Good and Bad Dates with Models
Using an incorrect date for the ex-date in option pricing can lead to
unfavorable results. If the ex-dividend date is not known because it has yet
to be declared, it must be estimated and adjusted as need be after it is
formally announced. Traders note past dividend history and estimate the
expected dividend stream accordingly. Once the dividend is declared, the
ex-date is known and can be entered properly into the pricing model. Not
executing due diligence to find correct known ex-dates can lead to trouble.
Using a bad date in the model can yield dubious theoretical values that can
be misleading or worse—especially around the expiration.
Say a call is trading at 2.30 the day before the ex-date of a $0.25
dividend, which happens to be thirty days before expiration. The next day,
of course, the stock may have moved higher or lower. Assume for
illustrative purposes, to compare apples to apples as it were, that the stock is
trading at the same price—in this case, $76.
If the trader is using the correct date in the model, the option value will
adjust to take into account the effect of the dividend expiring, or reaching
its ex-date, when the number of days to expiration left changes from 30 to
29. The call trading postdividend will be worth more relative to the same
stock price. If the dividend date the trader is using in the model is wrong,
say one day later than it should be, the dividend will still be an input of the
theoretical value. The calculated value will be too low. It will be wrong.
Exhibit 8.1 compares the values of a 30-day call on the ex-date given the
right and the wrong dividend.
EXHIBIT 8.1 Comparison of 30-day call values