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

Author

Listed:
  • 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)

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.

Suggested Citation

  • D. Madan & B. Roynette & M. Yor, 2009. "Put Option Prices As Joint Distribution Functions In Strike And Maturity: The Black–Scholes Case," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1075-1090.
    • Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:08:n:s0219024909005580
    DOI: 10.1142/S0219024909005580
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