Discrete-Time Pricing and Optimal Exercise of American Perpetual Warrants in the Geometric Random Walk Model

Journal Article · Fri Feb 15 04:00:00 EST 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-012-9182-0· OSTI ID:22156530

Bozkaya, Efe B. ^[1]

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1. Sabancı 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, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 67; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DUALITY
GEOMETRY
GRAPH THEORY
INTEREST RATE
LINEAR PROGRAMMING
MARKOV PROCESS
PRICES
PROBABILITY
RANDOMNESS