A Tradable Instrument for Stochastic Dividend Discounting

Summary

The document poses a derivatives and market-design question in a zero-interest-rate setting. It considers a stock whose dividend rate is stochastic and asks whether a publicly traded instrument could have a time-zero value equal to the expected exponential of the negative cumulative dividend rate over a specified horizon. The desired payoff is described by analogy with a bond discounted at the stock’s dividend rate.

No answer, construction, pricing method, or evidence is included, so the document does not identify an instrument that meets the stated criterion. It leaves open whether the target value could be replicated with traded securities or whether an exchange-listed contract would be needed. Any proposed solution would depend on how the dividend process is modeled, what assets can be traded, and the market’s pricing measure; those assumptions are not specified here.

Key ideas

• The question concerns a stock with a stochastic dividend rate in a zero-rate environment.
• The target is a publicly traded instrument linked to the expected cumulative dividend discount factor.
• The proposed analogy is a bond whose discount rate follows the stock’s dividend rate.
• The document does not provide a replication strategy, instrument, or pricing argument.
• A solution would require assumptions about the dividend process and tradable assets.

Tags

# Publicly traded instrument analogous to a bond with discount rate equal to a stock dividend rate


# Publicly traded instrument analogous to a bond with discount rate equal to a stock dividend rate












Suppose we have a stock paying a stochastic dividend at rate $q$ in a zero interest rate environment. Is there a publicly traded (non-over-the-counter, meaning not specially designed for an entity) instrument, synthesized or not, with present value $\mathbf E[e^{-\int_0^t q\,d\tau}]$ at time $t=0$? It is analogous to a bond with discount rate set at the dividend rate.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.