Mapping Swap Cash Flows Across Discount and Forward Curves

Summary

The discussion concerns sensitivity-preserving cash-flow mapping for a fixed-versus-Euribor six-month interest rate swap under a multi-curve framework. The question asks how to assign cash flows to regulatory pillar dates when discounting uses an overnight curve and floating coupons depend on a separate forward curve. The response illustrates mapping amounts at payment dates to both the forward curve and the overnight discount curve, with example curve levels and swap rates showing how the mapped components can vary.

The examples suggest that mapping is not limited to fixed coupons: the forward-rate exposure and discounting exposure both matter, and curve shape and how far the swap is from market can affect the recorded discount-curve components. For a flat curve and an at-market swap, the response says discount-curve entries would be absent; steeper curves or off-market terms can produce more entries. This is a brief practitioner answer, not a full derivation or implementation guide. It does not specify a general interpolation algorithm or establish how the illustrative mapping should be adapted to other conventions or regulatory details.

Key ideas

• In a multi-curve swap framework, floating-rate exposure and discounting exposure are associated with different curves.
• The response illustrates assigning cash-flow amounts at dates to both the forward curve and the overnight discount curve.
• Curve slope and the swap’s distance from market can change the discount-curve components in the mapping.
• The answer gives illustrative cases rather than a general interpolation procedure or full regulatory methodology.

Tags

# Cash flow mapping on multi curve framework


# 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!

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/63399

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).

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