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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.

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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.
  • OAS Spread: Z-Spread adjusted for optionality (useful for bonds with embedded optionality). More info can be found here.
  • 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)?

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  • $\begingroup$ But is it mathematically right to calculate a spread as a division? I thought the spread was more as a differential. $\endgroup$
    – Coconut1299
    Aug 20, 2020 at 20:25
  • $\begingroup$ The spread should be a differential, yes. I’ve never seen it expressed as a ratio nor understand how it could be useful. Spreads are neat because they can directly give you an indication of perceived credit risk for a given issuer and. Say 10y swap rate is 1% and your BBB bond has a 3% yield - you can immediately see that you’re being compensated 2% to take on that additional credit/default risk. If you check Bloomberg, the above spreads are all market standard. $\endgroup$
    – oronimbus
    Aug 20, 2020 at 20:32

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