How Daily Settlement Changes Eurodollar Futures and Forward Pricing
Summary
The document compares a six-month Eurodollar futures contract with a forward contract at the same quoted rate. Its main pricing distinction is daily marking to market: futures gains and losses must be invested or funded as rates move, while a forward generally settles later. Because futures gains tend to occur when rates are low and losses when rates are high, the timing can make futures less valuable than an otherwise comparable forward. The explanation gives the general convexity adjustment: the difference depends on the covariance between the payoff and the stochastic discount factor, and it notes that a positive covariance lowers the futures price relative to the forward price.
The discussion also qualifies the comparison. OTC forwards may involve initial or variation margin and collateral, so they can create funding needs too. Clearing venue positioning and margin arrangements may affect relative value enough to outweigh the convexity effect. One answer emphasizes counterparty credit risk in forwards, but another notes that clearing can reduce that concern for both instruments; the preferred contract therefore depends on settlement and funding details, not just the headline rate.
Key ideas
- Daily futures settlement creates reinvestment and funding effects that a deferred-settlement forward may avoid.
- When payoff is positively correlated with the stochastic discount factor, the futures price is expected to be below the forward price.
- Margin and collateral on OTC contracts can reintroduce funding costs.
- Clearing venue positioning and margin differences can outweigh the usual convexity adjustment.
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Full text
# Eurodollar future vs Eurodollar forward contracts
# Eurodollar future vs Eurodollar forward contracts
You are considering two contracts: a Eurodollar futures contract with six months to maturity, selling at 5%, settled on three-month LIBOR, marked to market every day; and a Eurodollar forward contract with six months to maturity, selling at 5%, settled on three-month LIBOR
Which contract do you prefer?
I don't understand the answer given in Crack's Book Heard on the Street.
Could anyone else explain this to me please.
## Answer by ir7 (score 4, accepted)
https://quant.stackexchange.com/a/55266
I guess the author's argument is that, because of the frequent settlements, one needs to invest the mark-to-market gains and fund the losses. As the exchange traded futures contract is negatively correlated to interest rates, the mark-to-market gain happens when interest rates are low, so not a great time to invest, while the loss happens when interest rates are high, so not a great time to look for funding.
Over-the-counter (OTC) forward contract does not have to go through this pressure (even though these days some forms of initial margins, variation margins and collateralization - all of them needing to account for some funding/investing - are accompanying most OTC contracts).
Edit: In general, theoretically, there is an expectation that futures price is less than forward price, if the uknown amount (at expiry) is positively correlated to the (stochastic) discount factor.
Given $T$ expiry date and $S$ payment date and unknown ${\cal F}_T$-measurable amount $X$, $\beta_t = \exp (-\int_0^t r_udu)$ stochastic discount factor (its inverse, bank account value, being the standard numeraire here) and (zero-coupon) bond price $B(t,T)=\beta_t^{-1}\mathbf{E}[\beta_T | \cal{F}_t]$, we have:
$$ {\rm Fwd}_t^X = B(t,S)^{-1}\beta_t^{-1}\mathbf{E}_t[\beta_S X] $$
and, due to (continuous) resettlement (and other technical assumptions),
$$ {\rm Fut}_t^X = \mathbf{E}_t[X] $$
(making futures prices a martingale).
It can then be proved that the futures convexity correction is:
$${\rm Fut}_t^X = {\rm Fwd}_t^X - \beta_t^{-1} B(t,S)^{-1} \mathrm{Cov}_t(X, \beta_S). $$ Time $0$ relation is: $${\rm Fut}_0^X = {\rm Fwd}_0^X - B(0,S)^{-1} \mathrm{Cov}(X, \beta_S). $$
In the Libor futures/forward price context above (long futures contract), the covariance is positive.
(Proofs are available in Hunt and Kennedy's book, Financial derivatives in Theory and Practice.)
## Answer by Attack68 (score 2)
https://quant.stackexchange.com/a/55330
I have written a response here:
Why are FRA/futures convexity adjustments necessary?
The credit risk is eliminated in either case since, these days the future will trade on the exchange and the FRA contract will be settled with the clearing house.
There might actually be some value created dependent upon which futures exchange you trade: LCH versus EUREX can (at time) have significant value differentials solely due to the positioning of dealers looking to reduce concentrated exposure. This effect can outweigh convexity and can be in either direction. However, if you traded a future and a FRA across different exchanges you would want to ensure the carry charge on the required margin at each institution was smaller than the gain - if the two were traded at the same settlement venue then the margin would be much more reduced.
## Answer by John (score 1)
https://quant.stackexchange.com/a/55255
didn't read the book, but I would guess the future contract all else being equal.
the point being credit risk.
as mentioned the future contract is settled daily by the exchange. forwards are traded over the counter and settled at expiration, by that time, the party owing to the other could default on the payment.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.