When assessing callable bonds, the Z-spread might overstate the bond's true credit spread.

This is because the Z-spread calculation does not account for the value of the embedded call option.

Effectively, assuming it's worthless by setting volatility to zero, a simplification that ignores the options impact.

That's why it's also called the zero volatility spread.

Callable bonds, however, are generally priced lower than otherwise identical non callable bonds because they provide the issuer with an option to call or redeem the bond early.

Ignoring this call feature means the Z-spread calculation will reflect a higher spread than the true credit spread.

Essentially, the Z-spread adds a larger spread to match the bond's lower price, even though it's the call option, not only the credit spread that contributes to this price difference.

This is where the option adjusted spread, or OAS comes in.

The OAS adjusts for the impact of the call option on the bonds price.

It first estimates the price of the bond as if it were non callable, by removing the option value.

Then it recalculates the spread based on this adjusted price, isolating the credit risk from the options influence.

As a result, the OAS provides a more accurate picture of the bond's true credit spread.

By factoring in the options impact for callable bonds, the OAS will generally be lower than the Z-spread because it reflects the spread of a straight bond adjusted for the embedded option risk.