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American Step Options

Author

Listed:
  • Jerôme Detemple

    (BU - Boston University [Boston])

  • Souleymane Laminou Abdou

    (ESC [Rennes] - ESC Rennes School of Business)

  • Franck Moraux

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper examines the valuation of American knock-out and knock-in step options. The structures of the immediate exercise regions of the various contracts are identified. Typical properties of American vanilla calls, such as uniqueness of the optimal exercise boundary, upconnectedness of the exercise region or convexity of its t-section, are shown to fail in some cases. Early exercise premium representations of step option prices, involving the Laplace transforms of the joint laws of Brownian motion and its occupation times, are derived. Systems of coupled integral equations for the components of the exercise boundary are deduced. Numerical implementations document the behavior of the price and the hedging policy. The paper is the first to prove that finite maturity exotic American Options written on a single underlying asset can have multiple disconnected exercise regions described by a triplet of coupled boundaries.

Suggested Citation

  • Jerôme Detemple & Souleymane Laminou Abdou & Franck Moraux, 2020. "American Step Options," Post-Print halshs-02283374, HAL.
    • Handle: RePEc:hal:journl:halshs-02283374
    DOI: 10.1016/j.ejor.2019.09.009
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-02283374
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    References listed on IDEAS

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    Cited by:

    1. Shen, Jinye & Huang, Weizhang & Ma, Jingtang, 2024. "An efficient and provable sequential quadratic programming method for American and swing option pricing," European Journal of Operational Research, Elsevier, vol. 316(1), pages 19-35.
    2. Neofytos Rodosthenous & Hongzhong Zhang, 2020. "When to sell an asset amid anxiety about drawdowns," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1422-1460, October.
    3. Ebina, Takeshi & Matsushima, Noriaki & Nishide, Katsumasa, 2022. "Demand uncertainty, product differentiation, and entry timing under spatial competition," European Journal of Operational Research, Elsevier, vol. 303(1), pages 286-297.
    4. Carlos Esparcia & Elena Ibañez & Francisco Jareño, 2020. "Volatility Timing: Pricing Barrier Options on DAX XETRA Index," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    5. Walter Farkas & Ludovic Mathys, 2020. "Geometric Step Options with Jumps. Parity Relations, PIDEs, and Semi-Analytical Pricing," Papers 2002.09911, arXiv.org.
    6. Neofytos Rodosthenous & Hongzhong Zhang, 2020. "When to sell an asset amid anxiety about drawdowns," Papers 2006.00282, arXiv.org.

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    Keywords

    Multiple exercise boundaries.; Risk management; Step options; Multiple exercise boundaries; American options; Occupation time;
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