  Consider stochastic functional differential equations, whose coefficients
depend on past histories. The solution determines a non-Markov process. In the
present paper, we shall obtain the existence of smooth densities for joint
distributions of solutions, under the uniformly elliptic condition on the
diffusion coefficients, via the Malliavin calculus. As an application, we shall
study the computations of the Greeks on options associated with the asset price
dynamics models with delayed effects.
