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Pricing And Hedging European Options On Futures Spreads Using The Bachelier Spread Option Model

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  • Schaefer, Matthew P.

Abstract

The Bachelier model for pricing options on futures spreads (OFS) assumes changes in the underlying .futures prices and spread follow unrestricted arithmetic Brownian motion (UABM). The assumption of UABM allows for a convenient analytic solution for the price of an OFS. The same is not possible under the more traditional assumption of geometric Brownian motion (GBM). Given the additional complexity of methods for pricing and hedging OFS using GBM such as Monte Carlo simulation and binomial trees, it is worth investigating how results from the Bachelier model compare to these other methods. The Bachelier model is presented and then extended to price an OFS with three underlying commodities. Hedge parameters for both models are provided. Results indicate that for OFS with sufficiently low volatility, differences between the Bachelier model and methods assuming GBM are quite small.

Suggested Citation

  • Schaefer, Matthew P., 2002. "Pricing And Hedging European Options On Futures Spreads Using The Bachelier Spread Option Model," 2002 Conference, April 22-23, 2002, St. Louis, Missouri 19055, NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    • Handle: RePEc:ags:ncrtwo:19055
    DOI: 10.22004/ag.econ.19055
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    File URL: https://ageconsearch.umn.edu/record/19055/files/cp02sc01.pdf
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    References listed on IDEAS

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    1. Geoffrey Poitras, 1998. "Spread options, exchange options, and arithmetic Brownian motion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 18(5), pages 487-517, August.
    2. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    3. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    Cited by:

    1. Svetlozar Rachev & Nancy Asare Nyarko & Blessing Omotade & Peter Yegon, 2023. "Bachelier's Market Model for ESG Asset Pricing," Papers 2306.04158, arXiv.org.
    2. Nancy Asare Nyarko & Bhathiya Divelgama & Jagdish Gnawali & Blessing Omotade & Svetlozar T. Rachev & Peter Yegon, 2023. "Exploring Dynamic Asset Pricing within Bachelier’s Market Model," JRFM, MDPI, vol. 16(8), pages 1-18, July.
    3. Nancy Asare Nyarko & Bhathiya Divelgama & Jagdish Gnawali & Blessing Omotade & Svetlozar Rachev & Peter Yegon, 2023. "Exploring Dynamic Asset Pricing within Bachelier Market Model," Papers 2307.04059, arXiv.org.
    4. Kevin Patrick Darby, 2021. "Time is Money: The Equilibrium Trading Horizon and Optimal Arrival Price," Papers 2104.05844, arXiv.org.

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