Hedging of game options in discrete markets with transaction costs

Abstract

Game options introduced in [10] in 2000 were studied, by now, mostly in frictionless both complete and incomplete markets. In complete markets the fair price of a game option coincides with the value of an appropriate Dynkin's game, whereas in markets with friction and in incomplete ones there is a range of arbitrage free prices and superhedging comes into the picture. Here we consider game options in general discrete time markets with transaction costs and construct backward and forward induction algorithms for the computation of their prices and superhedging strategies from both seller's (upper arbitrage free price) and buyer's (lower arbitrage free price) points of view extending to the game options case most of the results from [12].

Keywords:

• game options
• transaction costs
• superhedging
• shortfall risk
• Dynkin games

Keywords:

• Primary 91B28
• Secondary 60G40, 91B30