Explain how the number of interest-rate paths used in the Monte Carlo simulation methodology is determined

What will be an ideal response?

The number of interest-rate paths used in the Monte Carlo simulation methodology is determined by the number of sample paths necessary to get a good statistical sample to obtain a price estimate within a tick. More details are given below.

What is the number of scenario paths or repetitions, N, needed to value a RMBS? A typical OAS run will be done for 512 to 1,024 interest-rate paths. The scenarios generated using the simulation method look very realistic and, furthermore, reproduce today's Treasury curve. By employing this technique, the money manager is effectively saying that Treasuries are fairly priced today and that the objective is to determine whether a specific RMBS is rich or cheap relative to Treasuries.

The number of interest-rate paths determines how "good" the estimate is, not relative to the truth but relative to the model. The more paths, the more average spread tends to settle down. It is
a statistical sampling problem.

Most Monte Carlo simulation models use some form of variance reduction to cut down on the number of sample paths necessary to get a good statistical sample. Variance reduction techniques allow us to obtain price estimates within a tick. By this we mean that if the model is used to generate more scenarios, price estimates from the model will not change by more than a tick. For example, if 1,024 paths are used to obtain the estimated price for a tranche, there is little more information to be had from the model by generating more than that number of paths. (For some very sensitive CMO tranches, more paths may be needed to estimate prices within one tick.)