In this paper we introduce an option pricing model with stocha-
stic volatility which can be made to exactly match a given arbitrage free
implied volatility surface (IVF). The dynamics of the IVF implied by the
model - which we call a near stable IVF structure - is in good accordance
with reality. Moreover, the system can be adapted to other dynamics. The
model is easy to implement and easy to use (at least in theory, as it has not
been implemented yet). It is designed as a two-factor markovian tree model.
By a special construction method one can endow the tree with comparative-
ly many knots near the beginning, but still keep the growth of the number
of knots under control. Also due to the construction method problems like
negative probabilities, which are typical for some option pricing tree models,
do not occur .