dc.contributor.author Vanderbei, R. J. en_US dc.contributor.author Pınar, M. Ç. en_US dc.contributor.author Bozkaya, E. B. en_US dc.date.accessioned 2016-02-08T09:40:57Z dc.date.available 2016-02-08T09:40:57Z dc.date.issued 2013 en_US dc.identifier.issn 0095-4616 dc.identifier.uri http://hdl.handle.net/11693/21086 dc.description.abstract An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put. en_US dc.language.iso English en_US dc.source.title Applied Mathematics and Optimization en_US dc.relation.isversionof http://dx.doi.org/10.1007/s00245-012-9182-0 en_US dc.subject American perpetual warrants en_US dc.subject Duality en_US dc.subject Linear programming en_US dc.subject Optimal exercise en_US dc.subject Optimal stopping en_US dc.subject Pricing en_US dc.subject Random walk en_US dc.subject American perpetual warrants en_US dc.subject Duality en_US dc.subject Optimal exercise en_US dc.subject Optimal stopping en_US dc.subject Random Walk en_US dc.subject Costs en_US dc.subject Factor analysis en_US dc.subject Linear programming en_US dc.subject Markov processes en_US dc.subject Optimization en_US dc.subject Economics en_US dc.title Discrete-time pricing and optimal exercise of American perpetual warrants in the geometric random walk model en_US dc.type Article en_US dc.department Department of Industrial Engineering en_US dc.citation.spage 97 en_US dc.citation.epage 122 en_US dc.citation.volumeNumber 67 en_US dc.citation.issueNumber 1 en_US dc.identifier.doi 10.1007/s00245-012-9182-0 en_US dc.identifier.eissn 1432-0606
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