Perpetual American options

Svetlana Boyarchenko and Sergei Z. Levendorskiĭ
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Sergei Z. Levendorskiĭ: Rostov State University of Economics, Russia

Chapter 5 in Non-Gaussian Merton-Black-Scholes Theory, 2002, pp 121-149 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractThe following sections are included:The reduction to a free boundary problem for the stationary generalized Black-Scholes equationGeneral discussionFree boundary value problem for the price of the perpetual American optionMain LemmaPerpetual American put: the optimal exercise price and the rational put priceMain TheoremProof of optimality in the class $\mathcal{M}_0$Proof of optimality in the class $\mathcal{M}$Failure of the smooth pasting principle for some RLPE's and its substituteApproximate formulas for the case of model RLPEProof of Theorem 5.2Perpetual American callMain resultsProof of optimality in the case of unbounded payoffsPut-like and call-like options: the case of more general payoffsPut-like optionsCall-like optionsCommentary

Keywords: Non-Gaussian Models; Merton-Black-Scholes Theory; Levy Processes; American Options; European Options; Feller Processes (search for similar items in EconPapers)
Date: 2002
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