Abstract
This article studies the modelling of discrete cash dividends. We distinguish the escrowed dividend model from the stock price process jumping downwards at ex-dividend dates. We show how dividend jumps impact the second moment of the stock terminal distribution. This distinctive feature precludes usual implied volatility data from being directly input in such a type of model, since they are extracted from another pricing framework. A preliminary volatility adjustment to discrete cash dividends is then described. This global adjustment leads to a refinement of the local volatility surface. This refinement appears to be quite natural theoretically speaking. It proves also to be very efficient numerically, at least for the simplest products such as American-style options.
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