This is possibly a very stupid question but I want to know how the price of a floating-floating interest rate basis swap (e.g. pay 3M Libor+spread and receive 6M Libor for 5 years) is affected by a parallel, upwards shift of the yield curve by an absolute amount of basis points, as a general rule of thumb. It may be stupid because parallel shifts should not affect a basis swap much but..Is it fair to say that at initiation/ATM both legs will move by the same amount and so that the swap would still be worth zero even after the parallel shift? My thinking is that since interest rates are the same on both legs at initiation, a parallel shift would move both legs by the same amount and therefore the net value of the two legs would remain zero. For swaps that are not ATM it is trickier and it would not be possible to say anything in general? If the basis between 3M and 6M has shrunk since initiation, so the person receiving 3M+spread and paying 6M has made a profit. This means that the 3M+spread curve is higher than the 6M curve. If a parallel shift of e.g. 10 basis points is applied to both curves then the ?lower? 6M curve is more affected in relative terms than the ?higher? 3M+spread curve. In other words, the value of the 6M curve is more affected than the 3M+spread curve and this would imply that the person paying 6M while receiving 3M+spread makes a loss due to the parallel shift of the curve. Hence, a swap that is ITM for the long rate payer makes a loss due to the shift of the curve. By contrast, a swap that is OTM for the long rate payer makes a profit due to the shift of the curve. Does makes any sense or am I completely off track?

Assuming you shift both your 3m and 6m curves by the same amount, a par basis swap will probably still have a PV of 0 (although, god knows, there may be some higher-order convexity effects). For an off-mkt swap, there will likely be a PV effect, similarly to what happens with vanilla swaps.

Wouldn't the impact be close to the duration figure? Surely that's the whole point of calculating the interest rate sensitivity? (Adjusted for the spread)

QuoteOriginally posted by: BigAndyDWouldn't the impact be close to the duration figure? Surely that's the whole point of calculating the interest rate sensitivity? (Adjusted for the spread)What's the duration of a tenor basis swap?

Swapping 3m for 6m it would be small but still some impact

> What's the duration of a tenor basis swap?To first order, it is the difference in duration of the initial fixing on each side. With OIS discounting there are higher order effects.

The easiest way is to look at EUR 3M-6M basis swap. It is usually quoted as a difference of two plain IRS, 3M and 6M. If 3M and 6M par rates change by the same amount, the basis spread (difference between those two) obviously remains the same. So the par basis swap should be still at par. Off-par swap can have some small PnL, if you assume that the discount rate (EONIA ?) is also changing.For other currencies, the effect may be slightly larger because the frequency and day count convention for basis spread does not match those of plain IRS.

QuoteOriginally posted by: Jim> What's the duration of a tenor basis swap?To first order, it is the difference in duration of the initial fixing on each side. With OIS discounting there are higher order effects.'Twas a rhetorical question on my part...