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

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      Author(s)
      Vanderbei, R. J.
      Pınar, M. Ç.
      Bozkaya, E. B.
      Date
      2013
      Source Title
      Applied Mathematics and Optimization
      Print ISSN
      0095-4616
      Electronic ISSN
      1432-0606
      Volume
      67
      Issue
      1
      Pages
      97 - 122
      Language
      English
      Type
      Article
      Item Usage Stats
      148
      views
      96
      downloads
      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.
      Keywords
      American perpetual warrants
      Duality
      Linear programming
      Optimal exercise
      Optimal stopping
      Pricing
      Random walk
      American perpetual warrants
      Duality
      Optimal exercise
      Optimal stopping
      Random Walk
      Costs
      Factor analysis
      Linear programming
      Markov processes
      Optimization
      Economics
      Permalink
      http://hdl.handle.net/11693/21086
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s00245-012-9182-0
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      • Department of Industrial Engineering 702
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