What Z-Spreads and OAS Say About Credit and Default Risk

Summary

The document distinguishes spread-based bond valuation from explicit default modeling. A Z-spread discounts a bond’s promised cash flows at risk-free rates plus a constant spread, treating those cash flows as certain to arrive. The spread measures the extra discounting required by the market price; by itself, it does not identify why investors demand that compensation.

That distinction resolves the apparent claim that a Z-spread assumes zero recovery: the calculation does not specify a recovery rate because it does not model default and recovery events at all. A defaultable-bond model instead allows promised payments to be missed and substitutes possible recovery amounts. The discussion notes that liquidity and other factors may also affect observed spreads, so a spread cannot be read as a pure measure of default risk. Although the question mentions option-adjusted spread, the answer does not explain its option adjustment in detail.

Key ideas

• A Z-spread discounts promised bond cash flows using risk-free rates plus a constant spread.
• The Z-spread does not specify recovery because the calculation treats cash flows as certain rather than modeling default.
• A measured spread can reflect liquidity and other pricing factors as well as compensation associated with credit.
• Explicit defaultable-bond models represent missed payments and possible recovery cash flows.

Tags

# How to understand "OAS assumes the recovery rate of the bond is 0" and "OAS" does not include credit risk?


# How to understand "OAS assumes the recovery rate of the bond is 0" and "OAS" does not include credit risk?












My confusion is, the OAS comes from Z-spread with adjustment on option value. Does it mean the z-spread is assuming that the bond never defaults so that it does not include the "credit risk"? How can it doesn't include default risk meanwhile assuming recovery rate = 0?

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/63717

I'm not quite comfortable with saying that Z-spread assumes 0 recovery in case of default. Rather, such spread calculations don't consider the bond to be a defaultable instrument at all. Its cash are certain to be paid. But they are discounted more than risk-free rate. We don't care why they are discounted (non-zero probability of default, liquidity...) We just calculate how much more they are discounted.

In contrast, there are ways to consider a bond as a defaultable instrument (for example, Bielecki ; Duffie & Singleton ; et al). For each cash flow, we allow for the possibility that it won't be paid, but we'll get some recovery instead.

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