Pricing American continuous-installment options under stochastic volatility model

This paper presents an integral equation approach for pricing American continuous-installment options when the stock price follows Heston's stochastic volatility model. By exploiting a log-linear relationship of the free boundary function with respect to volatility changes and using the decomposition technique and Fourier inversion transform, we drive integral expressions of the initial premium along with the optimal stopping and early exercise boundaries for this option. This offers a system of nonlinear Volterra integral equations for determining the two free boundaries, which can be used to estimate the option price. Numerical integration technique accompanied with the Newton–Rahpson iteration procedure is proposed for solving the integral equations. The method is implemented, and some numerical examples are provided to examine the boundary properties and the option price behavior. The computational efficiency of this method is also considered.