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.
CITATION STYLE
Gapeev, P. V., & Rodosthenous, N. (2014). On the pricing of perpetual American compound options. In Inspired by Finance: The Musiela Festschrift (pp. 283–304). Springer International Publishing. https://doi.org/10.1007/978-3-319-02069-3_13
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