At the same stock price of $76 per share, the call is worth $0.13 more
after the dividend is taken out of the valuation. Barring any changes in
implied volatility (IV) or the interest rate, the market prices of the options
should reflect this change. A trader using an ex-date in the model that is
farther in the future than the actual ex-date will still have the dividend as
part of the generated theoretical value. With the ex-date just one day later,
the call would be worth 2.27. The difference in option value is due to the
effect of theta—in this case, $0.03.
With a bad date, the value of 2.27 would likely be significantly below
market price, causing the market value of the option to look more expensive
than it actually is. If the trader did not know the date was wrong, he would
need to raise IV to make the theoretical value match the market. This option
has a vega of 0.08, which translates into a difference of about two IV points
for the theoretical values 2.43 and 2.27. The trader would perceive the call
to be trading at an IV two points higher than the market indicates.