Pricing cancellable American put options on the finite time horizon

The purpose of this paper is to present a numerical approach for pricing cancellable American put options, also known as game or Israeli options, on the finite time horizon. These options generalize the concept of American derivatives adding an early exercise right for the option's writer to the existing holder's right. The writer has to pay a penalty amount above the usual option payment to use this right. We first obtain the shape of the optimal regions for both participants. Then we approximate the optimal exercise boundaries maximizing the option's writer and holder financial expectations using some first exit properties of the Brownian motion. We also construct an efficient pricing algorithm based on these boundaries. A semiclosed form formula is derived when the underlying asset starts above the strike.