# Dividend adjustment on SABR formula for interpolating implied volatility

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?

• 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? Feb 27, 2022 at 8:00
• From the forward we usually subtract the dividends that are due between now and the time of the forward. Feb 27, 2022 at 8:00