Interest Rate Swap Delta from Discounting and Floating-Rate Projections

Summary

The document frames the rate sensitivity of a pay-fixed, receive-floating interest rate swap as three contributions: discounting floating coupons, discounting fixed coupons, and projecting floating cash flows. It asks how the magnitudes of those components relate, including whether one can be inferred from the others or whether one of the negative contributions is generally larger.

The response points to an external treatment of swap PV01 and DV01 that calculates partial derivatives and then uses practical approximations. It describes the component estimates as depending on discount factors, accrual fractions, and estimates of existing floating rates. This gives a useful direction for analyzing the decomposition, but the document itself includes no equations, derivation, or worked numerical example, so it does not establish a universal ordering or identity among the components. Applying such approximations requires attention to the instrument's cash-flow schedule and rate conventions.

Key ideas

• A pay-fixed, receive-floating swap has delta contributions from both discounting and floating-rate projection.
• The document characterizes floating-coupon discounting as positive for the fixed-rate payer and the other two contributions as negative.
• Partial derivatives can be used to estimate the three sensitivity components.
• The cited approximations depend on discount factors, accrual fractions, and projected floating rates.
• No general inequality or exact relationship among the components is provided in the document.

Tags

# How do the different parts of a Swap contribute to its delta?


# How do the different parts of a Swap contribute to its delta?












A swap (pay fixed, receive float) has exposure to interest rates in 3 ways: discounting floating coupons, discounting fixed coupons, and projecting floating cashflows.

We know that for us as the payer of the fixed rate, the first has a positive delta, the second has a negative delta, and the third has negative delta.

But are there formulas (equations, inequalities) that are of general interest and relate the sizing of these 3 different contributors to each other?

For example, can we determine 1 from the other 2?

Or can we say which one of the two negative contributors is larger?

## Answer by Attack68 (score 1, accepted)

https://quant.stackexchange.com/a/85394

If you look at this answer: interest rate swap: PV01 vs DV01

The section on "Real Portfolio PV01" calculates the partial derivatives and then makes reasonable approximations. It estimates the 3 components that you are talking about, and it shows they are expressed in terms of discount factors, day count fractions and existing estimates of floating rates.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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