# Discrete Dividends

The natural extension of the classical model in the equity world is to add a discontinuity to the diffusion to represent the jump due to the dividend.

The modeling of the amount of the drop differentates the models.

This modeling can possibly rely on the existing spot factor. In general, this is enough except when we tackle options on dividends. In that case, we look at the proper dividend convexity. For this situation, we need a proper dividend factor.

We shall concentrate on one-factor models only. Within this class of model, we have different possible assumptions.

We assume that analysts have come with a modeling of the expected dividends to be paid in the future. We need in/out modeling to be able to shift this amountin the future depending on the equity path.

If we zoom in on the contribution of the dividends in the P&L equation, we have:

where Dr is the realized dividend amount.

At the same time, the model price has implicitely made the assumption that the dividend model = Dm

So, the total cost due to the difference between the realized dividends Dr and the modeled ones Dm generates an impact in the pricing of:

To obtain the fair valuation, we need to obtain the right modeling of the dividends.

The process of the spot in the presence of discrete dividends is given by:

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