PUT OPTION PRICES AS JOINT DISTRIBUTION FUNCTIONSIN STRIKE AND MATURITY: THE BLACK—SCHOLES CASE

摘要

For a large class of R_+ valued, continuous local martingales(tt ≥0), with M_0= 1 andM = 0, the put quantity: П_M(K, t) = E ((K - M_t)~+)turns out to be the distributionfunction in both variables K and t, for K ≤ 1 and t ≥ 0, of a probability γ_M on[0, 1] × [0, ∞[. In this paper, the first in a series of three, we discuss in detail the casewhere M_t= ε_t :=exp(t-t/2),for (B_t, t ≥ 0) a standard Brownian motion.