The path integral method developed in the author's previous work is applied to solve extended Heston models. A transition probability density is obtained for Heston models with stochastic interest rates described by Vasicek and CIR processes. Option pricing formulas are derived for both cases. The analytic solutions are valid when the Wiener process driving the interest rate is uncorrelated with the Wiener processes of the asset price and volatility. In the presence of such correlations, the model no longer admits an analytic solution, which is consistent with results reported in other studies.
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