In this paper new analytical and numerical approaches to valuating
path-dependent options of European type have been developed. The model of
stochastic volatility as a basic model has been chosen. For European options we
could improve the path integral method, proposed B. Baaquie, and generalized it
to the case of path-dependent options, where the payoff function depends on the
history of changes in the underlying asset. The dependence of the implied
volatility on the parameters of the stochastic volatility model has been
studied. It is shown that with proper choice of model parameters one can
accurately reproduce the actual behavior of implied volatility. As a
consequence, it can assess more accurately the value of options. It should be
noted that the methods developed here allow evaluating options with any payoff
function.