Finance Stochast. 4, 443–463 (2000) c  Springer-Verlag 2000 Game options Yuri Kifer Institute of Mathematics, The Hebrew University, Givat Ram 91904 Jerusalem, Israel (e-mail: kifer@math.huji.ac.il) Abstract. I introduce and study new derivative securities which I call game options (or Israeli options to put them in line with American, European, Asian, Russian etc. ones). These are contracts which enable both their buyer and seller to stop them at any time and then the buyer can exercise the right to buy (call option) or to sell (put option) a specified security for certain agreed price. If the contract is terminated by the seller he must pay certain penalty to the buyer. A more general case of game contingent claims is considered. The analysis is based on the theory of optimal stopping games (Dynkin’s games). Game options can be sold cheaper than usual American options and their introduction could diversify financial markets. Key words: American option pricing, optimal stopping game JEL Classification: G13, C73 Mathematics Subject Classification (1991): 90A09, 60J40, 90D15 1 Introduction A standard (B , S )-securities market consists of a nonrandom (riskless) component B t , which is described as a savings account (or price of a bond) at time t with an interest r , and of a random (risky) component S t , which can be described as the price of a stock at time t . Both discrete time t ∈ Z + = {0, 1, 2,... } Dedicated to E.B.Dynkin on his 75th birthday Partially supported by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany). Manuscript received: June 1999; final version received: November 1999