Why Futures-Style Options on Futures Are Not Discounted
Summary
The document distinguishes futures-style options on futures from traditional options on futures to explain when discounting applies. In the futures-style contract, gains and losses are settled through variation margin, so the option itself behaves like a futures position rather than requiring an upfront premium. The answer states that this convention removes discounting from the option valuation and gives American and European versions the same price in this setting.
Traditional options on futures instead require the buyer to pay a premium, while variation margin is generally collected from the seller to reduce clearinghouse credit risk. Their premium is discounted, and American and European exercise styles can have different values. A second explanation frames the distinction through risk-neutral pricing: prices are discounted, whereas cumulative cash flows such as dividends are not; a futures position has zero purchase price and its margin flows play the cumulative cash-flow role. The account is conceptual and relies on the contract’s settlement conventions, so it should not be generalized to every product described informally as an option on futures.
Key ideas
- Futures-style options settle value through variation margin rather than an upfront premium.
- Under this settlement convention, futures-style options on futures are priced without discounting.
- Traditional premium-paid options on futures require discounting and may have an early exercise premium.
- The martingale explanation treats futures margin flows like cumulative cash flows rather than a purchased asset price.
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Full text
# For options on futures why is there no discounting?
# For options on futures why is there no discounting?
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
## Answer by river_rat (score 5)
https://quant.stackexchange.com/a/70433
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.
## Answer by Kurt G. (score 2)
https://quant.stackexchange.com/a/70438
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.