Dear all, I tried to value a floating leg of an IRS (5Y maturity, paying euribor 6m, each 6 months) using a discount factor curve taken at the end of september 2009. I noticed that results using a spline interpolation of the discount factor curve differ from the results using a exponential interpolation of the discount factor curve, more than expected. Does someone encountered the same behaviour, and could this be attributed to the peculiar shape of the actual depo-swap curve up to 7Y: pronounced upward slope ? Thank you. André

the value of the floating leg should largely be independent of the way you interpolate. this is because the forward rate between t and T (let's call it L(t,T)) is given purely by the discount factors at t and Tdf(t) * 1/(1+L(t,T)*(T-t)) = df(T)hence L(t,T) = (df(t)/df(T)-1)/(T-t)the cash flow at time T is set at time t and its PV is given byL(t,T)*(T-T)*df(T) = df(t) - df(T)now you will see that if you sum up all the cash flows then the intermediate discount factros all drop out and the PV of the floating leg isdf(t0) - df(Tn) where t0 is the time of the next cash flow and df(tn) is the last flow.

The telescopic df(t0) - df(Tn) property of a floating leg is never been exact if you take correct dates into account, but accurate enough to be used.Anyway it doesn't hold if your discounting curve is different from the curve you use for estimating forward Libor rates, which is often the case nowadays. If this is your situation then an interpolation dependency is to be expected.ciao -- Nando

"The telescopic df(t0) - df(Tn) property of a floating leg is never been exact if you take correct dates into account, but accurate enough to be used."Not meaning to ruffle any one's feathers here, but the "telescopic" approximation is frequently exact because the rate forecast and accrual periods often do coincide exactly. Errors with this approximation are the exception, rather than the rule and are usually "small" as has been pointed out.

Quote Anyway it doesn't hold if your discounting curve is different from the curve you use for estimating forward Libor rates, which is often the case nowadays. If this is your situation then an interpolation dependency is to be expected a good point but well beyond the original post which does not mention different curves.

Hi, maybe I should give some details about the way the fair value calculation of the floating leg is done: I'm using an Excel based financial software. The market inputs needed for the FV calculation of a general floating leg are two discount factor curves and the index fixing (in my case the Euribor 6M fixing), beyond the contractual details. One of the discount factor curve is used for forcasting forward Libor rates, while another is used to discount the deterministically forecasted cash flows. In my particular case, I'm using the same discount factor curve, both for forcasting and disocunting. I'm not sure that the software computed the floating leg FV using the "telescopic" property of a floater: df(0) - df(Tn). I think that it rather calculates at each fixing date the forward Libor rate using the formula: L(t,T) = (df(t)/df(T)-1)/(T-t), as indicated in the first answer at my query. When pricing the fixed leg of the swap, using the same df curve as for the floating leg, there is very insignificant dollar difference between a cubic-spline and an exponential interpolation. This is not the case for the floating leg, when there is significant dollar difference between a cubic-spline and an exponential one. I suspect that this behaviour comes from the foward Libor rates forecasting. An exponential interpolation is adapted for a stable forward rate environment (a quite "flat" depo-swap curve, like the one end 2008), while this could not be adapted in the actual environment, when the forward Libor 6m rates embedded in the depo-swap curve have a steepening increasing up to 5Y maturity. I'm trying to asses if in the actual interest rate environment, interpolation issue is a relevant one.thanks for your answers.

Quote I'm not sure that the software computed the floating leg FV using the "telescopic" property of a floater: df(0) - df(Tn). I think that it rather calculates at each fixing date the forward Libor rate using the formula: L(t,T) = (df(t)/df(T)-1)/(T-t), as indicated in the first answer at my query. it doesn't matter if it doesnt do it explicity - it should come out in the wash.I think the problem here is that the software should be interpolating rates rather than discount factors.

I thought that it is more precise to interpolate on discounts rather than on interest rates, due to the relatively smoothing introduced by the transformation: 1/(1+r)^t or exp(-t*r).

lets say the curve was flat @ 10% and letw say we wanted to figure out the discount fcator for year 2 given year 1 and 3 df's or ratesfor year the df is 0.904837, year 3 the df is 0.740818interploting the df's gives you a df for year 2 of 0.822828interpolating the rate (which gives you 10%) gives a df of 0.818731

You gotta appreciate DaveAngel's aproach to the questions on the board. Intuitive, adequate simplification and, most importantly good, complete examples.Thanks,Alk

QuoteOriginally posted by: AlkmeneYou gotta appreciate DaveAngel's aproach to the questions on the board. Intuitive, adequate simplification and, most importantly good, complete examples.Thanks,Alk