On the impact of the penalty on the cancellable American options

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.