In loose terms, Z spreads is a compensation for credit risk of the issuer. Because of the credit risk, the Z-spread to Treasuries for a corporate bond tends to be positive. This reflects the fact that corporate bonds are worth less than treasuries with similar maturity and coupon. The higher the credit risk the higher the Z spread to Treasuries. A positive Z spread indicates that the security has an investment value and a negative Z spread indicates that the security is rich compared with treasuries.
Option Adjusted Spread is a measure of the credit risk for callable or putable bonds. For bonds with embedded options, the Z spread is often not meaningful. This is because it is usually not appropriate to value a these bonds simply by discounting its scheduled payments. To value bonds with options, one must take into account volatility in interest rates so that the risk of the bond being called can be considered.
Asset Swap Spread compares the present value of the series of fixed payments from the bond and the present value of the floating payments. It is the spread that investors receive for swapping a fixed annual coupon against a floating payment. The floating rate received from such swap is generally considered as less sensitive to interest rate movements, as the payment flows are reset every quarter according to market conditions. Investors receive a higher coupon if rates increase or a lower coupon if rates decline.
One other important consideration while comparing bond credit spreads is a type of benchmark used by investors. It is either treasury rates of a LIBOR rate. For a corporate bond it is often more meaningful to choose LIBOR rather than treasuries. This is mainly because LIBOR rates are considered as close to risk free in a real world, where most corporate bonds do not have liquidity and safe haven benefits of Treasuries. Therefore a Z-spread over LIBOR is likely to reflect more accurate picture of the credit risk in a corporate bond. Moreover, to value a particular fixed income security most commonly used zero coupon curves are the government and LIBOR.