Define the Z-spread and OAS. For a callable BB bond trading at 101 with a YTW of 5.5%, its Z-spread is 320 bps and OAS is 280 bps. Explain exactly what the 40 bps difference represents and how you would use it to value the call option.

The Z-spread is the constant spread over the risk-free curve that equates the discounted cash flows (assuming no exercise of the call) to the market price. The OAS subtracts the value of the embedded call option, so the difference (Z-spread minus OAS) represents the option-adjusted spread value of the call feature in basis points. Here, 40 bps is the market’s valuation of the call option expressed as a yield spread. If you converted that 40 bps to an option premium in price terms, you could back out the implied option value. In effect, the bond would trade at a Z-spread of 320 bps if it were non-callable; the call option reduces the yield advantage to the investor, so the OAS of 280 bps represents the pure credit and liquidity spread after adjusting for the call risk. Follow-up pressure: (1) If the issuer’s credit improves dramatically, how would you expect the Z-spread and OAS to move relative to each other? (2) How would a change in interest rate volatility affect the OAS, holding credit spread constant? (3) Suppose you buy the bond and simultaneously buy a receiver swaption to hedge the call. How would you assess the hedge’s effectiveness using OAS?