Abstract

The paper concerns high-order collocation implementation of the integral equation approach for pricing American options with stochastic volatility. As shown in Detemple and Tian (2002) , the value of American options can be written as the sum of the corresponding European option price and the early exercise premium (EEP). This EEP representation results in a nonlinear Volterra integral equation for the optimal exercise boundary. There are no efficient and reliable numerical methods for solving the integral equations in the literature. The aim of this paper is to develop a high-order collocation method for solving the nonlinear integral equations. Collocation methods are widely studied in the area of numerical integral equations. After the exercise boundary is resolved, the value of the American options is obtained by evaluating the EEP representation.

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