Linear Stochastic Dividend Model

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. * EPFL and Swiss Finance Institute. 1 In reality, dividends are paid out discretely instead of continuously. Most liquid dividend derivatives, however, reference dividends paid by a stock index, in which case continuously paid dividends are considered an acceptable approximation.

A term structure model for dividends and interest rates

“…This process has, however, no guarantee to be monotonically increasing, meaning that negative dividends can occur frequently. Willems (2019b) jointly specifies dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate is a nonnegative process mean-reverting around a constant fraction of the stock price. The model of Willems (2019b) is in fact a special case of the general framework introduced in our paper, although it is different from the LJD model and does not incorporate stochastic interest rates.…”

“…Willems (2019b) jointly specifies dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate is a nonnegative process mean-reverting around a constant fraction of the stock price. The model of Willems (2019b) is in fact a special case of the general framework introduced in our paper, although it is different from the LJD model and does not incorporate stochastic interest rates. We add to this literature by allowing for stochastic interest rates, which is important for the valuation of interest rate-dividend hybrid products or long-dated dividend derivatives (e.g., the dividend paying stock).…”