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Options on the minimum or the maximum of two average prices

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  • Xueping Wu
  • Jin Zhang

Abstract

This paper studies options on the minimum/maximum of two average prices. We provide a closed-form pricing formula for the option with geometric averaging starting at any time before maturity. We show overwhelming numerical evidence that the variance reduction technique with the help of the above closed-form solution dramatically improves the accuracy of the simulated price of an option with arithmetic averaging. The proposed options are found widely applicable in risk management and in the design of incentive contracts. The paper also discusses some parity relationships within the family of average-rate options and provides the upper and lower bounds for the proposed options with arithmetic averaging. Copyright Kluwer Academic Publishers 1999

Suggested Citation

  • Xueping Wu & Jin Zhang, 1999. "Options on the minimum or the maximum of two average prices," Review of Derivatives Research, Springer, vol. 3(2), pages 183-204, May.
    • Handle: RePEc:kap:revdev:v:3:y:1999:i:2:p:183-204
    DOI: 10.1023/A:1009658511492
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    References listed on IDEAS

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    Cited by:

    1. Wang, Xingchun, 2021. "Valuation of options on the maximum of two prices with default risk under GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    2. Ahmadian, D. & Ballestra, L.V. & Shokrollahi, F., 2022. "A Monte-Carlo approach for pricing arithmetic Asian rainbow options under the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Katelijne A.E. Carbonez & Van Thi Tuong Nguyen & Piet Sercu, 2011. "Hedging with Two Futures Contracts: Simplicity Pays," European Financial Management, European Financial Management Association, vol. 17(5), pages 806-834, November.
    4. Wang, Xingchun, 2020. "Pricing options on the maximum or minimum of multi-assets under jump-diffusion processes," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 16-26.
    5. Jr-Yan Wang & Hsiao-Chuan Wang & Yi-Chen Ko & Mao-Wei Hung, 2017. "Rainbow trend options: valuation and applications," Review of Derivatives Research, Springer, vol. 20(2), pages 91-133, July.
    6. Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).

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