  This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit
formula for pricing European options when the underlying stock price follows a
non-linear stochastic delay equation with fixed delays in the drift and
diffusion terms. In this article, we look at models of the stock price
described by stochastic functional differential equations with variable delays.
We present a class of examples of stock dynamics with variable delays that
permit an explicit form for the option pricing formula. As in [A.H.M.P], the
market is complete with no arbitrage. This is achieved through the existence of
an equivalent martingale measure. In subsequent work, the authors intend to
test the models in [A.H.M.P] and the present article against real market data.
