Abstract
In this paper, we establish the way in which the alternating direction implicit (ADI) finite different method can be applied to option pricing problems. We develop ADI schemes for both European call option values written on a single underlying asset and American call option values on the maximum or minimum of two underlying assets. While Stulz (1982) assumes no dividend streams for the underlying assets, here we extend his model to American-type and allows for continuous dividend yields for each underlying asset. We address the problem of option pricing on multiple underlying assets, and provide theoretical justifications for the numerical stability of the ADI schemes that we develops in this paper. Our ADI schemes are shown to be unconditionally stable.
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