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Commodity price modelling that matches current observables: a new approach


  • K. R. Miltersen


We develop a stochastic model of the spot commodity price and the spot convenience yield such that the model matches the current term structure of forward and futures prices, the current term structure of forward and futures volatilities, and the inter-temporal pattern of the volatility of the forward and futures prices. We let the underlying commodity price be a geometric Brownian motion and we let the spot convenience yield have a mean-reverting structure. The flexibility of the model, which makes it possible to simultaneously achieve all these goals, comes from allowing the volatility of the spot commodity price, the speed of mean-reversion parameter, the mean-reversion parameter, and the diffusion parameter of the spot convenience yield all to be time-varying deterministic functions.

Suggested Citation

  • K. R. Miltersen, 2003. "Commodity price modelling that matches current observables: a new approach," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 51-58.
  • Handle: RePEc:taf:quantf:v:3:y:2003:i:1:p:51-58 DOI: 10.1080/713666159

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    References listed on IDEAS

    1. Beckers, Stan, 1980. " The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
    2. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
    3. Platen, Eckhard, 2000. "A minimal financial market model," SFB 373 Discussion Papers 2000,91, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv.
    6. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
    7. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-219, March.
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    Cited by:

    1. John Crosby, 2008. "A multi-factor jump-diffusion model for commodities," Quantitative Finance, Taylor & Francis Journals, pages 181-200.
    2. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    3. Mahapatra, Santosh & Levental, Shlomo & Narasimhan, Ram, 2017. "Market price uncertainty, risk aversion and procurement: Combining contracts and open market sourcing alternatives," International Journal of Production Economics, Elsevier, vol. 185(C), pages 34-51.
    4. Patrik Karlsson & Kay F Pilz & Erik Schlogl, 2016. "Calibrating Market Model to Commodity and Interest Rate Risk," Research Paper Series 372, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Aviral Kumar Tiwari & Aruna Kumar Dash & Subhendu Dutta, 2015. "Testing the mean reversion in prices of agricultural commodities in India," Economics Bulletin, AccessEcon, vol. 35(3), pages 1928-1940.
    6. Anders B. Trolle & Eduardo S. Schwartz, 2006. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," NBER Working Papers 12744, National Bureau of Economic Research, Inc.
    7. repec:eee:eneeco:v:67:y:2017:i:c:p:182-201 is not listed on IDEAS
    8. Leif Andersen, 2010. "Markov models for commodity futures: theory and practice," Quantitative Finance, Taylor & Francis Journals, pages 831-854.
    9. 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.
    10. repec:uts:finphd:37 is not listed on IDEAS
    11. Carl Chiarella & Boda Kang & Christina Nikitopoulos-Sklibosios & Thuy-Duong To, 2012. "Humps in the Volatility Structure of the Crude Oil Futures Market," Research Paper Series 308, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Gonzalo Cortazar & Simon Gutierrez & Hector Ortega, 2016. "Empirical Performance of Commodity Pricing Models: When is it Worthwhile to Use a Stochastic Volatility Specification?," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(5), pages 457-487, May.
    13. Anh Ngoc Lai & Constantin Mellios, 2016. "Valuation of commodity derivatives with an unobservable convenience yield," Post-Print halshs-01183166, HAL.
    14. K. F. Pilz & E. Schlögl, 2013. "A hybrid commodity and interest rate market model," Quantitative Finance, Taylor & Francis Journals, pages 543-560.
    15. Joanna Janczura, 2014. "Pricing electricity derivatives within a Markov regime-switching model: a risk premium approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(1), pages 1-30, February.

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