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

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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Year of publication:	2009
Authors:	MADAN, D. ; ROYNETTE, B. ; YOR, M.
Published in:	International Journal of Theoretical and Applied Finance (IJTAF). - World Scientific Publishing Co. Pte. Ltd., ISSN 1793-6322. - Vol. 12.2009, 08, p. 1075-1090
Publisher:	World Scientific Publishing Co. Pte. Ltd.
Subject:	First and last passage times \| pseudo-inverse \| local time-space calculus \| Black–Scholes set up

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Extent:	application/pdf text/html
Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10008493069