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Commodity derivatives valuation with autoregressive and moving average components in the price dynamics

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  • Paschke, Raphael
  • Prokopczuk, Marcel

Abstract

In this paper, we develop a continuous time factor model of commodity prices that allows for higher-order autoregressive and moving average components. We document the need for these components by analyzing the convenience yield's time series dynamics. The model we propose is analytically tractable and allows us to derive closed-form pricing formulas for futures and options. Empirically, we estimate a parsimonious version of the general model for the crude oil futures market and demonstrate the model's superior performance in pricing nearby futures contracts in- and out-of-sample. Most notably, the model substantially improves the pricing of long-horizon contracts with information from the short end of the futures curve.

Suggested Citation

  • Paschke, Raphael & Prokopczuk, Marcel, 2010. "Commodity derivatives valuation with autoregressive and moving average components in the price dynamics," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2742-2752, November.
    • Handle: RePEc:eee:jbfina:v:34:y:2010:i:11:p:2742-2752
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    Cited by:

    1. Fred Espen Benth, 2021. "Pricing of Commodity and Energy Derivatives for Polynomial Processes," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    2. Benth, Fred Espen & Koekebakker, Steen, 2015. "Pricing of forwards and other derivatives in cointegrated commodity markets," Energy Economics, Elsevier, vol. 52(PA), pages 104-117.
    3. Joshua G. Maples & B. Wade Brorsen, 2022. "Handling the discontinuity in futures prices when time series modeling of commodity cash and futures prices," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 70(2), pages 139-152, June.
    4. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2012. "Does stock return predictability affect ESO fair value?," European Journal of Operational Research, Elsevier, vol. 223(1), pages 188-202.
    5. Abootaleb Shirvani & Svetlozar T. Rachev & Frank J. Fabozzi, 2019. "A Rational Finance Explanation of the Stock Predictability Puzzle," Papers 1911.02194, arXiv.org.
    6. Ni, Jian & Chu, Lap Keung & Wu, Feng & Sculli, Domenic & Shi, Yuan, 2012. "A multi-stage financial hedging approach for the procurement of manufacturing materials," European Journal of Operational Research, Elsevier, vol. 221(2), pages 424-431.
    7. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    8. Kang, Boda & Nikitopoulos, Christina Sklibosios & Prokopczuk, Marcel, 2020. "Economic determinants of oil futures volatility: A term structure perspective," Energy Economics, Elsevier, vol. 88(C).
    9. Lorenzo Mercuri & Andrea Perchiazzo & Edit Rroji, 2020. "Finite Mixture Approximation of CARMA(p,q) Models," Papers 2005.10130, arXiv.org, revised May 2020.
    10. Farkas, Walter & Gourier, Elise & Huitema, Robert & Necula, Ciprian, 2017. "A two-factor cointegrated commodity price model with an application to spread option pricing," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 249-268.
    11. Roberto Louis Forestal & Shih-Ming Pi, 2021. "Using Artificial Neural networks and Optimal Scaling Model to Forecast Agriculture Commodity Price: An Ecological-economic Approach," Advances in Management and Applied Economics, SCIENPRESS Ltd, vol. 11(3), pages 1-3.
    12. Anh Ngoc Lai & Constantin Mellios, 2016. "Valuation of commodity derivatives with an unobservable convenience yield," Post-Print halshs-01183166, HAL.
    13. Marcel Prokopczuk & Yingying Wu, 2013. "Estimating term structure models with the Kalman filter," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 4, pages 97-113, Edward Elgar Publishing.
    14. Fred Espen Benth & Claudia Kluppelberg & Gernot Muller & Linda Vos, 2012. "Futures pricing in electricity markets based on stable CARMA spot models," Papers 1201.1151, arXiv.org.
    15. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    16. Bisht Deepak & Laha, A. K., 2017. "Pricing Option on Commodity Futures under String Shock," IIMA Working Papers WP 2017-07-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    17. Fred Espen Benth & Asma Khedher & Mich`ele Vanmaele, 2017. "Pricing of commodity derivatives on processes with memory," Papers 1711.00307, arXiv.org.
    18. Spodniak, Petr & Bertsch, Valentin, 2017. "Determinants of power spreads in electricity futures markets: A multinational analysis," Papers WP580, Economic and Social Research Institute (ESRI).
    19. Juri Hinz & Tanya Tarnopolskaya & Jeremy Yee, 2020. "Efficient algorithms of pathwise dynamic programming for decision optimization in mining operations," Annals of Operations Research, Springer, vol. 286(1), pages 583-615, March.
    20. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Valuing commodity options and futures options with changing economic conditions," Economic Modelling, Elsevier, vol. 51(C), pages 524-533.
    21. Lu, Botao & Ma, Feng & Wang, Jiqian & Ding, Hui & Wahab, M.I.M., 2021. "Harnessing the decomposed realized measures for volatility forecasting: Evidence from the US stock market," International Review of Economics & Finance, Elsevier, vol. 72(C), pages 672-689.
    22. Fred Espen Benth & Asma Khedher & Michèle Vanmaele, 2020. "Pricing of Commodity Derivatives on Processes with Memory," Risks, MDPI, vol. 8(1), pages 1-32, January.
    23. Benth, Fred Espen & Klüppelberg, Claudia & Müller, Gernot & Vos, Linda, 2014. "Futures pricing in electricity markets based on stable CARMA spot models," Energy Economics, Elsevier, vol. 44(C), pages 392-406.
    24. Rauch, Johannes & Krayzler, Mikhail & Brunner, Bernhard & Zagst, Rudi, 2013. "Pricing of derivatives on commodity indices," International Review of Financial Analysis, Elsevier, vol. 29(C), pages 143-151.

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