Monoyios, Michael (2010) Optimal exercise of an executive stock option by an insider. International Journal of Theoretical and Applied Finance . (In Press)

PDF
275kB 
Abstract
We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the expected discounted payoff over all stopping times with regard to an enlarged filtration which includes the inside information. This leads to a stopping problem governed by a timeinhomogeneous diffusion and a calltype reward. We establish conditions under which the option value exhibits time decay, and derive the smooth fit condition for the solution to the free boundary problem governing the maximum expected reward, and derive the early exercise decomposition of the value function. The resulting integral equation for the unknown exercise boundary is solved numerically and this shows that the insider may exercise the option before maturity, in situations when an agent without the privileged information may not. Hence we show that early exercise may arise due to the agent having inside information on the future stock price.
Item Type:  Article 

Subjects:  O  Z > Probability theory and stochastic processes 
ID Code:  972 
Deposited By:  Professor Michael Monoyios 
Deposited On:  16 Sep 2010 06:54 
Last Modified:  29 May 2015 18:39 
Repository Staff Only: item control page