# Option Adjusted Spread

Option adjusted spread (OAS) is a constant spread that when added to the interest rates used to discount the cash flows produces a theoretical value of the bond that is equal to the market price of the bond. It is an alternative way of expressing the difference that lies between the theoretical value and the observed market price, i.e. in the form of a yield spread rather than a difference in prices.

In order to demonstrate how the OAS is determined for the Mortgage Pass Through Security in our model we have followed the steps given below:

- For illustrations purposes, the observed market price is assumed to be the value of the MBS calculated using a constant discount rate equal to the 30-year fixed mortgage rate observed in the market assuming prepayments occur at 100% of PSA.
- We use an OAS Monte Carlo simulation approach to generate 100 interest rate paths. These interest rates are assumed to be short term rates to which the OAS is added to determine the rates at which MBS cash flows will be discounted. The simulated interest rates are also used to determine the prepayment rates for the MBS.
- In order to determine the relationship between the prepayment rates and the interest rates we have developed a prepayment rate function which is a function of interest rates using linear regression and based on the historical relationship between these two rates.

- Based on the simulated rates the future Mortgage Pass Through cash flows for each interest rate path are calculated. The cash flows are discounted by interest rates plus a “guess” OAS to determine 100 theoretical prices for one unit of Mortgage Pass Through Security.
- A simple average of the theoretical price over all paths is calculated and the model solves for an OAS that equates this average simulated price to the observed market price.