Estimating Interest Rate Swap Exposure Between Recoupon Dates

Summary

The document explains how to think about exposure for an interest rate swap whose mark-to-market is settled and whose fixed rate is reset to the prevailing rate for the remaining term. At the reset, the swap’s value is zero because the new fixed rate balances the present values of its two legs. This describes current mark-to-market exposure, rather than sensitivity to subsequent market movements.

For risk sensitivity between resets, the discussion points to DV01 or BPV multiplied by the change in market rates. Since the rate is reset at each recoupon date, the future value change is tied to rate moves over that period; this can be represented within an interest rate model. The analogy is to repricing a bond after a yield shift. The explanation is conceptual and gives no numerical example or detailed modeling procedure. It also leaves the precise exposure measure dependent on what the user means by exposure, and does not address calculation of DV01 itself.

Key ideas

• At a recoupon date, resetting the fixed rate to the prevailing swap rate makes the swap’s mark-to-market value zero.
• Between resets, monetary sensitivity can be approximated using DV01 or BPV multiplied by a market rate change.
• The reset interval limits the rate movement relevant to the next period’s exposure.
• The document does not specify a detailed model or numerical procedure for estimating exposure.

Tags

# Exposure calculation of a re-coupon swap


# Exposure calculation of a re-coupon swap












How to calculate the exposure of a recoupon swap (when the MTM of an i.r. swap is settled and the fixed rate is reset to the prevailing swap rate for the residual maturity).

It's used to reduce the exposure and resulting charges i.e as a risk mitigation technique. But exactly how to model this through replication or adjustment etc.

## Answer by Antoine Conze (score 1)

https://quant.stackexchange.com/a/37977

If the MtM is settled and the fixed rate reset every period, then the exposure in the future is at most the BPV times the swap rate change over one period, easily modeled within any interest rate model framework.

## Answer by Passing Through (score 0)

https://quant.stackexchange.com/a/71890

It isn’t clear to me what question you’re asking when you say “exposure”.

If you mean MtM exposure then at the recoupon point the exposure is zero. This is because the fixed rate has been re-determined to ensure the PV of both legs (pay and receive) is zero.

If you mean what is the MtM exposure in risk terms ie how sensitive the position is, in monetary terms, to future changes in market rates then this is DV01 (x) change in market rate. This is same principle as revaluing a bond for a parallel shift in the yield curve.

I presume you are not asking how to calculate the DV01 of an IRS as this is no different for a recouponed position as a non-recouponed position.

Hope this helps.

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