Suppose we want to find a reasonable approximation for the interest rate for a period of x months starting somewhere in the future (say period [t1,t2]) based on Euribor. My plan was the following:1) Use Bloomberg to download Euribor quotes for months (eg via EUR012M Index) and European swap quotes for years (eg via EUSA5 Curncy, said to have day count convention 30/360). My assumption is that we can connect the two curves without any correction factor2) Perform linear interpolation to find quotes for period now->t1 and now->t2 from the two most nearby quotes3) Derive implied forward rate r_t1->t2 from: (1+r_now->t1)^t1 * (1+r_t1->t2)^(t2-t1) = (1+r_now->t2)^t2 where t1 and t2 are measured in days / 360, and r_now->t1 is the number we found by interpolation.Any comments? Do we need to worry about connection between curves, the linear interpolation or day count conventions? regards allu

QuoteOriginally posted by: allu(1+r_now->t1)^t1 * (1+r_t1->t2)^(t2-t1) = (1+r_now->t2)^t2 Euribor has a maturity <= 12 months, being simple interest instead of compound. In case t2 <= 12 months, you won't need swap rates. In case t2 > 12 months, you shouldn't interpolate in the swap rates to get r_now->t2: you're looking for a rate equivalent to a zero coupon bond (like in the case of the euribor: knowing euribor 6m is equivalent to knowing P(0, 6m) and viceversa), but you're getting a rate linked to a exchange of floating/fixed flows.

Dear Manolom,Good to hear that the two different rates cannot just be connected, due to different ways of calculating the rates: simple versus compound. I didn’t realize that. Agree this is not a problem for the t2<12 months case as we only have true Euribor quotes (for convenience I call the European swap quotes also Euribor). If t2>12months, I am not fully clear what impact it has.Note, in my setting both t1 and t2 are not matching one of the traded quotes. So I guess we need some type of interpolation, and the approach is differing between the three cases 1: t1<12 months, t2<12 months, 2: t1 < 12 months & t2>12 months, and 3: t1 > 12 months, t2>12months. Especially the second one is interesting. Can you write down how you would derive the implied interest if t1<12 months, t2>12 months? Asked Bloomberg which calculations they perform when they show a forward rate. Via FWCM EUR we can get forward rate but only for a number of standard time to maturities. They say these calculations belong to Bloomberg and are not shared. regards allu

As I have commented already in several other threads, beware of using naked Euribor quotes... You will be getting some very strange forwards if you just do what you are doing.

How would you adjust "naked EURIBOR rates" to get forward rates ( and I am not taking here about convexity adj)?

You have to adopt a common basis for the rates. For instance, if you're building a 3m curve, the 6m EURIBOR will need to be adjusted to make it consistent with a rate that is basis 3m. Same for all the other quotes.

Thanks for your answer. A follow up question. What money market instruments would you use to construct the 3m or 6m curve up to the first EURIBOR future?

I personally use spot EONIAs and apply a spread to them. I have used live depo rates in the past, but they're much too 'live' for my taste (i.e. random ticks will occasionally cause all sorts of weird stuff to happen to your curve, which isn't what you want).

What spreads do you apply to EONIAs, given that one builds 6m swap curve.

That I can't really tell you. Actually, I could but then I'd have to kill you.The general idea is that you create yourself an objective function (which mkt instruments you want to reprice and with what sort of tolerance). You then solve for the spreads.

I see, you have collection of market instruments (any maturity) but only the short end of your curve is calibrated to them.Is this right? Thanks for your time.

No, you can use as many or all mkt instruments to calibrate your front end spreads. That's a trade-off you will need to establish for yourself.