How do you value a callable bond and what's the relationship between OAS and the call option?

Callable bonds give the issuer the right to redeem the bond before maturity, typically when interest rates fall. Because this option benefits the issuer at the investor's expense, callable bonds trade at a discount to otherwise identical option-free bonds.

The Fundamental Relationship:

Value(callable) = Value(option-free) - Value(call option)

The investor effectively sells a call option to the issuer. When rates drop, the issuer exercises by calling the bond and refinancing at lower rates. The investor loses the upside of holding a high-coupon bond in a low-rate environment.

Numerical Example:

Riverton Municipal Authority issues two 10-year, 5.5% coupon bonds:

• Bond A (option-free): priced at $1,042.50 at a YTM of 5.0%
• Bond B (callable at par after year 5): priced at $1,018.30

Implied call option value: $1,042.50 - $1,018.30 = $24.20

The investor "pays" for the call option through a lower purchase price (or equivalently, demands a higher yield).

Yield Spreads for Callable Bonds:

• Z-spread: The constant spread added to each benchmark spot rate that makes the discounted cash flows equal the bond's market price. For callables, it bundles together credit risk AND the cost of the embedded option.
• OAS (Option-Adjusted Spread): Removes the option cost, leaving only the spread attributable to credit risk and liquidity.
• Option Cost = Z-spread - OAS

Example:

Riverton Bond B has:

• Z-spread: 85 bps
• OAS: 55 bps
• Option cost: 85 - 55 = 30 bps

The 30 bps option cost represents the annualized value of the call feature. If a comparable option-free bond from Riverton has a Z-spread of 55 bps, the callable bond's extra 30 bps of Z-spread is entirely explained by the embedded option.

Why Investors Accept Callable Bonds:

1. Higher yield (compensation for the call risk)
2. Callable bonds dominate municipal and agency markets — sometimes there's no option-free alternative
3. Some investors have shorter horizons and are less affected by call risk

Exam Tip: For callable bonds, OAS < Z-spread. For putable bonds, OAS > Z-spread (the put benefits the investor). This is one of the most frequently tested concepts in Level I Fixed Income.

Dive deeper into embedded options in our CFA Level I course.