Investigating Mean Reversion Phenomenon and Forecasting Natural Gas Daily Spot Prices Using Ornstein-Uhlenbeck Mean Reverting Model

Document Type : پژوهشی

Authors

• narges salehnia
• Ahmad Seifi
• Mohammad Ali Falahi
• Mohammad hossein Mahdavi Adeli

Ferdowsi University of Mashhad

https://doi.org/10.22067/pm.v25i15.57467

Abstract

Introduction
Economic growth has been tied to the growth of fuels consumption like natural gas. The inherent features of natural gas market like its dependence on wellhead price, long-distance transportation costs, gas pipeline systems, economies of scale, non-existence of monopoly market for the end user, large proportion of fixed costs compared to variable costs, relatively low income elasticities, etc., have created different market structures which affect the price (Khaleghi, 2010; Whitesitt, 2005; Mansour Kiaei, 2008). Moreover, extensive governmental interventions in gas pricing, have led to the adoption of diversified pricing systems so that there is not any global gas price (Jensen, 2011; Vafee Najjar, 2008).
The gas market has experienced dramatic changes that began with the liberalization process of the market in the 1980s, the result of which was the creation of a spot market (Jafari Samimi et al., 2007; Manzoor & Niakan, 2011; Apergis, Bowden, & Payne, 2015). This market determines the opportunities offered by firms and investors, especially the opportunity cost of stagnant assets by price detecting. Hence, spot prices estimation that uses behavioral characteristics like mean reversion can be useful in future prices evolution (Hull, 2000).
In financial economics literature, it is thought that mean reversion is a sign of inefficient market, and it runs counter to the assumption of random walk. Exley, Mehta, & Smith (2004) state that mean reversion is not necessarily a sign of inefficiency in the market. They believe that it could be due to risk aversion or return distribution over time. Since the world's most mobile gas market, which determines the basic price of the gas exchanges in other countries, including Iran, is located in the U.S. Henry Hub, this hub is being mentioned here.
Methodology
Departures from normal price spreads are possible in the short run under abnormal market conditions, but in the long run, supply will be adjusted and the prices will move to the level dictated by the marginal cost of production. The basic theory of microeconomics states that in the long run, the price of an energy commodity must be related to its long-run marginal cost (Begg & Smith, 2007; Rahimi, 2008). In this paper, we analyze mean reversion, which was first described by Vasicek (1977) and was subsequently widely adapted.
Mean reversion is a normal logarithmic diffusion process, but its variance is not proportional to the incremental time intervals. The variance initially grows and then stabilizes in a certain amount (Geman, 2005; Wittig, 2007). This process has contains two components: the first one indicates drift with rate of mean reversion speed and equilibrium long run mean, and the second component of this process is diffusion term and shows its randomness.
Results and Discussion
This paper aims at mean reversion verification, estimating Ornstein-Uhlenbeck Mean Reverting Model (OUMRM) and forecasting gas daily prices based on Henry Hub data (07/01/1997-20/03/2012). Using different mean-reverting statistics like Unit-Root, autocorrelation coefficients reveal that price returns of natural gas prices do not follow a random walk process. Therefore, there can be a sign of mean reversion. The non-decreasing gradual correlation coefficients of returns indicate that the historical information available in long-term lags can be effective in determining future prices like information in the short-term lags.
The results show the existence of mean reversion using the methods of linear regression and maximum likelihood. The long-run mean price is 4.16 $/mmBtu and it takes the market around 48 weeks to remove daily price shocks. Finally, it is observed that performance evaluation criteria are highly dependent on the number of random simulation paths and the best performances are satisfied with 1000 simulation paths mean.
Conclusion
Energy price changes and volatilities have led to an increase in the uncertainty and potential value of predicted prices. Hence, providing models for accurate prediction of natural gas prices with regard to its characteristics like mean reversion is important because it can be applied to determine a wide range of regulatory decisions both on the supply and demand sides of the market. The results of this study is similar to Geman (2007), Skorodumov (2008), Cheong (2009), and Chikibvou and Chinhamu’s (2013) studies and reveas that the existence of the mean reversion phenomenon varies depending on the length of the study period.
Moreover, because of the mobility and transparency of information in gas markets in recent years, as returning to the recent periods, the mean reversion speed becomes higher. It shows higher adjusting speed of mean reversion and faster removal of price distortion caused by shocks. In addition, the more we approach to the recent years, the more long-run mean price is. This implies that investors and traders are expecting a surge in prices and the price volatility in the prices above long-run mean is higher than the prices below it. Therefore, these achievements in determining the behavior of this commodity can lead to a reduction in risk and a great help in predicting the path of the price of long-term contracts.

Keywords

• Natural gas
• spot price
• Mean reversion
• Ornstein-Uhlenbeck Model

References

[1] Apergis, N., Bowden,N. & Payne, J.E. (2015). Downstream Integration of Natural Gas Prices Across U.S. States: Evidence from Deregulation Regime Shifts. Energy Economics, Vol.49, pp. 82-89.

[2] Balvers, R., Wu, Y., & Gilliland, E. (2000). Mean Reversion across National Stock Markets and Parametric Contrarian Investment Strategies. Journal of Finance, Vol. LV, pp. 745-72.

[3] Begg, S., & Smith, N. (2007). Sensitivity of Project Economics to Uncertainty in Type and Parameteres of Oil Price Models. SPE 110812, Annual Technical Conference and Exhibition, Anaheim.

[4] Bessembinder, H., Coughenour, J. F., Seguin, P. J., & Smoller, M. M. (1995). Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure. Journal of Finance, Vol. 50, No. 1, pp. 361-375, Mar.

[5] Bigerna, S., Bollino, A.C., and Polinori, P. (2015). Marginal Cost and Congestion in the Italian Electricity Market: An indirect estimation approach. Energy Policy, Vol. 85, pp. 445–454.

[6] Bjerksund, P. & Ekern, S. (1990). Managing Investment Opportunities Under Price Uncertainty: From "Last Chance" to "Wait and See" Strategies. Financial Management, Vol. 19, No. 3.

[7] Black, F. (1989). Mean Reversion and Consumption Smoothing. NBER Working Paper 2946, April. Also in: Review of Financial Studies 1990. Vol. 3, No. 1, pp. 107-114.

[8] Brock, W. A., Hsieh, D. A., & LeBaron, B. (1991). Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence. MIT Press, Cambridge, MA.

[9] Cao, W. (2010). Pricing Crude Oil Derivatives When Underlying Is a Mean Reverting Levy Process. Electronic copy available at: http://ssrn.com/abstract=170486.

[10] Cechetti, S. G., Lam, P. S., & Mark, N. C. (1990). Mean Reversion in Equilibrium. American Economic Review, Vol. 80, No. 3, pp. 398-418.

[11] Chaterjee, R. (2004). Gas/LNG Contract and Pricing. Gas Pricing Workshop at Institute for International Energy Studies (IIES), Tehran.

[12] Cheong, C.W. (2009). Modeling and Forecasting Crude Markets Using ARCH-type Models. Energy policy, pp. 2346-2355.

[13] Chikibvu, D., & Chinhamu, K. (2013). Random Walk or Mean Reversion? Empirical Evidence from the Crude Oil Market. Journal of the Turkish Statistical Association, Vol. 6, No. 1, pp. 1-9.

[14] Deng, J. S. (2000). Stochastic Models of Energy Commodity Prices and Their Applications: Mean-Reversion with Jumps and Spikes. University of California Energy Institute, Program on Workable Energy Regulation (POWER). http://www.ucei.berkeley.edu/PDF/pwp073.pdf.

[15] Dixit, R. K. & Pindyck, R. S. (1994). Investment under Uncertainty. Princeton University Press.

[16] EIA: U.S. Department of Energy, Energy Information Administration. (2003). Natural Gas Market Centers and Hubs: A 2003 Update. http://www.eia.doe.gov/pub/oil_gas/natural_gas/feature_articles/2003/market_hubs/mkthubsweb.html. Accessed November 2008.

[17] EIA: U.S. Energy Information Administration. (2011a). Annual Energy Review 2010. Retrieved 02.02, 2012, from: http://205.254.135.7/totalenergy/data/annual/pdf/aer.pdf/07/12/2015.

[18] Energy Charter Secretariat. (2007). Putting a Price on energy. Energy Charter Secretariat.

[19] Esunge, J. N., & Snyder-Beattie, A. (2011). Dissecting Two Approaches to Energy Prices. Journal of Mathematics and Statistics, Vol. 7, No. 2, pp. 98-102.

[20] Exley, J., Mehta, S., & Smith, A. (2004). Mean Reversion. Faculty & Institute of Actuaries, Finance and Investment Conference Brussels, June.

[21] Eydeland, A., & Wolyniec, K. (2003). Energy and Power Risk Management: New Developments in Modeling, Pricing and Hedging. John Wiley & Sons, Hoboken, NJ.

[22] Fama, E., & French, K. (1988). Permanent and Temporary Components of Stock Prices. The Journal of Political Economy, Vol. 96, No. 2, pp. 246–273.

[23] Fleming, J. (1998). The Impact of Energy Derivatives on the Crude Oil Market. Jones School of Management, Rice University, U.S.

[24] Fraser, P., & McKaig, A.G. (1999), Do Investors Expect Mean Reversion in Asset Prices? Journal of Business Finance and Accounting, Vol. 26, No. 1, pp. 57-81.

[25] Geman, H. (2007). Mean Reversion versus Random Walk in Oil and Natural Gas Prices. Advances in Mathematical Finance, Birkhäuser Boston.

[26] Geman, H., & Nguyen, V.N. (2005). Soybean Inventory and Forward Curve Dynamics. Management Science, Vol. 51, pp. 1076–1091.

[27] Gibson, R., & Schwartz, E. S. (1990). Stochastic Convenience Yield and the Pricing of Oil Contingent Claims. The Journal of Finance, Vol. 45, No. 3, pp. 959–976.

[28] Gillespie, D. T. (1996). Exact Numerical Simulation of the Ornstein-Uhlenbeck Process and Its Integral. Physical Review E, Vol. 54, No. 2, pp. 2084–2091.

[29] Griffin, D., & Tversky, A. (1992).The Weighing of Evidence and the Determinants of Confidence. Cognitive Psychology, Vol. 24, pp. 411-435.

[30] Gourieroux, C., & Monfort, A. (2010). Statistics and Econometric Models: General Concepts, Estimation, Prediction and Algorithms (Themes in Modern Econometrics). Vol. 1, Cambridge University Press.

[31] Haesun, P., Mjelde, J.W. and Bessler, D. A. (2008). Price Interactions and Discovery Among Natural Gas Spot Markets in North America. Energy Policy, 2008, Vol. 36, Issue 1, pp. 290-302.

[32] Harvey, C. R. (1995). Predictable Risk and Return in Emerging Markets. Review of Financial Studies, Vol. 8, No. 3, pp. 773-816.

[33] Hassan, K. M., Haque, M., & Lawrence, S. (2006). An Empirical Analysis of Emerging Stock Markets of Europe. Quarterly Journal of Business and Economics, Vol. 45, No. 1 & 2, pp. 31-52.

[34] Hull, J.C. (2000). Options, Futures and other Derivatives. 4th ed., Prentice Hall, NJ.

[35] International Gas Union (IGU). (2009). Price Formation Mechanisms: 2009 Survey. http://www.encharter.org/fileadmin/user_upload/document/Oil_and_Gas_Pricing_2007_ENG.pdf

[36] International Energy Agency(IEA), World Energy Outlook 2015; International Energy Agency: Paris, France, 2015.

[37] Jafari Samimi, A., Baradaran Hashemi, A. & Dehghani, T. (2007). A Model for The Study of the Natural Gas Storage Effect on the Price Volatilities. Tahghighate Eghtesadi, Vol. 76, pp. 119-142. (In Persian)

[38] Jensen, J. T. (2011). Asian Natural Gas Markets Supply Infrastructure and Pricing Issues. The National Bureau of Asian Research, 2011 Pacific Energy Summit: Unlocking the Potential of Natural Gas in the Asia Pacific. http://www.nbr.org/downloads/pdfs/eta/PES_2011_Jensen.pdf

[39] Khaleghi, S. (2005). Methodology of Gas Price Determination in World Market. Collected Studies on Energy Economic 1, 24-37. (In Persian)

[40] Kim, J.H. (2006). Wild Bootstrapping Variance Ratio Tests. Economics Letter, Vol. 92, pp. 38-43.

[41] Kloeden, P. E., & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. Vol. 23, Ed. 1, ISBN: 9783642081071, Publisher: Springer Berlin.

[42] Lari-Lavassani, A., Sadeghi, A. A., & Ware, T. (2001). Modelling and Implementing Mean Reverting Price Processes in Energy Markets. International Energy Credit Association.

[43] Laugthton, D.G., & Jacoby, H. D. (1993). Reversion, Timing Options, and Long-term Decision Making. Financial Management, Vol. 33, pp. 225-240.

[44] Lo, A.W., & Mackinlay, A.C. (1988). Stock Market Prices Do Not Follow Random Walk: Evidence From a Simple Specification Test. Review of Financial Studies, Vol. 1, pp. 41-66.

[45] Lutz, B. (2010). Pricing of Derivatives on Mean -Reverting Assets. Economics and Mathematical Systems, Berlin: Springer-Verlag Berlin Heidelberg Gmbh.

[46] Mansour Kiaei, E. (2008). Estimation Of Long Term Relationship Between Oil And Liquefied Natural Gas Prices Through The Error Correction Model. Quarterly Energy Economics Review, Vol. 5, No. 18, pp. 99-122. (In Persian)

[47] Manzoor, D. & Niakan, L. (2011). Risk Management in Oil & Gas Industry: Necessities and Tools. Iran energy Journal, No. 1, Vol. 15, pp. 1-18. (In Persian)

[48] Metcalf, G. E. & Hasset, K. A. (1995). Investment under Alternative Return Assumptions Comparing Random Walks and Mean Reversion. Journal of Economic Dynamics and Control, Vol.19, November, pp. 1471-1488.

[49] Mobarek, A., & Keasey, K. (2002). Weak-Form Market Efficiency of and Emerging Market: Evidence from Dhaka Stock Market of Bangladesh. [E-document] [Retrieved October 26, 2005] From: http://www.bath.ac.uk/centers/ CDS/Enbs-papers/Mobarek_new.htm.

[50] Mtunya, A. (2010). Modelling Electricity Spot Price Time Series Using Colored Noise Forces. Master Thesis, University of Dares Salaam, Dares Salaam, Tanzania.

[51] Naeem, M. (2010). A Comparison of Electricity Spot Prices Simulation Using ARMA-GARCH and Mean-Reverting Model. Master Thesis, Lappeenranta University of Technology, Lappeenranta, Finland.

[52] Oksendal, B. (2000). Stochastic Differential Equations: An Introduction with Applications. Fifth Edition, Springer-Verlag Heidelberg New York, pp. 1-360.

[53] Önalan, O. (2009). Financial Modelling with Ornstein–Uhlenbeck Processes Driven by Levy Process. Proceedings of the World Congress on Engineering, Vol. 2. http://www.iaeng.org/publication/WCE2009/WCE2009_pp1350-1355.pdf

[54] Phillips, P. C. B., & Yu, J. (2005). Jackknifing Bond Option Prices. The Review of Financial Studies, Vol. 18, No. 2 (Summer), pp. 707-742.

[55] Pilipovic, D. (1998). Energy Risk- Valuing and Managing Energy Derivatives. McGraw-Hill.

[56] Pindyck, R. (2001). The Dynamics of Commodity Spot and Future Markets: A Primer. The Energy Journal, Vol. 22, No. 3, pp. 1–29.

[57] Pindyck, R., & Rubinfeld, D. (1991). Econometric Models & Economic Forecasts. McGraw-Hill, 3rd Ed.

[58] Poshakwale, S. (1996). Evidence on Weak Form Efficiency and Day of the Week Effect in the Indian stock Market. Finance India, Vol. 10, No. 3, pp. 605-616.

[59] Poterba, J. M., & Summers, L. H. (1988). Mean Reversion in Stock Prices: Evidence and Implications. Journal of Financial Economics, Vol. 22, No. 1, pp. 27–59.

[60] Rahimi, G. A. (2008). Considering Natural Gas Pricing Mechanisms in Different Regions, Quarterly Energy Economic Review, Vol. 13, pp. 69-121. (In Persian)

[61] Ross, S.A. (1997). Hedging Long Run Commitments: Exercises in Incomplete Market Pricing. Banca Monte Econom, No.26, pp. 99-132.

[62] Salazar, J., & Lambert, A. (2010). Fama and McBeth Revisited : A Critique, Aestimatio. The IEB International Journal of Finance, Vol. 1, pp. 48-71.

[63] Schwartz, E. S. (1997). The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging. Journal of Finance, Vol. 52, pp. 923-973.

[64] Serletis, A., & Rosenberg, A. (2009). Mean Reversion in the US Stock Market. Chaos, Solutions and Fractals, Vol. 40, pp. 2007-2015.

[65] Skorodumov, B. (2008). Estimation of mean reversion in Oil and Gas Markets. Technical Report, Mitsui & Co., Energy Risk Management LTD. http://skorodumov.net/pdf/report_oct_08.pdf

[66] Smith, W. T. (2010). On the Simulation and Estimation of the Mean-Reverting Ornstein-Uhlenbeck Process Especially as Applied to Commodities Markets and Modelling. February, Verson 1.01. http://www.scribd.com/doc/36512213/On-the-Simlation-and-Estimation-of-the-MR-OU-Process-With-MATLAB.

[67] Summers, L. H. (1986). Does the Stock Market Rationally Reflect Fundamental Values? Journal of Finance, Vol. 41, pp. 591-601.

[68] Uhlenbeck, G. E. & Ornstein, L. S. (1930). On the Theory of Brownian Motion. Physical Review, Vol.36, No.5, pp. 0823-0841 (reprinted in N. Wax, eds., Selected Papers on Noise and Stochastic Processes, Dover Pub., 1954, pp. 93-111.

[69] Vafee Najjar, D. (2008). Analyzing Income and Price Demand Elasticities in IWEM Model (IWEM Model Review and Perspective). Quarterly Energy Economics Review, No. 13, pp. 6-32. (In Persian)

[70] Vasicek, O. A. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, Vol. 5, No. 2, pp. 177-188.

[71] Whitesitt, A. (2010). Over-the-Counter Energy Derivatives. Director of Financial Trading, ACES Power Marketing.

[72] Wikipedia. (2011). http://en.wikipedia.org/wiki/Ornstein–Uhlenbeck_process Accessed April 2011.

[73] Wittig, H. (2007). Derivatives in the Gas Industry: Valuation of Natural Gas Storage Facilities. Master Thesis, University of ST. Gallen, and Graduate School of Business, Economics, Law and Social Sciences, pp. 1-131.

[74] Wright, J. H. (2000). Alternative Variance Ratio Tests Using Rank and Signs. Journal of Business and Economic Statistic, Vol. 18, pp. 1-9.

[75] Yu, J. (2009). Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Model.

September. http://www.mysmu.edu/faculty/yujun/Research/bias02.pdf.