Unifying Black-Scholes type formulae which involve Brownian last passage times up to a finite horizon

D. Madan (1) , Bernard Roynette (2) , Marc Yor (3)

1 Robert H. Smith School of Business
2 IECN - Institut Élie Cartan de Nancy
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

The authors recently discovered some interesting relations between the Black-Scholes formula and last passage times of the Brownian exponential martingales, which invites one to seek analogous results for last passage times up to a finite horizon. This is achieved in the present paper, where Yuri's formula, as originally presented in Akahori, Imamura and yano (2008), is also derived.

Domaines: Probabilités [math.PR]

D. Madan, Bernard Roynette, Marc Yor. Unifying Black-Scholes type formulae which involve Brownian last passage times up to a finite horizon. 2008. ⟨hal-00275490⟩