Nominal spread, Static spread, Zero-volatility spread, Option-adjusted spread

Nominal spread – simpliest

Nominal spread = (YTM of the bond – YTM of a Treasury security of similar maturity)

Limitations of nominal spread:
· Does not account for term structure of interest rates (no arbitrage pricing).
· Ignores affect of embedded options.

Static spread (Z-spread)
· Spread not over the treasury’s YTM but over each of the spot rates in a given treasury term structure, ie. same spread is added to all risk-free spot rates.
· more accurate than nominal spread as it is based upon the arbitrage free spot rates.
· Equal to nominal spread if yield curve is perfectly flat.

PV = CF1/(1+Z1 +SS) +CF2/(1+Z2 +SS)³+ CF3/(1+Z3+SS)³ , by trial & error to find SS (Z-spread)

Zero-volatility spread (Z-spread):
· Spread over the entire Treasury spot rate curve.
· Accounts for the term structure of interest rates, but ignores the affect of embedded options.
· Difference between Z-spread and nominal spread is greatest for amortizing bonds, for longterm high-coupon bonds, and for steep yield curves.

Option-adjusted spread (OAS):
· Spread over entire Treasury spot rate curve after accounting for embedded options.
· OAS is highly dependent on the model used to calculate the spread and the assumption for interest rate volatility.
· Higher interest rate volatility assumed » Lower OAS.

Option cost = Z-spread - OAS.

For option-free bonds OAS = Z-spread.
For option value greater than 0( call), OAS smaller than Z-spread;
For option value smaller than 0 (put), OAS greater than Z-spreadNominal spread may be misleading in the case of securities with embedded options. Buy securities with largest OAS for a given duration.