# Cash flow mapping on multi curve framework

I am trying to map cash flows according to FRTB pillar dates, on an Interest Rate Swap fixed Vs Euribor 6 months. Using the sensitivity preserving approach, under the OIS framework, this has to be done with respect to both the discounting rate sensitivity (i.e. Eonia), and the forward rate sensitivity (EUR 6m). Unfortunately I cannot find a way to interpolate cash flows with respect to the forward rate, since the sensitivity is not expressed as a function of the cash flows. I'm actually starting to think this cannot be done! Does anyone have any idea? As always, any help would be very much appreciated. Thanks!

From recollection don't you only map the fixed cashflows?

If the 6m rate is 1% and your swap is at 0.5% then on a notional of 100 you map:

6m curve @6m: +1
OIS curve @6m: -0.5

If the 6m6m forward rate is 1.25% then on an 1Y irs struct at 2% your flows would be:

6m curve @6m: +1
OIS curve @6m: +1
6m curve @1y: +1.25
OIS curve @1y: +0.75

On a flat curve, with a swap that was at market, you would not record anything to the discount curve (which is true) and for a steeper curve, and/or with a swap that was way off market you be recording much more elements to the OIS discounting curve, (which is alos practically true).

• Thank you for the answer, but I did not understand your point. Actually, both legs are OIS discounted, therefore the market convention doesn't come in place. The main problem is that, considering FRTB dates (i.e. 3m,6m, 1y, 2y, 3y, 5y, 10y, 15y, 20y, 30y), how do you interpolate cash flows, preserving sensitivity with respect to the forward rate? Do I have to assume that the forward rate is going to be computed over the whole period (i.e. for 5y cash flow, it would be the forward 3 to 5 years) ? Apr 15, 2021 at 7:26