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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1$\begingroup$ i suspect you'll be able to get reasonably close to this payoff using div futures, but i'm not aware of anything which matches this exactly... $\endgroup$– willCommented Jul 15, 2021 at 19:49
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$\begingroup$ Are you looking for an instrument that will pay $1$ at time $t$ for certain and that has a present value of $\mathbf E[e^{-\int_0^t q\,d\tau}]$, today,i.e. a cash flow "discounted" at the yield rate? $\endgroup$– KermittfrogCommented Jul 16, 2021 at 8:49
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$\begingroup$ @Kermittfrog: Yes. I suppose you are hinting it does not work by the arbitrage argument. $\endgroup$– HansCommented Jul 16, 2021 at 21:06
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$\begingroup$ Thanks. That condition was not clear to me from your question. I find the question is really interesting, but I have no ansatz at hand. $\endgroup$– KermittfrogCommented Jul 17, 2021 at 4:11
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