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.

  • 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... $\endgroup$
    – will
    Jul 15, 2021 at 19:49
  • $\begingroup$ 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? $\endgroup$ Jul 16, 2021 at 8:49
  • $\begingroup$ @Kermittfrog: Yes. I suppose you are hinting it does not work by the arbitrage argument. $\endgroup$
    – Hans
    Jul 16, 2021 at 21:06
  • $\begingroup$ 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. $\endgroup$ Jul 17, 2021 at 4:11


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.