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Markov models for commodity futures: theory and practice

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  • Leif Andersen

Abstract

The objective of this paper is to develop a generic, yet practical, framework for the construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by spikes in the spot process. In the first, largely theoretical, part of the paper we derive a series of useful results concerning the low-dimensional Markov representation of the dynamics of an entire term structure of futures prices. Extending previous results in the literature, we cover jump-diffusive models with stochastic volatility as well as several classes of regime-switching models. To demonstrate the process of building models for a specific commodity market, the second part of the paper applies a selection of our theoretical results to the exercise of constructing and calibrating derivatives trading models for USD natural gas. Special attention is paid to the incorporation of empirical seasonality effects in futures prices, in implied volatilities and their 'smile', and in correlations between futures contracts of different maturities. European option pricing in our proposed gas model is closed form and of the same complexity as the Black-Scholes formula.

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  • Leif Andersen, 2010. "Markov models for commodity futures: theory and practice," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 831-854.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:8:p:831-854
    DOI: 10.1080/14697680903493599
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    References listed on IDEAS

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    2. Anna Maria Gambaro & Nicola Secomandi, 2021. "A Discussion of Non‐Gaussian Price Processes for Energy and Commodity Operations," Production and Operations Management, Production and Operations Management Society, vol. 30(1), pages 47-67, January.
    3. Cummins, Mark & Kiely, Greg & Murphy, Bernard, 2018. "Gas storage valuation under multifactor Lévy processes," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 167-184.
    4. Orcan Ogetbil & Bernhard Hientzsch, 2024. "Inflation Models with Correlation and Skew," Papers 2405.05101, arXiv.org.
    5. Daniel Leonhardt & Antony Ware & Rudi Zagst, 2017. "A Cointegrated Regime-Switching Model Approach with Jumps Applied to Natural Gas Futures Prices," Risks, MDPI, vol. 5(3), pages 1-19, September.
    6. Zura Kakushadze & Juan Andrés Serur, 2018. "151 Trading Strategies," Springer Books, Springer, number 978-3-030-02792-6, January.
    7. Crosby, John & Frau, Carme, 2022. "Jumps in commodity prices: New approaches for pricing plain vanilla options," Energy Economics, Elsevier, vol. 114(C).
    8. Ewald, Christian & Zou, Yihan, 2021. "Analytic formulas for futures and options for a linear quadratic jump diffusion model with seasonal stochastic volatility and convenience yield: Do fish jump?," European Journal of Operational Research, Elsevier, vol. 294(2), pages 801-815.
    9. Guiotto, Paolo, 2022. "A note on the spot-forward parity under stochastic cost of carry," Energy Economics, Elsevier, vol. 112(C).
    10. Liu, Yifeng & Yang, Jian, 2015. "Joint pricing-procurement control under fluctuating raw material costs," International Journal of Production Economics, Elsevier, vol. 168(C), pages 91-104.
    11. Mehrdoust, Farshid & Noorani, Idin & Kanniainen, Juho, 2024. "Valuation of option price in commodity markets described by a Markov-switching model: A case study of WTI crude oil market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 228-269.
    12. Orcan Ogetbil & Bernhard Hientzsch, 2022. "A Flexible Commodity Skew Model with Maturity Effects," Papers 2212.07972, arXiv.org.
    13. Kim, Jungmu & Park, Yuen Jung & Ryu, Doojin, 2017. "Stochastic volatility of the futures prices of emission allowances: A Bayesian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 714-724.

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