Risk Sensitivities of a Single-Currency Basis Swap
Summary
The discussion describes how to think about risk in a single-currency swap exchanging floating payments based on different tenors, such as six-month and three-month rates. It separates sensitivity to changes in the tenor basis from outright rate delta. A basis sensitivity can be measured by shifting one tenor’s forward rates while holding the other tenor’s forwards constant, representing a widening or narrowing of the spread.
The swap can also have discounting sensitivity to the collateral agreement curve, along with projection risk in both forward curves. Outright delta is generally concentrated in the short-end stub, where one tenor may already have fixed while the other has not. The explanations are qualitative and describe common risk dimensions; actual sensitivities depend on the trade’s cash flows, fixing state, curves, and valuation setup.
Key ideas
- A tenor basis swap has sensitivity to changes in the spread between its forward curves.
- Risk can be measured by shifting one tenor’s forwards while holding the other tenor constant.
- Outright delta may arise alongside basis risk, especially around unfixed short-end cash flows.
- Discounting and both projection curves can contribute to the swap’s total sensitivity.
- The precise risk depends on fixings, cash flows, and valuation conventions.
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# Single currency basis swap Risk sensitivity # Single currency basis swap Risk sensitivity How do I concretely quantify the delta of a single currency basis swap (ex:3mv6m LIBOR) ? Would you look at the PV impact for every bps change in the 3v6 tenor basis spread ? Thanks in advance. ## Answer by Mehness (score 1) https://quant.stackexchange.com/a/31131 Been away from a trading desk for a while and was not in flow rates, but presume you'd have a delta to the CSA curve (a discounting delta), and 2 projection deltas, one to 3m and opposing one to 6m. Neglecting the deviation of the sum from zero then quantum of delta overlap is effectively what you describe above I would guess? (i.e. I agree, however this is the basis delta to which you are sensitive if the legs compress / decompress, however there may also be some small residual outright delta if the 6m or 3m leg dominate, in addition as I say to some small discounting delta) ## Answer by dm63 (score 1) https://quant.stackexchange.com/a/31222 The risk of a 6s vs3s basis swap is usually expressed in two dimensions a) the risk to the 6s 3s basis swap widening ( i.e. Increasing the forwards for 6s by 1bp in parallel while keeping the forwards for 3s constant ) and the delta risk ( moving the forwards for 3s upwards by 1bp). Typically delta risk is only present in the "stub" at the short end of the curve. Beyond the next 6mo libor setting , it's a pure basis swap , but prior to that there may be outright delta risk if 6 mo libor has been set and one 3 mo libor has not yet been set.
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