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More paths can be used, say 500, for agency CMOs. The main reason for long processing is the nature of non-agency collateral and its heterogeneity. Even under the weighted averaged collateral aggregation mode, input fields like prepay penalty details or rate resets are not clustered. It leads to hundreds or even thousands of pieces of collateral.
Our OAS users can vary the path numbers and change them when going from one CMO to the next. This position-level assignment improves the efficiency of batch processing.
3. Shuffle the seeds. The AD&Co. OAS system lets you apply the same or different set of paths to various position lines. As pointed out in the May 2007 Pipeline article, starting each position run from random seeds is a powerful and simple recipe. And if all we are interested in is compiling an aggregate report, we can reduce the workload by using just a few Monte-Carlo paths per position.
Random shuffling of path sets between consecutive positions creates enough randomness in the overall run. To illustrate this point, let us consider a portfolio made up of 1,000 identical positions. Running 2 random paths per position seeded randomly is equivalent to running 2,000 random paths, from the portfolio stand-point. In contrast, running 2 random, but the same, paths per position, is no different than running only 2 paths for the entire portfolio. The May 2007 Pipeline article shows that using this method when computing the expected losses in a sub-prime pool leads to an accuracy exceeding 1%. This is an improvement by a factor of 20 to 50 compared to the traditional method that employs the same set of paths for each position. Of course, for each instrument, computing the Greeks must employ the same seed as running OAS.
Unless positions need to be accurately valued against each other (e.g. asset versus hedge, specified pool versus TBA), using the same set of paths for every position is never advantageous. Even if positions are somewhat heterogeneous, using random seeding will be as accurate for each position and more accurate for the portfolio’s summary than using the same-seeding.
