线性随机股利模型

摘要：

在本文中，我们提出了一个新的定价模型的股票和股息衍生品。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，股息率为非负。在其最简单的形式中，该模型的特点是股息率是围绕股价的一个常数部分均值回复。与更为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布易于处理。该模型是非仿射的，但属于更一般的多项式过程类，这使得我们能够显式地计算股票价格和累积股息的所有条件矩。特别是，我们有股票和股息期货价格的封闭式表达式。股票和股息期权的价格准确地近似使用矩匹配技术的最大熵原理的基础上。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。