title   
  

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

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:26 Jun 2014 15:21

Repository Staff Only: item control page