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Is it possible to bootstrap at least an approximate 6 month LIBOR curve (actually NIBOR, for Norway, in my case) if rates for 3 month FRAs are known? For example, say we know the rates for 1x4, 7x10, and 10x13 FRAs. Can we deduce any points on the 6 month curve?

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    $\begingroup$ Do you have any basis between NIBOR or LIBOR? $\endgroup$ – MattR Dec 21 '16 at 0:09
  • $\begingroup$ @MattR No basis spreads are available. $\endgroup$ – Math Dec 21 '16 at 0:12
  • $\begingroup$ So just to clarify, you want to obtain a 6M Curve with only 3M quotes. Do you have any product with 6M yields implied? If you don't you might obtain the 6M NIBOR by just compouding the 3M to 6M and assuming that 1x4FRA x 4xFRA = 6M Rate. $\endgroup$ – MattR Dec 21 '16 at 10:44
  • $\begingroup$ @MattR Well I do have 6 month swaps available with tenors 3 years or larger, but here I'm trying to get the short end. $\endgroup$ – Math Dec 21 '16 at 11:18
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    $\begingroup$ i get your point, it just reminds me of how 3M libor use to be against 6M libor when the credit spread wasn't taken into account. Would you say that (1+FRA3M) x (1+FRA3M) doesnt work at all? $\endgroup$ – MattR Dec 21 '16 at 11:48
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No, you can't. You can never deduce the 3M/6M basis spread from 3 month instruments alone.

If you consider the OIS curve riskless, you can interpret the 3 month curve as riskless rate + additional cost for things like credit risk, liquidity and so on. The 6 month rate contains even more of these credit risk and liquidity cost. How much exactly though is impossible to say from 3 month rates alone.

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    $\begingroup$ This is what I was afraid of $\endgroup$ – Math Dec 21 '16 at 0:40
  • $\begingroup$ If there's no basis being trade maybe there's no implied credit risk. $\endgroup$ – MattR Dec 21 '16 at 10:47
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You would need spot rates to anchor on. For example, in addition to the forward rates, if you have one-month spot, then you can calculate four-month spot based on your forward. you can impute the spot between one and four months.

To your question specifically, if you have spot at one-month and seven-month, then you can impute the six-month spot. Other combination like four and seven would work, too. The idea to is have spots on both sides so that you can impute.

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