Discrete-time pricing and optimal exercise of American perpetual warrants in the geometric random walk model
Author
Vanderbei, R. J.
Pınar, M. Ç.
Bozkaya, E. B.
Date
2013Source Title
Applied Mathematics and Optimization
Print ISSN
0095-4616
Electronic ISSN
1432-0606
Volume
67
Issue
1
Pages
97 - 122
Language
English
Type
ArticleItem Usage Stats
60
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Show full item recordAbstract
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 warrantsDuality
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/11693/21086Published Version (Please cite this version)
http://dx.doi.org/10.1007/s00245-012-9182-0Collections
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