A quote from Natenberg's Option Pricing and Volatility, on stock index futures and how variation margin can change their price.

Ignoring dividends, the fair value of a stock index forward contract is F = S × (1 + r × t)

For each point increase in the index, the index futures contract should rise by 1 + r × t. If we think of the cash index as the underlying contract, we can apply the concept of the delta to the futures contract in much the same way we do to an option contract. The delta is the rate at which the value of a contract will change with respect to movement in the underlying contract. If the goal is to be delta neutral, for each futures contract we hold, we must hold an opposing cash index position equal to 1 + r × t.

Wouldn't this line of logic hold for all futures? I presume this implies that the typical forward price doesn't hold for futures necessarily, because of this delta risk (and interest rate risk). Is there a way to quantify how much more or less a future should go for because of this variation margin? I know that there often can be a premium for certain futures like commodity futures; is a variation margin premium a common feature in futures markets?


1 Answer 1


Caveat - not a Commodity/Equity person but:

Assuming both the index forward and index future are collateralised at the same rate, then I don't think there should be any tangible difference in price/delta (if the contracts are set up the same).

The difference came about (in the past) when exchange traded index futures were subject to daily VM exchanges (and IM) whereas OTC transactions (i.e. index forwards) usually, didn't require any collateralization. The most famous place this bias existed was in Eurodollar futures (I am sure there are a plethora of threads here on this), where they used to trade at a discount to FRAs (i.e. the FRA implied rate = ED Rate - Convexity bias). Now days, nearly everything is collateralised with daily exchanges of VM and IM and this bias has dissipated to a large extent.

The contango/backwardation of futures is not directly a symptom of margins. It is more to do with the carrying costs of the commodity/equity/bond/asset itself.

  • $\begingroup$ The convexity bias is still there for sofr futures? Try price blues or greens without it as its around 9 bps at the back of the blues. Single period swaps only match futures if the collateral interest rate is zero. $\endgroup$
    – river_rat
    Commented May 25 at 20:08
  • $\begingroup$ Fair, I haven't looked. Why ? As I can trade SPS cleared via CME versus SoFR future, with high netting.. or is this a manifestation of LCH/CME basis $\endgroup$
    – user68819
    Commented May 25 at 20:38
  • 1
    $\begingroup$ Convexity bias on FRAs/Stir futures has nothing to do with collateral interest rates paid on money in the account. This is easily observed by noting the convexity bias for greens/blues on Euribor is broadly the same for negative, or positive, or zero rates, which have all been experience recently. The convexity bias is due to the fact the that the products price against the same index and so can be exactly delta hedged by each other but that when doing that one product has more gamma that the other. That gamma has value and creates the adjustment, always in same direction. $\endgroup$
    – Attack68
    Commented May 26 at 7:24
  • $\begingroup$ There is no gamma with an SPS or a future, both are linear instruments. A sps with a gold standard CSA but zero collateral interest rate prices as a forward expectation under the risk-neutral measure ie as a future. Any other interest rate on collateral (fed funds, sofr etc) changes the measure you are using and that measure change is the convexity adj. Roughly, one you make money now and the other you make money in the future discounted by the collateral rate. $\endgroup$
    – river_rat
    Commented May 26 at 10:10
  • $\begingroup$ A single period interest rate swap, does, in fact, contain gamma, whilst the STIR future has zero. Please see quant.stackexchange.com/a/45804/29443 . $\endgroup$
    – Attack68
    Commented May 26 at 17:55

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