General Duality for Perpetual American Options

Aurélien Alfonsi (1, 2) , Benjamin Jourdain (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
2 Institut für Mathematik [Berlin]

In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] 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.

Mots clés: Perpetual American options; Dupire's formula; Call-Put Duality; Calibration of volatility; Optimal stopping

Domaines: Probabilités [math.PR]

Aurélien Alfonsi, Benjamin Jourdain. General Duality for Perpetual American Options. International Journal of Theoretical and Applied Finance, 2008, http://www.worldscientific.com/doi/abs/10.1142/S0219024908004920. ⟨hal-00121600⟩