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Sector Formula for Approximation of Spread Option Value & Greeks and Its Applications

Author

Listed:
  • Roza Galeeva

    (Department of Applied Mathematics and Statistics, Whiting School of Engineering, Johns Hopkins University, Homewood Campus, Baltimore, MD 21218, USA)

  • Zi Wang

    (Questrom School of Business, Boston University, 595 Commonwealth Av., Boston, MA 02215, USA)

Abstract

The goal of this paper is to derive closed-form approximation formulas for the spread option value and Greeks by using double integration and investigating the exercise boundary. We have found that the straight-line approximation suggested in previous research does not perform well for curved exercise boundaries. We propose a novel approach: to integrate in a sector and find a closed-form formula expressed in terms of the bivariate normal CDF. We call it the sector formula. Numerical tests show the good accuracy of our sector formula. We demonstrate applications of the formula to the market data of calendar spread options for three major commodities, WTI, Natural Gas, and Corn, listed on the CME site as of May, April, and June 2024.

Suggested Citation

  • Roza Galeeva & Zi Wang, 2024. "Sector Formula for Approximation of Spread Option Value & Greeks and Its Applications," Commodities, MDPI, vol. 3(3), pages 1-33, July.
    • Handle: RePEc:gam:jcommo:v:3:y:2024:i:3:p:17-313:d:1443919
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    References listed on IDEAS

    as
    1. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    2. Guillaume Coqueret & Bertrand Tavin, 2020. "A note on implied correlation for bivariate contracts," Economics Bulletin, AccessEcon, vol. 40(2), pages 1388-1396.
    3. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    4. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    Full references (including those not matched with items on IDEAS)

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