Because the binomial interest rate tree model is a backward induction process that does not consider current interest rates in comparison to historical interest rates in estimating prepayments (i.e. the interest rate path), it cannot be used to value ABS/MBS securities.

Understanding the interest rate path is critical for valuing ABS/MBS because the interest rate path will inform prepayment assumptions, as borrowers tend to refinance when interest rates drop.

## Steps in a Monte Carlo Simulation

- A Monte Carlo simulation program will create thousands of interest paths that the ABS/MBS could follow over its life.
- The paths are adjusted so the model is “arbitrage free”, meaning that the model correctly values current on the run Treasuries.
- For each interest rate path modeled, the simulator will forecast monthly prepayments for the life of the security.
- The simulator calculates cash flows paid on each interest rate path utilizing forecasted prepayment rates.
- A present value of each path is calculated by the simulator based on the cash flows and discount rates for each path.
- The simulator averages the present values for each path in step 5. This value is the expected value of the security, if it were risk free.
- A constant spread is added by the simulator to the arbitrage free Treasury rates calculated in step 2; the cash flows from step 4 are discounted with the new discount rate.
- The simulator averages all the present values for step 7 and compares this to the current price of the security. If the average present value is too low, then the constant spread in step 7 will be reduced.

## Monte Carlo Simulation and the Option Adjusted Spread (OAS)

The difference between the OAS and the Z-spread can be interpreted as the value of the embedded option, stated in basis points. The Z-spread will be greater than the OAS spread.

In order for the OAS to be accurate:

- Volatility assumptions must closely approximate future volatility.
- Prepayment assumptions must closely approximate prepayment realized.
- The Monte Carlo simulator model correctly values on the run Treasuries
- The OAS ensures that the average price across all interest rate paths equals the security’s current price.

If the assumptions are accurate and comparable for multiple ABS/MBS securities, then the ABS/MBS with the higher OAS is considered the better value.

OAS = Z-spread, when interest rate volatility is assumed to be zero.

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