Discrete-Time Pricing and Optimal Exercise of American Perpetual Warrants in the Geometric Random Walk Model
- Sabanc Latin-Small-Letter-Dotless-I University, Faculty of Administrative Sciences (Turkey)
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.
- OSTI ID:
- 22156530
- Journal Information:
- Applied Mathematics and Optimization, Vol. 67, Issue 1; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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