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Review of Finance 2003 7(3):361-383; doi:10.1023/B:EUFI.0000022128.44728.4c
© 2003 by European Finance Association
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Right arrow G12 - Asset Pricing; Trading volume; Bond Interest Rates
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Pricing and Hedging American Options Using Approximations by Kim Integral Equations*

Siim Kallast1 and Andi Kivinukk2

1 Tallinn Pedagogical University Narva Str. 25, Tallinn 10120, Estonia E-mail: siim.kallast{at}rlk.ee
2 Tallinn Pedagogical University Narva Str. 25, Tallinn 10120, Estonia E-mail: andik{at}tpu.ee

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.

Key Words: American options • early exercise boundary • hedging parameters • integral equations • numerical procedures • optimal exercise


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