Choosing Spread and Risk Measures for Callable Bonds

Summary

The note explains why callable bonds should not automatically be analyzed as if they run to maturity. When an issuer is likely to call, calculating spread and interest-rate risk to maturity can give misleading results. A common practical approach is to find the yield to worst and calculate spreads and risk measures to the call date that produces it; this is presented as workable when exercise is highly likely.

That approach can become unstable when the yield to an early call is close to the yield to maturity, because the selected yield-to-worst date may change often and reported spreads or risks can jump. In such cases, the note recommends option-adjusted spread analysis and including vega among risk measures. It also describes manually specifying an expected call date when exercise expectations are based on reasons the yield comparison does not capture. These are practical guidelines rather than a detailed valuation model, and the note does not specify how to estimate exercise probabilities or the inputs for OAS.

Key ideas

• Analyzing a callable bond to maturity can misstate spread and risk when an earlier call is likely.
• A practical approach is to calculate measures to the call date that gives the yield to worst.
• Yield-to-worst measures can jump when the call-date yield is close to the maturity yield.
• Option-adjusted spread and vega can be more suitable when the likely exercise date is uncertain.
• An expected call date can be specified directly when exercise expectations come from other considerations.

Tags

# Z spread for callable bond


# Z spread for callable bond












I see many definitions online for z spread with formulas written for a bond, how do they change if the bond is callable? Or is z spread calculated to maturity in this case?

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/71540

It is not a good idea to ignore the call feature and to calculate spreads, yields, risks, and other bond maths to maturity. For many callable bonds, clearly the issuer is certain to call the bond much earlier. Then the spreads and risks (dv01..) would be very misleading.

Practically, the most common methodology is to calculate yield to worst, and then to calculate all spreads, risks, etc to the call date that gave rise to the YTW. This works well enough for bonds where the probability of exercise is close to 1.

However this is not good when the yield from exercising soon is very close to the yield to maturity. The YTW date might change frequently, and the spreads and risks might jump by a lot. For these situations, instead of Z-spread, try option adjsted spread (OAS); and include vega with your risk measures.

In rare cases you just know that the issuer will or will not exercise for some reason irrespective of what yield appears to be worse. For this, you want to be able to manually specify the expected call date and skip the ytw analysis.

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