Hedging of swing game options in continuous time

Abstract

This paper introduces and studies hedging for game (Israeli) style extension of swing options in continuous time considered as multiple exercise derivatives of a base security, evolving according to the geometric Brownian motion. Assuming that the underlying security can be traded without restrictions, we derive a formula for the valuation of multiple exercise options via classical hedging arguments. This paper extends to the continuous time case the discrete time valuation results which requires substantial additional machinery such as, for instance, regularity results for value processes of Dynkin's games and the study of multiple stopping Dynkin's games. Earlier papers on valuation of multiple exercise American options viewed it only as a multiple stopping problem.