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Apparently for options on futures there's no discounting. Why is that, how do we demonstrate that, and , I would have thought the rate of interest the exchange pays you on your margin would have impact

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  • $\begingroup$ What do you mean by "there's no discounting"? Option pricing formulas certainly take time value of money into account for future payoffs. $\endgroup$
    – D Stanley
    Apr 6, 2022 at 18:23
  • $\begingroup$ The formula for futures is the Black 1976 formula en.wikipedia.org/wiki/Black_model $\endgroup$
    – nbbo2
    Apr 6, 2022 at 19:08
  • $\begingroup$ traders apparently use fwd premum version of black 76. i am asking for a proof of why thats correct , and what is impact of the interest on the margin for that $\endgroup$
    – Randor
    Apr 7, 2022 at 10:13

2 Answers 2

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For futures style options on futures you are correct, there is no discounting. That is because the option contract is itself a future and pays variation margin. These are quite popular on some emerging market exchanges because there is no early exercise premium on these options (american style and european style puts and calls have the same price).

For traditional options on futures you do discount the premium as the buyer of the option pays premium and variation margin is only demanded from the option seller to minimize credit risk to the clearing house. There is also a difference between american and european style options in this case which must be taken into account.

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  • $\begingroup$ I agree that you do not discount the price of the option (the premium), because you do not invest any cash in the option when you buy it, however you still discount the payoff (if any) which will occur at time T, i.e. in the future. So there is still an "exp(-rT)" in the Black 1976 formula. The statement in the question "there is no discounting for options on futures" is an oversimplification or abbreviated language that leaves this detail out. $\endgroup$
    – nbbo2
    Apr 7, 2022 at 7:41
  • $\begingroup$ hi @noob2 , if you look at settlement prices the exchange publishes for example, they are not discounted. so it seems strange to me . the exchange typically pays RFR on your margin , so the trade is equivalent to a OTC trades that have standard CSA , and such OTC trades are priced spot prem, so why not same for option on futures? $\endgroup$
    – Randor
    Apr 7, 2022 at 7:53
  • $\begingroup$ I think you are right. $\endgroup$
    – nbbo2
    Apr 7, 2022 at 7:56
  • $\begingroup$ also, note that in both futures style and traditional style (aka EQ style i believe) , in both cases you have an upfront payment (either premium , or the Initial Margin (IM)). the IM would be of similar magnitude to the premium i would think and can be thought of as like the premium and so there should be discounting. @noob2 i did not understand in which case you say there is discounting done today for futures options $\endgroup$
    – Randor
    Apr 7, 2022 at 7:57
  • $\begingroup$ To be clear, for a future style option on a future there is no discounting of in the black formula. This is independent of the initial margin required, even if no initial margin is called you still do not discount the black formula. $\endgroup$
    – river_rat
    Apr 8, 2022 at 21:07
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A more theoretical reason why futures and options on futures do not have to be discounted is developed in the very nice treatment of futures within the martingale/no arbitrage framework in Darrell Duffie's book Dynamic Asset Pricing Theory. It boils down to the following:

  • An arbitrary asset is a pair of a price process $S_t$ and a cumulative dividend process $D_t$. The price $S_t$ is what you pay to get the asset, and $D_{t+dt}-D_t$ are the dividends you receive in the interval $[t,t+dt]$ when you hold the asset.

  • The no-arbitrage theory dictates that under the risk-neutral measure the discounted price process $S_te^{-rt}$ is a martinagle, while for the dividend process $D_t$ no discounting is required to make it a martingale.

  • A future has price $S_t$ identically zero (we don't have to buy it) but its margin account is nothing else than a cumulative dividend process $D_t$ that can go negative (when it goes negative you have to put more cash in - margin calls). The thing is that the option on the future is the option on $D_t$ (which doesn't have to be discounted to be a martingale).

  • For those who have no copy of Duffie's book around a related discussion can be found here.

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  • $\begingroup$ is Dt the accumulated value of all dividends paid on asset in the past up till today, accumulated at the interest rate the exchange pays? what is the affect of changing the rate of interest the exchange pays you on margin? for OTC derivatives with standard CSA , these are priced with discounting , so why not for exchange traded? what about options on equities , on exchange these are priced with discounting, why is that then? $\endgroup$
    – Randor
    Apr 7, 2022 at 10:23
  • $\begingroup$ In the case of a future $D_t$ is the cash in your margin account. Including whatever interest the exchange pays. That interest is absorbed in $D_t$. Your comment includes far too many questions that go beyond this post. Think about it and start a new question with focus and details. $\endgroup$
    – Kurt G.
    Apr 7, 2022 at 11:26
  • $\begingroup$ when the exchange pays interest on the margin equal to the ois rate , then it looks to me like cashflows are same as if the derivative were traded OTC with a standard CSA. in which case, why in the OTC case is the value discounted , whereas in the exchange case it is not? $\endgroup$
    – Randor
    Apr 7, 2022 at 12:21

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