Variation Margin, Futures Pricing, and Convexity Bias
Summary
The document asks whether daily variation margin changes futures prices relative to forwards, using stock-index futures as its starting point. It notes that a forward’s fair value reflects financing and asks how the resulting sensitivity to the cash index affects futures delta and hedging. The response says there need not be a meaningful price or delta difference when the forward and future are collateralized at the same rate and otherwise have matching terms.
Historically, exchange-traded futures with daily variation-margin settlements could differ from uncollateralized over-the-counter forwards. The response cites Eurodollar futures trading below comparable forward-rate agreements as an example of convexity bias. It says widespread daily collateralization has reduced this effect. Futures contango or backwardation, it adds, generally reflects the underlying asset’s carrying costs rather than margin mechanics. The explanation is concise and gives no formula for estimating the bias; the size and direction of any difference depend on contract terms and the collateral arrangements involved.
Key ideas
- Variation margin can contribute to pricing differences between futures and forwards when their collateral terms differ.
- Matching collateralization rates and contract structures can remove a tangible price or delta difference.
- Historical Eurodollar futures exhibited a convexity bias relative to forward-rate agreements.
- Daily collateralization has reduced this bias in many markets.
- Contango and backwardation generally arise from asset carry costs rather than margin payments.
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Full text
# variation margin affecting futures price # variation margin affecting futures price 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? ## Answer by user68819 (score 1) https://quant.stackexchange.com/a/79497 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.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.