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

Analytical and Numerical Approaches to Pricing the Path-Dependent Options with Stochastic Volatility