Numerical investigation of early exercise in American puts with discrete dividends

ABSTRACT It is well known that early exercise of an American put may not be optimal for some time before the asset goes ex-dividend. This in turn implies that the early exercise boundary is not as smooth as for a put with a constant dividend yield. It is the purpose of this paper to illustrate that a straightforward numerical implementation of the time discrete method of lines for the Black–Scholes equation can readily cope with the disappearance and reappearance of the early exercise boundary. The performance of the method is illustrated by computing option prices when dividends are paid discretely at a known rate or known amount, as well as with a constant dividend yield.