Why 3s1s Basis Swap Levels Cannot Be Derived Directly from FRA-OIS

Summary

The document asks how to infer a fair level for a 3s1s single-currency basis swap from one-month and three-month LIBOR and OIS levels, including how to hedge stub exposure when LIBOR is not directly tradable. The answer cautions that the 3s1s basis does not follow from an arbitrage relationship using those inputs alone, so they cannot determine a unique fair quote.

It suggests a qualitative estimate by comparing the forward term structure of FRA-OIS spreads with spot levels. If forward FRA-OIS is tighter than spot, the 3s1s basis may have a similar term-structure shape. This is an assumption-based indication, not a hedge construction or pricing formula. Market flows can move the traded basis away from the intuitive level, and the response does not specify how to quantify that effect, price a particular swap, or hedge its stub risk. Readers should treat the proposed relationship as a market heuristic rather than a guaranteed fair-value calculation.

Key ideas

• The 3s1s basis cannot be uniquely calculated by arbitrage from the stated FRA-OIS inputs alone.
• Forward-versus-spot FRA-OIS levels may provide a qualitative clue to the basis term structure.
• A similar term-structure pattern is an assumption, not a pricing identity.
• Market flows can move the observed basis away from levels suggested by that heuristic.
• The response does not provide a specific stub hedge or quantitative valuation procedure.

Tags

# How to calculate fair 3s1s basis levels


# How to calculate fair 3s1s basis levels












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?

Thanks

## Answer by dm63 (score 1, accepted)

https://quant.stackexchange.com/a/30794

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.