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American step options

Jérôme Detemple, Souleymane Laminou Abdou and Franck Moraux ()

European Journal of Operational Research, 2020, vol. 282, issue 1, 363-385

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, up-connectedness 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.

Keywords: Risk management; American options; Step options; Occupation time; Multiple exercise boundaries (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:282:y:2020:i:1:p:363-385

DOI: 10.1016/j.ejor.2019.09.009

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European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

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