Pricing and Hedging American Options Using Approximations by Kim Integral Equations *

Abstract

We present an approximation method for pricing and hedging American options written on a dividend-paying asset. This method is based on Kim (1990) equations. We demonstrate that a simple approximation of the Kim integral equations by quadrature formulas leads to an efficient and accurate numerical procedure. This approximation is accompanied by the Newton–Raphson iteration procedure in order to compute the optimal exercise boundary at each time point. The proposed sequence of approximations converges monotonically, convergence is fast and accuracy is high, even for long maturity options. We compare numerically our results with other competing approaches by different authors. JEL classification codes: G12, G13, C63.