An alternative expression for the Black-Scholes formula in terms of Brownian first and last passage times

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 celebrated Black-Scholes formula which gives the price of a European option, may be expressed as the cumulative function of a last passage time of Brownian motion. A related result involving first passage times is also obtained.

Mots clés: Black-Sholes formula; last passage times; time-inversion; Cameron-Martin relationship; reflection principle

Domaines: Probabilités [math.PR]

D. Madan, Bernard Roynette, Marc Yor. An alternative expression for the Black-Scholes formula in terms of Brownian first and last passage times. 2008. ⟨hal-00257403⟩