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Put Option Prices As Joint Distribution Functions In Strike And Maturity: The Black–Scholes Case

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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; Institut Universitaire de France, France)

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    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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 12 (2009)
    Issue (Month): 08 ()
    Pages: 1075-1090

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    Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:08:p:1075-1090

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    Related research

    Keywords: First and last passage times; pseudo-inverse; local time-space calculus; Black–Scholes set up;

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