  We present a path integral method to derive closed-form solutions for option
prices in a stochastic volatility model. The method is explained in detail for
the pricing of a plain vanilla option. The flexibility of our approach is
demonstrated by extending the realm of closed-form option price formulas to the
case where both the volatility and interest rates are stochastic. This
flexibility is promising for the treatment of exotic options. Our new
analytical formulas are tested with numerical Monte Carlo simulations.
