Explanation

Option-Adjusted Spread (OAS) is the constant spread that must be added to the benchmark spot rate curve to make the theoretical value of a security equal to its market price, after adjusting for embedded options.

For callable bonds:

• The embedded call option gives the issuer the right to call (redeem) the bond before maturity
• As interest rate volatility increases, the value of the embedded call option increases
• This is because higher volatility increases the probability that interest rates will fall sufficiently to make calling the bond advantageous for the issuer

Relationship between volatility and OAS:

• Higher volatility → Higher call option value → Lower bond value (from investor's perspective)
• To maintain the same market price with lower theoretical value, the OAS must decrease
• Therefore, as volatility increases, the OAS of a callable bond decreases

This relationship exists because the OAS represents the compensation investors receive for credit risk and other factors AFTER adjusting for the embedded option. When the option becomes more valuable (due to higher volatility), less additional spread is needed to explain the bond's market price.