Reading the Black-Scholes Formula in Terms of First and Last Passage Times

Abstract

We first recall the classical Black-Scholes formula (Theorem 1.1), and then give two new formulations of it: the first one in terms of first and last passage times of a Brownian motion with drift (Theorem 1.2 and Theorem 1.3), the second one as an expectation with respect to the law of \(B_{1}^{2}\) (Theorem 1.4).