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.
