Estimating IRS Receiver Duration and Rate Sensitivity

Summary

The answer models an interest rate swap as an asset leg and a liability leg, then expresses generalized duration as the asset value times its duration minus the liability value times its duration. The sign reflects the liability’s negative contribution to the swap’s cash flows. This gives a framework for combining the rate sensitivities of the two legs when assessing an IRS receiver.

For delta, the response points to a convexity-based bound attributed to the Fong–Vasicek theorem, relating percentage value variation to the difference in generalized convexities and a maximum slope change in the bond-price term structure. It does not work through the receiver-specific signs, define a precise delta convention, or provide an example. The brief answer therefore offers a conceptual starting point, but further assumptions and derivation are needed to compute a practical swap delta.

Key ideas

• An interest rate swap can be viewed as an asset leg paired with a liability leg.
• The response combines leg durations by weighting them by their values and subtracting the liability contribution.
• It attributes a convexity-based bound on relative value changes to the Fong–Vasicek theorem.
• The answer does not provide enough detail to calculate a specific receiver delta.

Tags

# Macaulay duration of an IRS receiver


# Macaulay duration of an IRS receiver












how can I compute the duration of an IRS receiver? and how can I use it to compute the Delta of IRS?

## Answer by Akai M (score 1)

https://quant.stackexchange.com/a/51857

An Interest Rate Swap can be decomposed into a portfolio made up by just one asset and one liability. In that way you are able to compiute the generalized duration as a weighted average, where the weights are the values of the two legs of the swap contract: $D = A*D^A - L*D^L$ , where L stands for liability and A stands for asset. Note that the minus sign is due to the fact that a liability obviusly has a negative impact on our cash flows. I guess for Delta you mean the relative variation based on Fong-Vasicek theorem, which state that the percent variation of the final value of the contract is given by the following: $\Delta V/V \geq K*(C^A-C^L) $ , where K stands for the maximum variation of the slope due to a shift of the two term structure of bond prices, while C rapresents the generalized convexity.

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