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

Christophe Profeta (), Bernard Roynette () and Marc Yor
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Christophe Profeta: Université Nancy I
Bernard Roynette: Université Nancy I
Marc Yor: Université Paris VI

Chapter Chapter 1 in Option Prices as Probabilities, 2010, pp 1-20 from Springer

Abstract: 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).

Date: 2010
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DOI: 10.1007/978-3-642-10395-7_1

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