch, Islamic Azad University, Shahriyar, Iran

3 Faculty of Social Sciences & AMP; Economics, Alzahra University, Thehrn, Iran



This study, attempts to estimate and compare four different models of jump-diffusion class combined with stochastic volatility that are based on stochastic differential equations, and their parameters latent variables are estimated by Markov chain Monte Carlo (MCMC) methods. In the Stochastic Volatility with Correlated Jumps (SVCJ) model, volatilities are scholastic, and the term jump is added to both scholastic prices and volatilities. The results of this study showed that this model is more efficient than the others are, as it provides a significantly better fit to the data, and therefore, corrects the shortcomings of the previous models and that it is closer to the actual market prices. Therefore, our estimating model under the Monte Carlo simulation allows an analysis on oil prices during certain times in the periods of tension and shock in the oil market


[1] Alquist, R., Kilian, L., Vigfusson, R.J., Forecasting the Price of Oil. In G. Elliot and A. Timmersmann (ed.), Handbook of Economic Forecasting, Amsterdam: North Holland, 2013, 2, P. 427-507.
[2] Agah, M., Malekpoor, H., Bagheri, A., Investigating the Effect of Financial Constraints and Different Levels of Agency Cost on Investment Efficiency. Advances in Mathematical Finance and Applications, 2017, 2(4), P. 31-47. Doi: 10.22034/amfa.2017.536264
[3] Ahmadi, R., Kordloei, H., The Effect of Financial Distress on the Investment Behavior of Companies Listed on Tehran Stock ExchangeAdvances in Mathematical Finance and Applications, 2018, 3(4), P. 17-28. Doi: 10.22034/amfa.2019.565459.1108
[4] Bates, D.S., Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options. Review of Financial Studies,1996, 9, P. 69–107. Doi: 10.3386/w4596.
[5] Barsky, R.B., Kilian, L., Do We Really Know that Oil Caused the Great Stagflation? A Monetary Alternative. In B.S. Bernanke and K. Rogoff (ed.) NBER Macroeconomics Annual, Cambridge: MIT Press., 2001, 16, P. 137-183.
[6] Barsky, R.B., Kilian, L., Oil and the Macroeconomy since the 1970s. Journal of Economic Perspectives, 2004, 18(4), P. 115-134.
[7] Black, F., Studies of Stock Price Volatility Changes. Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economics Statistics Section, 1976, P. 177-181.
[8] Black, F., Scholes, M., The Pricing of Options and Corporate Liabilities, Journal of Political Economy, Published By: The University of Chicago Press, 1973, 81(3), P. 637-654, https://www.jstor.org/stable/1831029
[9] Kilian, L., The Economic Effects of Energy Price Shocks. Journal of Economic Literature, 2008, 46(4), P. 871-909.
[10] Baumeister, C., Kilian, L., Fourty Years of Oil Price Fluctuations: Why the Price of Oil May Still Surprise Us. Journal of Economic Perspectives, 2016, 30(1), P. 139-160.
[11] Baumeister, C., Kilian, L., Understanding the Decline in the Price of Oil since June 2014. Journal of the Association of Environmental and Resource Economics, 2016, 3(1), P. 131-158.
[12] Baumeister, C., Kilian, L., Real-Time Forecasts of the Real Price of Oil. Journal of Business and Economic Statistics, 2012, 30, P. 326-336.
[13] Baumeister, C., Kilian, L., Real-Time Analysis of Oil Price Risks using Forecast Scenarios. IMF Economic Review, 2014, 62, P. 119-145.
[14] Chib, S., Greenberg, E., Markov Chain Monte Carlo Simulation Methods in Econometrics. Econometric Theory,1996, 12(3), P. 409-431. Doi: 10.1017/S0266466600006794.
[15] Dibachi, H., Behzadi, M.H., Izadikhah, M., Stochastic Modified MAJ Model for Measuring the Efficiency and Ranking of DMUs, Indian Journal of Science and Technology, 2015, 8(8), P. 1-7, Doi: 10.17485/ijst/2015/v8iS8/71505
[16] Economou, A., Agnolucci, P., Fattouh, B., De Lipis, V.,  A Structural Model of the World Oil Market: The Role of Investment Dynamics and Capacity Constraints in Explaining the Evolution of the Real Price of Oil Andreas, OIES PAPER: WPM 75,  Oxford Institute for Energy Studies, Registered Charity, 2017, 286084, P. 1-40.
[17] Estévez, G., Infante, S., Sáez, F., Estimation of general equilibrium model in dynamic economies using Markov Chain Monte Carlo methods. Rev. Mate. Teor. Aplic, 2012, 19(1), P. 7–36. Doi: 10.15517/rmta.v19i1.2102.
[18] Eraker, B., Do stock prices and volatility jump? Reconciling evidence from spot and option prices. The Journal of Finance, 2004, 59 (3), P. 1367–1403.
[19] Garcı́a, D., Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule. Journal of Economic Dynamics and Control, 2003, 27(10), P. 1855-1879. Doi: 10.1016/S0165-1889(02)00086-6.
[20] Hamilton, J. D., Understanding Crude Oil Prices. The Energy Journal, 2009, 30(2), P. 179-206.
[21] Heston, S.L., A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 1993, 6, P. 327–343. Doi: 10.1093/rfs/6.2.327
[22] Hong, H., Bian, Z., Chen, N., Leverage effect on stochastic volatility for option pricing in Hong Kong: A simulation and empirical study. The North American Journal of Economics and Finance, 2019, 100925.
[23] Huntington, H., Al-Fattah, S., Huang, Z., Gucwa, M., Nouri, A., Oil Markets and Price Movements: A Survey of Models, USAEE Working Paper No. 13-129, 2013, Doi: 10.2139/ssrn.2277330.
[24] Izadikhah, M., Khoshroo, A., Energy management in crop production using a novel fuzzy data envelopment analysis model, RAIRO-Oper. Res., 2018, 52 (2), P. 595-617, Doi: 10.1051/ro/2017082
[25] Izadikhah, M., Farzipoor Saen, R., Ranking sustainable suppliers by context-dependent data envelopment analysis. Ann Oper Res, 2020, 293, P.607–637, Doi: 10.1007/s10479-019-03370-4
[26] Karbasi Yazdi, H., Mohammadian, M., Effect of Profitability Indices on the Capital Structure of Listed Companies in Tehran Stock Exchange. Advances in Mathematical Finance and Applications, 2017, 2(3), P. 1-11. Doi: 10.22034/amfa.2017.533085
[27] Kilian, L., The Economic Effects of Energy Price Shocks. Journal of Economic Literature, 2008, 46(4), P. 871-909.
[28] Kilian, L., Oil Price Shocks: Causes and Consequences. Annual Review of Resource Economics, 2014, 6(2014), P. 133-154.
[29] Kim, J., Park, Y.J., Ryu, D., Stochastic volatility of the futures prices of emission allowances: A Bayesian approach, Physica A, 2017, 465 (2017), P. 714–724.
[30] Lian., L., Szu-Lang., C., Jun, H., State-dependent jump risks for American gold futures option pricing. The North American Journal of Economics and Finance, 2015, 1(1), 33, P. 115-133. Doi:  10.1016/j.najef.2015.04.001.
[31] Li, D., Clements,  A.,  Drovandi, C., Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo. Econometrics and Statistics, 2020, Doi: 10.1016/j.ecosta.2020.02.002.
[32] Le Sage, J.P., Chih, Y-Y., Vance, C., Markov chain Monte Carlo estimation of spatial dynamic panel models for large samples, Computational Statistics & Data Analysis, 2019, 138, P. 107-125. Doi: 10.1016/j.csda.2019.04.003.
[33] Longstaff, F.A., Schwartz, E.S., Valuing American options by simulation: A simple least-squares approach. Review of Financial Studies, 2001, 14, P. 113–147. Doi: 10.1093/rfs/14.1.113.
[34] Lux, T., Estimation of agent-based models using sequential Monte Carlo methods. Journal of Economic Dynamics and Control, 2018, 91, P. 391-408. Doi: 10.1016/j.jedc.2018.01.021
[35] Ma, J.,  Li, W., Zheng, H., Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model.  European Journal of Operational Research, 2020, 280(2), P. 428-440. Doi: 10.1016/j.ejor.2019.07.041.
[36] Merton, R.C., Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 1976, 3, P. 124–144. Doi: 10.1016/0304-405X(76)90022-2.
[37] Cox, J.C., Ingersoll, Jr. J.E., Ross, S., A theory of the term structure of interest rates, Econometrica, 1985, 53(2), P. 385-407, Doi: 10.2307/1911242, https://www.jstor.org/stable/1911242
[38] Rezaei, N., Elmi, Z., Behavioral Finance Models and Behavioral Biases in Stock Price Forecasting. Advances in Mathematical Finance and Applications, 2018, 3(4), P. 67-82. Doi: 10.22034/amfa.2019.576127.1118
[39] Shao, J., Papaioannou, D.A., Pantelousbc , A.A., Pricing and simulating catastrophe risk bonds in a Markov-dependent environment. Applied Mathematics and Computation, 2017, 309(15), P. 68-84. Doi: 10.1016/j.amc.2017.03.041
[40] Tone, K., Toloo, M., Izadikhah, M., A modified slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research, 2020, 287 (2), P. 560-571, Doi: 10.1016/j.ejor.2020.04.019.