Linear Stochastic Dividend Model

18 Pages Posted: 16 Aug 2019 Last revised: 26 Aug 2019

See all articles by Sander Willems

Sander Willems

Ecole Polytechnique Fédérale de Lausanne

Date Written: August , 2019


In this paper we propose a new model for pricing stock and dividend derivatives. We jointly specify dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate non-negative. In its simplest form, the model features a dividend rate that is mean-reverting around a constant fraction of the stock price. The advantage of directly specifying dynamics for the dividend rate, as opposed to the more common approach of modeling the dividend yield, is that it is easier to keep the distribution of cumulative dividends tractable. The model is non-affine but does belong to the more general class of polynomial processes, which allows us to compute all conditional moments of the stock price and the cumulative dividends explicitly. In particular, we have closed-form expressions for the prices of stock and dividend futures. Prices of stock and dividend options are accurately approximated using a moment matching technique based on the principle of maximal entropy.

Keywords: dividend derivatives, term-structure models, derivative pricing, polynomial processes

Suggested Citation

Willems, Sander, Linear Stochastic Dividend Model (August , 2019). Available at SSRN: or

Sander Willems (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900

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