Common Measures of Bond Spreads Versus Swap Rates

Summary

The document explains that a ratio of the swap bid–ask spread to the bond bid–ask spread is not a standard bond-versus-swap spread measure. Instead, the appropriate definition depends on the comparison being made and the desired treatment of the bond’s cash flows and interest-rate exposure.

It outlines three common measures. An I-spread compares bond yield with an interpolated swap rate and is described as relatively simple to calculate. A Z-spread is the constant increment to zero-coupon discount rates that makes discounted bond cash flows match the market price. A par-par asset swap spread represents the funding spread associated with hedging the bond’s interest-rate risk, with the swap premium tied to the difference between par and the clean bond price. These definitions are conceptual summaries; benchmark choice, such as the swap curve and reference tenor, affects the result, and more detailed pricing methods may require specialized tools.

Key ideas

• A bid–ask spread ratio does not by itself define a conventional bond-to-swap spread.
• An I-spread compares a bond yield with an interpolated swap rate.
• A Z-spread is calibrated so discounted bond cash flows reproduce the observed market price.
• A par-par asset swap spread reflects the funding spread in a hedge of the bond’s rate risk.
• Spread calculations depend on benchmark choices, including the swap curve and reference tenor.

Tags

# Proper way to calculate spread between bonds and Swap


# Proper way to calculate spread between bonds and Swap












In the place I work they are calculating the spread between bonds and swaps as follow...

Bonds vs Swap spread = (Swap bid-ask spread) / (Bonds bid-ask spread)

Is this the "right" way to calculate spreads between two instruments? Or what would be the proper way? The inputs are basically bid and asks.

## Answer by oronimbus (score 2)

https://quant.stackexchange.com/a/57506

There are different bond spreads. I’ll outline some common ones:

- I-Spread: Interpolated (fair market) swap rate minus bond yield, this is also effectively the same as a matched maturity asset swap spread (MMS ASW). This is the most simple kind of swap which requires no additional pricing library like the other spreads below.

- Z-Spread: constant (or ‘zero volatility’) spread over zero coupon rates used to discount the bond’s cashflows to match market price. Instead of discounting each cashflow with a constant rate, we’re now using a term structure. This document discusses the technicalities.



- Par-Par ASW: funding spread paid by investor to hedge bond’s interest rate risk in an IRS. The par-par ASW spread is chosen such that the swap premium is equal to 100 minus clean bond price. This is also explained in this paper.

Note that each of these spreads has certain nuances, for example, are you using an IBOR or OIS swap rate or what benchmark tenor are you using in your ASW (e.g 3m or 6m EURIBOR)?

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.