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A multi-factor jump-diffusion model for commodities

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  • John Crosby

Abstract

In this paper we develop an arbitrage-free model for the pricing of commodity derivatives. The model generates futures (or forward) commodity prices consistent with any initial term structure. The model is consistent with mean reversion in commodity prices and also generates stochastic convenience yields. Our model is a multi-factor jump-diffusion model, one specification of which allows the prices of long-dated futures contracts to jump by smaller magnitudes than short-dated futures contracts, which, to our knowledge, is a feature that has not previously appeared in the literature, in spite of it being in line with stylised empirical observations (especially for energy-related commodities). Our model also allows for stochastic interest rates. The model produces semi-analytic solutions for standard European options, which enable option prices to be evaluated in typically about 1/50th of a second (depending upon parameter values and the required accuracy). This opens the possibility to calibrate the model parameters by deriving implied parameters from the market prices of options. We perform such a calibration on crude oil options and show that, allowing long-dated futures contracts to jump by smaller magnitudes than short-dated contracts, gives a greatly enhanced fit.

Suggested Citation

  • John Crosby, 2008. "A multi-factor jump-diffusion model for commodities," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 181-200.
    • Handle: RePEc:taf:quantf:v:8:y:2008:i:2:p:181-200
    DOI: 10.1080/14697680701253021
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    References listed on IDEAS

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    3. Hilliard, Jimmy E. & Hilliard, Jitka, 2019. "A jump-diffusion model for pricing and hedging with margined options: An application to Brent crude oil contracts," Journal of Banking & Finance, Elsevier, vol. 98(C), pages 137-155.
    4. Feng, Ling & Wang, Jieyu, 2023. "Random sources correlations and carbon futures pricing," International Review of Financial Analysis, Elsevier, vol. 86(C).
    5. Benjamin Tin Chun Cheng, 2017. "Pricing and Hedging of Long-Dated Commodity Derivatives," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2017, January-A.
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    7. Crosby, John & Frau, Carme, 2022. "Jumps in commodity prices: New approaches for pricing plain vanilla options," Energy Economics, Elsevier, vol. 114(C).
    8. Hu, Zhihao & Yang, Ben-Zhang & He, Xin-Jiang & Yue, Jia, 2024. "Equilibrium pricing of European crude oil options with stochastic behaviour and jump risks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 212-230.
    9. Matt Thompson, 2013. "Optimal Economic Dispatch and Risk Management of Thermal Power Plants in Deregulated Markets," Operations Research, INFORMS, vol. 61(4), pages 791-809, August.
    10. 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.
    11. Svetlana Borovkova & Diego Mahakena, 2015. "News, volatility and jumps: the case of natural gas futures," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1217-1242, July.
    12. Chris Kenyon & Andrew Green, 2015. "Dirac Processes and Default Risk," Papers 1504.04581, arXiv.org.
    13. John Crosby, 2008. "Pricing a class of exotic commodity options in a multi-factor jump-diffusion model," Quantitative Finance, Taylor & Francis Journals, vol. 8(5), pages 471-483.

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