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Integrating Multiple Commodities in a Model of Stochastic Price Dynamics

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  • Paschke, Raphael
  • Prokopczuk, Marcel

Abstract

In this paper we develop a multi-factor model for the joint dynamics of related commodity spot prices in continuous time. We contribute to the existing literature by simultaneously considering various commodity markets in a single, consistent model. In an application we show the economic significance of our approach. We assume that the spot price processes can be characterized by the weighted sum of latent factors. Employing an essentially-affine model structure allows for rich dependencies among the latent factors and thus, the commodity prices. The co-integrated behavior between the different spot price dynamics is explicitly taken into account. Within this framework we derive closed-form solutions of futures prices. The Kalman Filter methodology is applied to estimate the model for crude oil, heating oil and gasoline futures contracts traded on the NYMEX. Empirically, we are able to identify a common non-stationary equilibrium factor driving the long-term price behavior and stationary factors affecting all three markets in a common way. Additionally, we identify factors which only impact subsets of the commodities considered. To demonstrate the economic consequences of our integrated approach, we evaluate the investment into a refinery from a financial management perspective and compare the results with an approach neglecting the co-movement of prices. This negligence leads to radical changes in the project's assessment.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5412.

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Date of creation: 23 Oct 2007
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Handle: RePEc:pra:mprapa:5412

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Keywords: Commodities; Integrated Model; Crude Oil; Heating Oil; Gasoline; Futures; Kalman Filter;

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  1. Pindyck, Robert S & Rotemberg, Julio J, 1990. "The Excess Co-movement of Commodity Prices," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 100(403), pages 1173-89, December.
  2. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 167-179.
  3. Miltersen, Kristian R. & Schwartz, Eduardo S., 1998. "Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 33(01), pages 33-59, March.
  4. Bryan R. Routledge & Duane J. Seppi & Chester S. Spatt, 2000. "Equilibrium Forward Curves for Commodities," Journal of Finance, American Finance Association, American Finance Association, vol. 55(3), pages 1297-1338, 06.
  5. Mihaela Manoliu & Stathis Tompaidis, 2002. "Energy futures prices: term structure models with Kalman filter estimation," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 9(1), pages 21-43.
  6. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, American Finance Association, vol. 57(1), pages 405-443, 02.
  7. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1551-80, November.
  8. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, American Finance Association, vol. 52(3), pages 923-73, July.
  9. Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
  10. Jaime Casassus & Pierre Collin-Dufresne, 2005. "Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates," Journal of Finance, American Finance Association, American Finance Association, vol. 60(5), pages 2283-2331, October.
  11. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 11(3), pages 215-260, August.
  12. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, INFORMS, vol. 46(7), pages 893-911, July.
  13. Gibson, Rajna & Schwartz, Eduardo S, 1990. " Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, American Finance Association, vol. 45(3), pages 959-76, July.
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Cited by:
  1. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "On the Stratonovich – Kalman - Bucy filtering algorithm application for accurate characterization of financial time series with use of state-space model by central banks," MPRA Paper 50235, University Library of Munich, Germany.
  2. Jaime Casassus & Peng Liu & Ke Tang, 2011. "Relative Scarcity of Commodities with a Long-Term Economic Relationship and the Correlation of Futures Returns," Documentos de Trabajo, Instituto de Economia. Pontificia Universidad Católica de Chile. 404, Instituto de Economia. Pontificia Universidad Católica de Chile..
  3. Füss, Roland & Mahringer, Steffen & Prokopczuk, Marcel, 2013. "Electricity Derivatives Pricing with Forward-Looking Information," Working Papers on Finance 1317, University of St. Gallen, School of Finance.
  4. Kovacevic, Raimund M. & Paraschiv, Florentina, 2012. "Medium-term Planning for Thermal Electricity Production," Working Papers on Finance 1220, University of St. Gallen, School of Finance.

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