Some calculations for Israeli options

Abstract.Recently Kifer (2000) introduced the concept of an Israeli (or Game) option. That is a general American-type option with the added possibility that the writer may terminate the contract early inducing a payment exceeding the holder’s claim had they exercised at that moment. Kifer shows that pricing and hedging of these options reduces to evaluating a saddle point problem associated with Dynkin games. In this short text we give two examples of perpetual Israeli options where the solutions are explicit.