A stock trades at 100 and goes ex-dividend tomorrow for $3.00. You hold a 90-strike American call expiring 7 days after the ex-date. The rate is 5% and the call has $0.04 of time value above intrinsic. Do you exercise, and what is the decision rule?

A stock trades at 100 and goes ex-dividend tomorrow for $3.00. You hold a 90-strike American call expiring 7 days after the ex-date. The rate is 5% and the call has $0.04 of time value above intrinsic. Do you exercise, and what is the decision rule?

Approach: Compare the dividend captured by exercising against the interest given up on the strike plus the option time value that is destroyed.

Exercise the call just before the ex-date. Exercising early captures the $3.00 dividend but pays the strike 7 days sooner, giving up interest on the strike of K*(1 - e^{-r*tau}) = 90*(1 - e^{-0.05*7/365}) = 90*0.000959 = $0.086, and it destroys the $0.04 of remaining time value. The trade is worth 3.00 - 0.086 - 0.04 = $2.874 per share, so exercise. The general rule is to exercise an American call only immediately before an ex-date, and only when the dividend exceeds the interest on the strike plus the time value, which is why deep in-the-money low-vol calls into a large dividend are the ones that get exercised.

Follow-up: How does the answer change if the dividend is $0.10 and the rate is 0%, and what does that imply about American calls on non-dividend stocks?

Key concepts: early exercise, dividend capture, time value, interest on the strike.