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American Step Options

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.
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https://halshs.archives-ouvertes.fr/halshs-02283374
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Submitted on : Tuesday, September 10, 2019 - 5:21:09 PM
Last modification on : Thursday, January 14, 2021 - 1:21:16 PM
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Jerôme Detemple, Souleymane Laminou Abdou, Franck Moraux. American Step Options. European Journal of Operational Research, Elsevier, 2020, 282 (1), pp.363-385. ⟨10.1016/j.ejor.2019.09.009⟩. ⟨halshs-02283374⟩

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