Discounted perpetual game put options.

• We determine the buyers and sellers optimal exercise regions. • We find optimal strategies for both participants. • We derive the equations for the exercise boundaries. • We obtain the fair option prices. • Numerical examples are presented. The aim of this study is to explore the behavior of perpetual game put options, also known as cancellable puts. Their main characteristic is the opportunity of the buyer and the seller to exercise prematurely. If the seller decides to terminate the option, he obliges to pay a penalty amount above the normal option fee. We include also a discount factor that provides an advantage for earlier option exercising. We obtain the optimal moments for both participants to end the option promptly. This allows us to turn the option pricing problem to a first exit problem. We base our examination on financial instruments with random maturities. These instruments permit one of the partakers to maximize his expected future profit. [ABSTRACT FROM AUTHOR]