The swap spread is based on swap fixed payer rates, which are given by LIBOR, and this is applicable to everyone. The swap spread (swap rate - treasury rate) is a measure of overall health in the financial markets and confidence.

Z-spread is the spread added to the treasury spot curve at every cash flow to equate with the given market price, it includes all premiums of risk.

OAS is the spread added between two option free, or two option embedded bonds with same maturities to remove the effect of options on the spread, so the OAS only measures Z-spread minus the option cost.

Z-spread includes all risk spreads.

OAS includes all risk spreads except option spreads.

OAS is _ not _ added to the spot curve. It’s added to the _ rates at the nodes in a binomial tree _; those rates are forward rates , not spot rates.

The option value is included in the market price, but is not included in the Z-spread methodology (i.e., we don’t explicitly assume that the option is exercised at any point); therefore, the spread itself must contain the option value.

In a binomial tree we explicitly include the value of the option (changing the cash flows when we believe that it will be exercised), so the methodology handles the option value, the spread does not.

Indeed, forward rates on binomial tree! Thanks a lot! I will edit the original post to reflect this comment.

I kind of got the idea behind the OAS spread.

What is still confusing me, is that OAS is smaller than Z.

Callable bond has a value less than a straight bond. Intuitively, but wrong obviously, it feels like the cash flows should be discounted with a higher spread when we have a callable bond (since its value is less).

Z = OAS + option cost. I understood the formula itself, as volatility decreases so does value of option cost and our OAS increases and approaches Z, but still not very clear on that option removed thing…

You’re assuming that the cash flows are the same for the straight bond and the callable bond. They’re not. The callable bond has lower average cash flows than the straight bond because it has some probability of being called (at a price lower than the market price of the corresponding straight bond).

The Z-spread for the callable bond is larger than the Z-spread for the straight bond for exactly the reason you mention: you’re discounting the same cash flows to get a lower market price. The OAS for the two bonds should be exactly the same (assuming the market accurately values the call option); thus, the OAS for the callable bond is less than its Z-spread, not because the OAS is lower, but because the Z-spread is higher.

In P338. of CFA Book 5, which states “A more convenient and relatively satifactory alternative is to uniformly raise the one-year forward rates derived from the default-free benchmark yield curve by a fixed spread, which is estimated from the market prices of suitable bonds of similar credit quality. This fixed spread is known as the zerovolatility spread, or Z-spread.”

May I know if it’s the same, whether the fixed spread is added to spot rate, or be it forward rates? Thanks.