Option Adjusted Spread

The spread is referred to as "option adjusted" spread since the spread takes into consideration the options embedded in the issue
The z-spread approach can be extended further when valuing securities where optionality makes a significant difference to the value
For instance if rates fall the price of a callable bond is unlikely to rise much above par - the issuer would redeem the bond (usually at par) and refinance at lower levels.
This is often based on the Black Derman Toy (BDT) model
The greater the volatility of interest rates, the greater this possibility and the lower the value of the callable bond.
the other 3 methods all incorporate the term structure of interest rates when evaluating (ie discounting using the yields of different maturities)

OAS = LIBOR + Spread
In an OAS model a potential future distribution of interest rates (which will be a function of interest rate volatility) generates a series of different future outcomes.
In the case of a callable bond, then in some cases a bond may be redeemed early while in others it would remain outstanding.
"average" cash flows can be calculated and discounted using the z-spread methodology
The spread is now added to the risk-free rates in order to make the present value equal to the market price, is known as the option adjusted spread.

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