  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.
