Modern Stochastics: Theory and Applications

The cancellable American options, also known as game options, are financial instruments that give a canceling right to the option’s writer in addition to the existing such holder’s right. The writer owes some penalty above the usual option payoff for using this right. We assume that this penalty consists of three parts – a proportion of the usual payoff, some number of shares of the underlying asset, and a fixed amount. It turns out that a cancellable option can be of one of the following three types – a regular American option, an American-style derivative that expires either at the maturity or when the underlying asset reaches the strike, or a real cancellable option. In this paper, the impact of the penalty on the option’s type is investigated. The perpetual case is only explored having in mind that it determines the kind of the finite maturity instruments in some sense.

The major characteristic of the cancellable American options is the existing writer’s right to cancel the contract prematurely paying some penalty amount. The main purpose of this paper is to introduce and examine a new subclass of such options for which the penalty which the writer owes for this right consists of three parts – a fixed amount, shares of the underlying asset, and a proportion of the usual option payment. We examine the asymptotic case in which the maturity is set to be infinity. We determine the optimal exercise regions for the option’s holder and writer and derive the fair option price.