GENERAL DUALITY FOR PERPETUAL AMERICAN OPTIONS

Aurélien Alfonsi () and Benjamin Jourdain ()
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Aurélien Alfonsi: CERMICS, project-team Mathfi, École des Ponts, ParisTech, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-vallée, France;
Benjamin Jourdain: CERMICS, project-team Mathfi, École des Ponts, ParisTech, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-vallée, France

International Journal of Theoretical and Applied Finance (IJTAF), 2008, vol. 11, issue 06, 545-566

Abstract: In this paper, we investigate the generalization of the Call-Put duality equality obtained in Alfonsi and Jourdain (preprint, 2006, available at ) for perpetual American options when the Call-Put payoff (y - x)+ is replaced by ϕ(x,y). It turns out that the duality still holds under monotonicity and concavity assumptions on ϕ. 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.

Keywords: Perpetual American options; Dupire's formula; Call-Put duality; calibration of volatility; optimal stopping (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0219024908004920

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