PUT OPTION PRICES AS JOINT DISTRIBUTION FUNCTIONS IN STRIKE AND MATURITY: THE BLACK–SCHOLES CASE

D. Madan (), B. Roynette () and M. Yor ()
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D. Madan: Robert H. Smith School of Business, Van Munching Hall, University of Maryland, College Park, MD. 20742, USA
B. Roynette: Institut Elie Cartan, Université Henri Poincaré, B.P. 239, 54506 Vandoeuvre les Nancy Cedex, France
M. Yor: Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 place Jussieu – Case 188, F – 75252 Paris Cedex 05, France;

International Journal of Theoretical and Applied Finance (IJTAF), 2009, vol. 12, issue 08, 1075-1090

Abstract: For a large class of ℝ+ valued, continuous local martingales (Mtt ≥ 0), with M0 = 1 and M∞ = 0, the put quantity: ΠM (K,t) = E ((K - Mt)+) turns out to be the distribution function in both variables K and t, for K ≤ 1 and t ≥ 0, of a probability γM on [0,1] × [0, ∞[. In this paper, the first in a series of three, we discuss in detail the case where $M_{t} = \mathcal{E}_{t}:= \exp (B_{t} - \frac{t}{2})$, for (Bt, t ≥ 0) a standard Brownian motion.

Keywords: First and last passage times; pseudo-inverse; local time-space calculus; Black–Scholes set up (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1142/S0219024909005580

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