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

## Author Info

()

(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 Contact details of provider: Web page: http://www.worldscinet.com/ijtaf/ijtaf.shtml Order Information: Email:

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