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Linear Stochastic Dividend Model

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  • Sander Willems

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.

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  • Sander Willems, 2019. "Linear Stochastic Dividend Model," Papers 1908.05850, arXiv.org, revised Aug 2019.
    • Handle: RePEc:arx:papers:1908.05850
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    References listed on IDEAS

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    1. R. S. Tunaru, 2018. "Dividend derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 63-81, January.
    2. Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jul 2019.
    3. Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.
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