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

In: Option Prices as Probabilities

Author

Listed:
  • Christophe Profeta

    (Université Nancy I)

  • Bernard Roynette

    (Université Nancy I)

  • Marc Yor

    (Université Paris VI)

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).

Suggested Citation

  • Christophe Profeta & Bernard Roynette & Marc Yor, 2010. "Reading the Black-Scholes Formula in Terms of First and Last Passage Times," Springer Finance, in: Option Prices as Probabilities, chapter 0, pages 1-20, Springer.
    • Handle: RePEc:spr:sprfcp:978-3-642-10395-7_1
    DOI: 10.1007/978-3-642-10395-7_1
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