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Estimating Interest Rate Swap P&L from Yield Changes and Duration

Article Quant Q&A · Author: Michael
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Summary

The document gives a quick approximation for the mark-to-market change on a fixed-rate interest rate swap after a small change in its quoted rate. The proposed method multiplies the rate move by the swap’s duration and notional, with the sign determined by whether the position gains or loses as rates move. For a one-day move, the answer treats carry and rolldown as negligible compared with the immediate rate effect.

The example considers a five-year, one-million-dollar swap and a five-basis-point rise in the quoted rate, using an approximate duration of 4.5 to estimate a loss of about $2,250 for a fixed-rate payer. This is a back-of-the-envelope estimate, not a full valuation: duration varies with the swap’s cash flows and market conditions, and carry, rolldown, convexity, curve changes, and conventions can matter over longer horizons or for more precise P&L attribution.

Key ideas

  • A small swap-rate move can be translated into approximate dollar P&L using duration and notional.
  • For a one-day horizon, carry and rolldown may be small relative to the direct rate move.
  • The sign of the P&L depends on the position and the direction of the rate change.
  • The duration-based estimate omits effects needed for a more complete valuation.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# Approximate dollar MTM of interest rate swaps


# Approximate dollar MTM of interest rate swaps












I'm definitely a fixed income tourist but I'm wondering if there's an easy way to back of the envelope approximate dollar PnL of an interest rate swap

For example, if I enter a $1m fixed 5y USD swap at 3% and tomorrow the quote rises 5bps to 3.05%, assuming I know the carry X bps and rolldown Y bps, what is my dollar PnL of the position?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/71328

If only one day has elapsed, the carry and roll down effect on the p/l is insignificant. The p/l is well approximated simply by multiplying the move in the quotation by the duration of the swap, which in the case of a 5yr swap is around 4.5. So the p/l would be 4.5*0.05%*1MM = about 2250 dollars.

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