# Linear Stochastic Dividend Model

## TL;DR

This paper introduces a new polynomial process-based model for stock and dividend derivatives, enabling explicit computation of moments and closed-form pricing of futures, with accurate option pricing via moment matching.

## Contribution

It proposes a novel stochastic dividend model that is tractable and non-affine, allowing explicit moment calculations and improved derivative pricing methods.

## Key findings

- Closed-form expressions for stock and dividend futures prices.
- Accurate approximation of stock and dividend options using moment matching.
- Model maintains positivity of stock and non-negativity of dividends.

## Abstract

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.