Explain the effect of interest rate volatility on option-adjusted spreads

The OAS depends on the volatility assumed in the tree. For a callable bond, a higher volatility raises the call's value, so the tree gives a lower value for the bond. With the market price unchanged, a smaller spread is needed to bring the model value down to the price, so the OAS falls. Lower assumed volatility has the opposite effect. For a putable bond, higher volatility raises the model value, so a larger OAS is needed. An analyst who understates volatility will overstate a callable bond's OAS and may wrongly judge it cheap. OAS comparisons are meaningful only when the bonds are valued with the same volatility assumption.