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The option-adjusted spread considers the variability of interest rates and prepayment rates. More advanced statistical modeling methods such as Monte Carlo analysis are often used to predict prepayment probabilities. The Z-spread provides the difference in basis points along the entire Treasury yield curve. Therefore, the cash flow is discounted at the Treasury spot rate, plus the Z-spread. However, the Z-spread does not include the value of embedded options in its calculation.

Embedded options can impact the present value of bonds. Mortgage-backed securities often include embedded options, since there is a significant risk of prepayment. Mortgage borrowers are more likely to refinance their mortgages if interest rates go down.

The embedded option means the future cash flows are alterable by the issuer since the bond can be called. The issuer may use the embedded option if interest rates drop. The embedded call allows the issuer to call the outstanding debt, pay it off and reissue it at a lower interest rate. By being able to reissue the debt at a lower interest rate, the issuer can reduce the cost of capital. Investors in bonds with embedded options, therefore, take on more risk.

If the bond is called, the investor will likely be forced to reinvest in other bonds with lower interest rates. Bonds with embedded call options often pay a yield premium over bonds with similar terms. Instead of Treasury securities, if we look at a corporate bond, we can follow the same approach.

Since, corporate bonds have credit risk, they are considered less worthy compared to a similar Treasury bond. This is reflected in the Z-spread of the corporate bond, which will be positive for the corporate bond.

Higher the credit risk, the higher is the Z-spread. For these bonds, Z-spread is not appropriate. Interest rate volatility plays a huge role here. We will need to use a model that takes into consideration the volatility interest rates which will help us in taking into account the risk of the bond being called.

It is possible to use various models. One appropriate model is the stochastic term structure model. We start with a curve of zero-coupon interest rates and also use some parameters for determining the volatility of these interest rates.

With these inputs, we can generate a large number of possible scenarios for future interest rates. These future interest rates can be above or below the current spot curve. We can use a rule to determine when the embedded option will be exercised.

We calculate the value of the security by discounting the payments in each scenario using the interest rates in that scenario. So, the calculation of OAS is relatable to the calculation of Z-spread. The OAS is the shift to the zero-coupon interest rates in all scenarios required to ensure that the model value the average value of all scenarios equals the market price of the bond.