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When using the Black-Scholes-Merton method for option valuation which takes into account dividends, does the dividend only get included into the calculation of options whose lifetime straddles the dividend exdiv date?

For example today is 16Nov2015. Lets say stock xyz has an upcoming exdiv date on 16Jan2016. If im valuing an option whose expiration is in either November or December, do I include January's dividend into that calculation because they expire before the exdiv date.

Or do I only include options whose expiration is after the exdiv date?

Or do I simply always include the stocks current dividend yield into the calculation,...regardless of whether the options expiration falls before or after the next exdiv?

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The dividend adjustment in the option formula represents compensation for dividend income that an ordinary stockholder will have entitlement to before expiry, but which you the option owner will not be entitled to.

If at expiry you exercise into a stock that has not gone exdiv, then you are entitled to the dividend, and so should not include it in your calculation. But you should include any dividends that were announced and went exdiv before expiry, and which you will thus never receive.

It is more complicated if expiry date is the same as exdiv date. From memory, it goes exdiv at a certain time of day. Typically options also have a specific time of expiry. Note also some european contracts go american on expiry day.

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  • $\begingroup$ So just to confirm one last thing. If im valuing an option today which expires next month and goes exdiv tomorrow, then obviously I include the dividend in the calculation. What happens in two days time after exdiv has completed. Does that dividend still get included in the calculation if valuing the option 2 days from now (because the exdiv has already passed)? ie: is there a difference if the valuation is done before the exdiv date vs afterwards $\endgroup$ – darkpool Nov 18 '15 at 6:05
  • $\begingroup$ IMHO the BSM (or continuous dividend formula) is best used for indexes, where a large number of small dividends are steadily occurring. For an individual stock, there are better ways to adjust for dividends, such as en.wikipedia.org/wiki/Black's_approximation or Geske (1979). $\endgroup$ – noob2 Nov 18 '15 at 17:43
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    $\begingroup$ @darkpool: as soon as it goes exdiv, the price of the stock will drop corresponding to the dividend amount. Now immediately after the price has dropped, you calculate the option price from the new spot price, but exclude the dividend. Then the option price should remain the same, because what you lose on the underlying price drop, you gain by excluding the dividend. $\endgroup$ – quis est ille Nov 19 '15 at 19:16

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