We are using a SABR model to interpolate the implied volatility surface. The model yields a formula for implied volatility that contains the following term:

$\ln \left(\frac{K}{F}\right)$

It is proposed to take into account cash dividends by modifying this part of the equation to:

$\ln \left(\frac{K+D}{F+D}\right)$

$D$ is Dividend adjustment for maturity $t$

$F$ is the forward contract value for maturity $t$

$K$ is the Strike value

Can you please explain the rationale of such a modification in the formula in order to take into account cash dividends?

  • 1
    $\begingroup$ My answers to this and this question show how to incorporate dividends into a forward for the stock. I do not quite understand why it was proposed that $D$ should also be added to the strike $K$. Also the sign of $D$ matters a lot. Is your $D$ positive or negative? $\endgroup$
    – Kurt G.
    Feb 27, 2022 at 8:00
  • $\begingroup$ From the forward we usually subtract the dividends that are due between now and the time of the forward. $\endgroup$
    – Kurt G.
    Feb 27, 2022 at 8:00


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