How is the option-adjusted spread (OAS) calculated for callable bonds and what does it represent?

The option-adjusted spread (OAS) is the constant spread added to every rate in the binomial tree that makes the model price equal to the bond's market price, after accounting for the embedded option.

Relationship Between Spreads:

> Z-Spread = OAS + Option Cost (in basis points)

For a callable bond: Z-Spread > OAS because the call option has positive value to the issuer (negative to the investor)

For a putable bond: Z-Spread < OAS because the put option has positive value to the investor

OAS Calculation Process (Simplified):

1. Build a calibrated arbitrage-free binomial tree
2. Add a trial spread (s) to every rate in the tree
3. Use backward induction to price the callable bond, exercising the call at nodes where it is optimal (Value > Call Price → set Value = Call Price)
4. Compare the model price to the market price
5. Adjust s and repeat until model price = market price
6. That s is the OAS

Example — Pemberton Energy 5.5% Callable at 101 (fictional):

What OAS Tells You:

• OAS isolates the credit and liquidity spread after removing the option effect
• A higher OAS means more compensation for credit/liquidity risk
• OAS allows apples-to-apples comparison between callable and non-callable bonds
• If two callable bonds have the same credit quality, the one with higher OAS is cheaper (more attractive)

Investment Decision: Compare OAS to your required spread for the credit quality. If OAS > required spread, the bond is undervalued.

Exam Tip: The CFA exam tests the relationship Z-Spread = OAS + Option Cost. Know the direction: for callables, OAS < Z-Spread. For putables, OAS > Z-Spread.

Explore OAS analysis in our CFA Level II practice questions.