Discrete-time pricing and optimal exercise of american perpetual warrants in the geometric random walk model
Applied Mathematics and Optimization
MetadataShow full item record
Please cite this item using this persistent URLhttp://hdl.handle.net/11693/21086
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. © 2012 Springer Science+Business Media New York.
- Research Paper 7144
Showing items related by title, author, creator and subject.
Urfaliog̃lu O.; Çetin, A.E.; Kuruog̃lu, E.E. (2008)A novel evolutionary global optimization approach based on adaptive covariance estimation is proposed. The proposed method samples from a multivariate Levy Skew Alpha-Stable distribution with the estimated covariance matrix ...
Optimal signaling and detector design for power-constrained binary communications systems over non-Gaussian channels Göken, C.; Gezici, S.; Arikan, O. (2010)In this letter, joint optimization of signal structures and detectors is studied for binary communications systems under average power constraints in the presence of additive non-Gaussian noise. First, it is observed that ...
Alper Yildirim, E. (2012)We consider linear optimization problems over the cone of copositive matrices. Such conic optimization problems, called copositive programs, arise from the reformulation of a wide variety of difficult optimization problems. ...