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

A path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models