How FRA Discounting Differs from Eurodollar Futures Settlement
Summary
The document asks why a forward rate agreement settlement is discounted at the start of its underlying interest period, while a Eurodollar futures payment is described without that discount. The question frames the issue from a borrower’s perspective and compares the settlement cash flow with the cost of borrowing over the period at the market rate. It highlights how treating the two quoted payments as interchangeable seems to change the effective borrowing cost.
The accepted response attributes the distinction to settlement timing: futures positions are marked to market and settled daily, whereas a forward is settled once at expiration, making discounting relevant to the forward payment. A further response cautions that forward and futures rates need not coincide and questions assumptions in the comparison. The discussion is a brief conceptual explanation rather than a full derivation. It does not quantify the impact of daily settlement or detail how rate differences arise, so the examples should not be taken as a complete valuation treatment.
Key ideas
- An FRA settlement is discounted because the forward payment is settled at a later date.
- Futures are marked to market daily, so their gains and losses are settled as they accrue.
- Forward and futures rates need not be identical, which affects comparisons between the contracts.
- The borrower cash flow example depends on assumptions about market rates and borrowing and investment terms.
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# Difference between settlement of Eurodollars and FRA
# Difference between settlement of Eurodollars and FRA
I am going through J.C. Hull's chapter on FRA and EuroDollar Futures.
- Taking the case of FRA. I assume $T_0$ is the time when two parties entered into a FRA to fix interest rates they get on a principal $P$ for the time between $T_1$ and $T_2$. I also assume they fixed the rate to be $R_F$. Now say time elapses and we are are time $T_1$. The market interest rate is $R_M$. Let us say $R_M > R_F$. Talking from perspective of the party who entered as a borrower, he will be paid at $T_1$, $G = P*(e^{R_M(T_2-T_1)}-e^{R_F(T_2-T1)})*e^{-R_M(T_2-T_1)}$ ( assuming all rates are expressed in continuous compound). This makes sense to me as the borrower can borrow $P$ from market at $T_1$ ( to $T_2$ ) and paying $L = P*e^{R_M(T_2-T_1)}$. Plus he can also invest amount $G$ he got for $T_1$ to $T_2$ again at rate $R_M$ earning $G^{'} = P*(e^{R_M(T_2-T_1)}-e^{R_F(T_2-T1)})$. So in net he will pay back $L-G = P*e^{R_F(T_2-T_1)}$. Which is what was intended ( assuming rate of borrowing and investing is same).
- In case of Eurodollar Future, the payment made at time $T_1$ according to hull is $P*(e^{R_M(T_2-T_1)}-e^{R_F(T_2-T1)})$. It is not dicounted. Doesn't this make the above scenario more favorable for the borrowing party ? If I repeat the same process above the amount the party pays back would be less than $L-G$ ( so that the party borrowed at a rate less than $R_F$, which is not what was agreed in the contract).
Did I misinterpret the book ?
PS: I am beginner. I apologize if I used something incorrectly or vaguely. Just having a hard time with this chapter being complete novice to finance.
## Answer by numerairX (score 3, accepted)
https://quant.stackexchange.com/a/42144
Futures trading are settled on a daily basis meaning in the end of day, your account will be adjusted by your PnL. So of course your payment on T1 is not discounted. However forward is settled only once at expiration, hence you discount the whole duration.
## Answer by Xiaohuolong (score 0)
https://quant.stackexchange.com/a/59641
I think he does mention this caveat in the last paragraph of Example 6.3, saying that a hedger could slightly reduce the size of the hedge to account for this. As for your question in particular, I feel like the problem is that you are assuming the forward rate is the same as the futures rate, while they don't necessarily need to be the same, and you are also assuming the realize spot rate at $T_1$ is greater than the forward rate.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.