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?


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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.

  • $\begingroup$ thanks for your insights! Isn't the reason z-spread is higher than risk free rate is because the risk of default? Yes we assumed that we will get every single cash flow, but the z-spread itself, based on the fact that it is higher than risk free, tells that z-spread actually includes the credit risk? @Dimitri Vulis $\endgroup$
    – Lisa
    May 2, 2021 at 21:14
  • $\begingroup$ Z-spread is how much you'd need to shift the swap curve in order for the present value of the bond's cash flows discounted with the shifted swap curve to match the observed bond price. It's unusual for Z-spread to be negative (treasuries in the U.S., Australia, New Zealand come to mind..) Z-spread can be attributed to credit risk (both probability of default and loss given default combined), but also liquidity risk, tax impact (especially munis). My advice is: read some good buy-side tutorials/primers on bond risks. A lot of random writings on the internet are confusing or outright wrong. $\endgroup$ May 3, 2021 at 14:04
  • $\begingroup$ Oops, I meant "sell-side tutorials", obviously, apologies! $\endgroup$ May 3, 2021 at 14:26

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