title
  

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

Warning The system is temporarily closed to updates for reporting purpose.

Vanderbei, Robert J. and Pınar, Mustafa C. and Bozkaya, Efe Burak (2013) Discrete-time pricing and optimal exercise of American perpetual warrants in the geometric random walk model. Applied Mathematics & Optimization, 67 (1). pp. 97-122. ISSN 0095-4616 (Print) 1432-0606 (Online)

Full text not available from this repository.

Official URL: http://dx.doi.org/10.1007/s00245-012-9182-0

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.

Item Type:Article
Uncontrolled Keywords:American perpetual warrants; Pricing; Optimal stopping; Optimal exercise; Random walk; Linear programming; Duality
Subjects:UNSPECIFIED
ID Code:24277
Deposited By:Efe Burak Bozkaya
Deposited On:26 Jun 2014 15:21
Last Modified:02 Aug 2019 10:19

Repository Staff Only: item control page