Why Swap Discount Curves May Not Price Corporate Bonds
Summary
The question asks whether spot rates bootstrapped from a par swap curve can discount a fixed-rate corporate bond. The response says that, in general, swap-derived rates alone are not enough to value the bond. Swap and bond cash flows differ in important ways: swaps are typically collateralized, while corporate bonds expose holders to issuer default risk and may also reflect thinner liquidity and bond-specific supply and demand.
The answer distinguishes the rate-market curve from the bond’s own pricing factors and identifies the unexplained residual spread over swaps as a key issue. For hedging pure interest-rate exposure, a practitioner may separate the swap curve used for rate risk from the bond’s residual spread. For risk calculations, a suitable issuer CDS might serve as a proxy for spread changes in some portfolios, although the answer notes that this becomes difficult. These are application-dependent approximations, not a general justification for using swap spot rates as the bond’s complete discount curve.
Key ideas
- Swap curves and corporate bond yields reflect different credit, collateral, and liquidity conditions.
- Swap-derived spot rates alone generally do not capture a corporate bond’s residual spread.
- For interest-rate hedging, bond risk can be separated into swap-curve exposure and spread exposure.
- Issuer CDS may sometimes proxy changes in residual spread for risk analysis, but requires care.
- Any use of swap rates for bond valuation depends on the application and a defensible spread model.
Tags
Full text
# Can I use spot rates bootstrapped from a swap curve to price a bond? # 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? ## Answer by Kermittfrog (score 4, accepted) https://quant.stackexchange.com/a/69974 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. 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. 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?
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