GENERAL DUALITY FOR PERPETUAL AMERICAN OPTIONS

In this paper, we investigate the generalization of the Call-Put duality equality obtained in Alfonsi and Jourdain (preprint, 2006, available at http://cermics.enpc.fr/reports/CERMICS-2006/CERMICS-2006-307.pdf) for perpetual American options when the Call-Put payoff (y - x)(+) is replaced by phi(x, y). It turns out that the duality still holds under monotonicity and concavity assumptions on phi. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the derivation of the Call-Put duality equality for European options. Last, we give some examples for which the optimal strategy is known explicitly.