Discrete-time pricing and optimal exercise of American perpetual warrants in the geometric random walk model

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dc.citation.epage122en_US
dc.citation.issueNumber1en_US
dc.citation.spage97en_US
dc.citation.volumeNumber67en_US
dc.contributor.authorVanderbei, R. J.en_US
dc.contributor.authorPınar, M. Ç.en_US
dc.contributor.authorBozkaya, E. B.en_US
dc.date.accessioned2016-02-08T09:40:57Z
dc.date.available2016-02-08T09:40:57Z
dc.date.issued2013en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractAn 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.identifier.doi10.1007/s00245-012-9182-0en_US
dc.identifier.eissn1432-0606
dc.identifier.issn0095-4616
dc.identifier.urihttp://hdl.handle.net/11693/21086
dc.language.isoEnglishen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00245-012-9182-0en_US
dc.source.titleApplied Mathematics and Optimizationen_US
dc.subjectAmerican perpetual warrantsen_US
dc.subjectDualityen_US
dc.subjectLinear programmingen_US
dc.subjectOptimal exerciseen_US
dc.subjectOptimal stoppingen_US
dc.subjectPricingen_US
dc.subjectRandom walken_US
dc.subjectAmerican perpetual warrantsen_US
dc.subjectDualityen_US
dc.subjectOptimal exerciseen_US
dc.subjectOptimal stoppingen_US
dc.subjectRandom Walken_US
dc.subjectCostsen_US
dc.subjectFactor analysisen_US
dc.subjectLinear programmingen_US
dc.subjectMarkov processesen_US
dc.subjectOptimizationen_US
dc.subjectEconomicsen_US
dc.titleDiscrete-time pricing and optimal exercise of American perpetual warrants in the geometric random walk modelen_US
dc.typeArticleen_US
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