How do embedded call and put options affect bond valuation and risk?

Bonds with embedded options have cash flows that depend on the path of interest rates, which fundamentally changes their valuation and risk profile compared to plain vanilla bonds.

The Building Blocks

• Callable bond = Straight bond − Call option (issuer owns the option)
• Price_callable = Price_straight − Value_of_call
• Investor is short the call, so the callable bond is always worth less than an equivalent straight bond.

• Putable bond = Straight bond + Put option (investor owns the option)
• Price_putable = Price_straight + Value_of_put
• Investor is long the put, so the putable bond is worth more.

Numerical Example

Consider a 10-year bond issued by Crestview Financial at a 5.5% coupon:

Option-Adjusted Spread (OAS)

OAS strips out the effect of the embedded option to give you a spread that reflects only credit risk and liquidity. It is computed by:

1. Building an interest rate tree (binomial or trinomial)
2. Calibrating the tree to match the term structure
3. Finding the constant spread added to each node that makes the model price equal the market price

For a callable bond, the Z-spread > OAS because the Z-spread includes compensation for the short call. The difference (Z-spread − OAS) is called the option cost.

Duration Impact

• Callable bonds have shorter effective duration than straight bonds when rates fall (because the call caps the price upside).
• Putable bonds have shorter effective duration when rates rise (the put floors the downside).
• Both exhibit negative convexity near the strike — the callable at low rates, the putable at high rates.

Exam Tip: When given OAS and Z-spread, always compute option cost = Z-spread − OAS. A higher option cost means the embedded option is more valuable.

Explore our FRM question bank for more fixed-income option valuation problems.