Hi,The simple compounding fwd fwd rate between t1, t2 is given by(1/DC) * [DF(t1) / DF(t2) -1](where day count is denoted as DC)Now consider an IR futures contract expiring at t1 into a rate with maturity t2. Assume there is no day to day settlement, no margining .. i.e the trade settles at t1 into the rate until t2Which of the following 2 values of f gives the correct futures prices (100 -f)(1) (1/DC) * [DF(t1) / DF(t2) -1](2) (1/DC) * [1 - DF(t2) / DF(t1)]Documentation for a trading system I have been looking at gives (2), whereas I've always assumed this hypothetical futures contract would be priced using (1)Can anyone shine any light?

if you are talking about exchange traded futures there is no discount factors or anything....dv01 for ed futures is fixed at 25 bucks per contract and the forward rate is what the screen says.....

Hi,Yes I appreciate your point here, with daily marking to market then P/L on a ED future will just be calculated from (basis points move) * tick value.The trading system that I have been looking at calculates a theoretical price for the contract assuming that settlement only occurs at the maturity date of the futures contract rather than on a day to day basis. In this case, I was surprised that the theoretical price is not just given by 100 - fwd/fwd rate.i.e. I expected it to use(1) 100(1 - (1/DayCount) * [DF(t1) / DF(t2) -1] )but it uses(2) 100(1- (1/DayCount) * [1 - DF(t2) / DF(t1)])I find this surprising since I have used discount factor boot strapping routines in the past that take the fwd fwd rate to be 100 - futures price (with an additive convexity adjustment.. but this is besides the point here). This to me implies that the correct expression should be (1).Does equation (2) hold any intuition for anyone?

Just reading your text your system returns price assuming settlement on futures expiry.Your standard eqn is for settlement at end of period as for SWAPS,FRAs etc, so multiply by ratio of DF2/DF1 to convert from FRA to future (and neglecting any other convexity effects)

thanks.So the system effectively fwd discounts the fra rate from t2 -> t1, so that the settlement amount on the future should then be calculated as a future value calculation rather than a NPV calculation.Just a case of discounting the rate and paying future value v. not discounting the rate and paying NPV. So in essence they are equivalent.

Not really sure what you are asking here. ED is valued by 100-fwd/fwd rate and then adjusted for conv. by a variety of different methods. Are you trying to use an FRA pricing methodolgy to value stirs ?

Hi,the original question was to do with the equation for 'fwd/fwd' used to get the futures price 100-fwd/fwd, in the absence of a convexity adjustment.I was expecting to see (1/DC) ( DF1/DF2 -1)but the system uses (1/DC) (1- DF2/DF1) = (DF2/DF1) * (1/DC) * (DF1/DF2 - 1)It's been pointed out that this must be to do with when the future settles compared to when the fra settles. The only way I can see it being correct is if the future pays 'FV' as opposed to NPV at t1 (with the rate already having been adjusted by the fwd Discount factor DF2/DF1). Then there wouldn't be an arbitrage between the equivalent FRA and this hypothetical futures contract.

I see what you are saying.I can't find any references for (2) and intuitively can't see the point. Have you asked the trading system vendor for the methodolgy ?

yep, they replied with one of those helpful 'it's convention' type comments. They also stated that the results are very close.. which isn't very surprising for reasonable values of the parameters, since if substitution L = (1/DC)(DF1/DF2-1) is made in both equations then one is just the first order truncated binomial expansion of the other.

Do you have the sources for equations (1) & (2) ?

This eqn is correct (ignoring effects of accruals) only on the futures settlement date.On all other dates prior to this it is incorrect for both discounting and convexity effects.Not sure why you would code it in this way at all.

This eqn is correct (ignoring effects of accruals) only on the futures settlement date.On all other dates prior to this it is incorrect for both discounting and convexity effects.Not sure why you would code it in this way at all.

Presumably, the discount factors would be taken from the futures settlement point. The equation(s) are a neater and more easily coded method than the implied forward calc