On the Pricing of Perpetual American Compound Options

Pavel V. Gapeev () and Neofytos Rodosthenous ()
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Pavel V. Gapeev: London School of Economics, Department of Mathematics
Neofytos Rodosthenous: London School of Economics, Department of Mathematics

A chapter in Inspired by Finance, 2014, pp 283-304 from Springer

Abstract: Abstract We present explicit solutions to the perpetual American compound option pricing problems in the Black-Merton-Scholes model. The method of proof is based on the reduction of the initial two-step optimal stopping problems for the underlying geometric Brownian motion to appropriate sequences of ordinary one-step problems. The latter are solved through their associated one-sided free-boundary problems and the subsequent martingale verification. We also obtain a closed form solution to the perpetual American chooser option pricing problem, by means of the analysis of the equivalent two-sided free-boundary problem.

Keywords: Perpetual American compound options; The Black–Merton–Scholes model; Geometric Brownian motion; Multi-step optimal stopping problem; First hitting time; Free-boundary problem; Local time-space formula; 91B28; 60G40; 34K10 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02069-3_13

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DOI: 10.1007/978-3-319-02069-3_13

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