The nominal spread is simply the difference in basis points between the Treasury and non-treasury security. For example, if the Stone & Co. bonds have a yield of 5.5% and the comparable Treasury security has a yield of 4.5% the nominal spread is 100 bps. (5.5% - 4.5%).
This measures the spread the investor would capture over the entire Treasury spot- rate curve if the bond was held to maturity. The Z-spread is calculated as the spread that will make the present value of cash flows from the non-treasury security when they are discounted at the Treasury spot rates plus the Z-spread equal to the non-Treasury securities price. This is done by trial and error. This is different than the nominal spread because the nominal spread just uses one point on the curve.

For example, take the spot curve and add 50 basis points to each rate on the curve. If the two year spot rate is 3%, the rate you would use to find the present value of that cash flow would be 3.50%. After you have calculated all of the present values for the cash flows, add them up and see whether they equal the bonds price. If they do, then you have found the Z-spread, if not, you have to go back to the drawing board and use a new spread until the present value of those cash flows equals the bonds price.
This takes the dollar difference between the fair price and the market price and converts it into a yield measure. The OAS helps reconcile the value to market price by finding a spread that will equate the two. This is also done on a trial-and-error basis and is very model dependent.
Remember:
1. Interest rate volatility is critical. The higher the volatility, the lower the OAS. Check this assumption when making comparisons.
2. The OAS is a spread over the Treasury spot-rate curve or benchmark that is used in the analysis.
3. As the name implies, the security's embedded option can change the cash flows and the value of the security should take this change in account. The difference between the OAS And the Z-spread is that the Z-spread doesn't take this into consideration.
• Option Cost
This cost can be derived by calculating the difference between the OAS at the assumed interest rate or yield volatile and the Z-spread.
Z-spread = OAS + option cost
Therefore,
Option Cost = Z-spread - OAS
The option cost is measured in this way because if rates do not change, the investor would earn the Z-spread. When future rates are uncertain, the speed tends to be different because of the embedded option. The option cost for a callable bond and most MBS and ABS securities are positive. This is because the issuer's ability to alter the bond's cash flows will result in an OAS that is less than the Z-spread. For puttable bonds the option cost is negative because of the investor's ability to alter the cash flows.
What are Forward Rates?

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