How would one calculate the fair level of 3s1s single currency basis swaps using simply the 1m & 3m libors and ois levels? (so you have fra-ois spread levels in both)

I understand that as the FRA-OIS basis widens, the fair level of 3s1s would increase, but unsure how that level is calculated?

So if one entered a 1y basis swap at Xbp over 1mth, how would the stub risk be hedged (in ois since libors are not tradeable) and how does that translate back to finding a fair 3s1s level?



1 Answer 1


The 3s 1s basis cannot be calculated in an arbitrage sense. You can make some reasonable assumptions. For example , if fra/iOS is tighter on s forward basis than spot, then 3s 1s is likely to have a similar term structure. But flows in the market may move it away from intuitive levels.

  • $\begingroup$ thanks. if (theoretically) you had fra/ois markets for every 3m and 1m set, then the 3s1s could be implied by that? ie if 1mth FRA-OIS is 15/14 and 3mth fra-ois is 30/29 for every day in this next year then the 1y 3s1s market implied is 16/14 (30-14) / (29-15) $\endgroup$
    – Sam4343
    Nov 1, 2016 at 18:01
  • 1
    $\begingroup$ yes that's true, with a minor quibble about daycount (30bp is quarterly, 14bp is monthly but it makes no difference at these rate levels) $\endgroup$
    – dm63
    Nov 2, 2016 at 2:17

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