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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)


    (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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    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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