# Can I use spot rates bootstrapped from a swap curve to price a bond?

Say that some corporation has a long position in a fixed rate bond. To turn this into a float-rate asset, they take a fixed paying position in a fixed/float swap. If we are given the par swap curve, we can bootstrap the par swap rates to discount the swap cash flows at the spot rates.

My question: Are we allowed to use these same spot rates to discount the bond as well, or would we need to have the yield curve to calculate spot rates based on the bond yield curve?

• It is unlikely that the bootsrapped swap curve will price the bond correctly if this bond is actively traded. Probably best to price the bond with a curve that gives the correct price, and the swap with a swap curve. Feb 21, 2022 at 19:38

The general - and short - answer would be no: Except for some hypothetical cases, unless you have a convincing model for the residual spread-over-swap, you cannot use swaps to value your bond.

##### Quick comparison

Bonds are traded in the bond market. The cash flows are uncollateralized (of course) and carry the default risk (amongst others) of the underlying entity. Their trading liquidity can be very thin, resulting in yet another yield / spread add-on. Additional supply-and-demand effects may drive prices for specific bonds (e.g. HQLA eligibility criteria).

Interest rate swaps are traded in the rates markets. The cash flows are collateralized, the underlying credit risk resembles an average of the corresponding IBOR panel members (in theory, at least). Commonly, swaps are more liquid.

##### What might be possible?

Depending on your targeted application, you may or may not get away with some rough approximations:

• If you want to hedge the pure interest rate risk of your bond, you could separate the bond discounting curve into an IRS curve (which you hedge using swaps) and some residual spread-over-IRS.
• If you want to calculate risk, you might come up with a portfolio / data availability example where could proxy the residual spread's variation using an adequate CDS on that entity, but things start to get tricky here.

Hope this helps?

• Yes, it definitely helps. Thanks a lot! Feb 23, 2022 at 9:32
• Nice answer, +1. Jan 24 at 17:36