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 nonnegative. 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 nonaffine 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.

中文翻译：

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线性随机红利模型

在本文中，我们提出了一种新的股票和股息衍生品定价模型。我们共同指定股票价格和股息率的动态，使得股票价格为正且股息率非负。在最简单的形式中，该模型的特点是股息率在股票价格的一个恒定比例附近进行均值回归。与更常见的股息收益率建模方法相比，直接指定股息率动态的优势在于更容易保持累积股息的分配易于处理。该模型是非仿射的，但属于更一般的多项式过程，它允许我们明确计算股票价格的所有条件矩和累积股息。特别是，我们有股票和股息期货价格的封闭式表达式。使用基于最大熵原理的矩匹配技术准确地近似股票和股息期权的价格。