Explanation

Option-Adjusted Spread (OAS) is defined as the constant spread that must be added to the 1-year forward rates in the binomial interest rate tree to make the theoretical value of a security equal to its market price.

Key points:

• In a zero volatility environment, the binomial tree collapses to a single path
• The OAS is added to the forward rates along this path
• This adjustment reconciles the bond's market price with its arbitrage-free value

Why forward rates?

• Forward rates represent the expected future short-term interest rates
• Adding a constant spread to forward rates accounts for credit risk and other risk premia
• This approach ensures consistency across the entire yield curve

Not spot rates or par rates because:

• Spot rates are for zero-coupon bonds of different maturities
• Par rates are for bonds trading at par
• Forward rates provide the most direct way to value bonds with embedded options in a binomial framework

In practice, OAS is calculated by iteratively adjusting the spread added to forward rates until the model price equals the market price.