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Unless positions need to be accurately valued against each other (e.g. asset versus hedge, specified pool versus TBA), using the same paths for every position is never advantageous. Even if loans are somewhat heterogeneous, using random seeding will be as accurate for each loan and more accurate for the portfolio’s summary than same-seeding. Furthermore, if the collateral was made of 1M loans (rather than 1K), we could even extend our faith in Monte-Carlo and, instead of running 2 randomly seeded paths for each loan, apply them to a few thousand of the largest loans.
In Exhibit 1, we demonstrate that using just a few paths per loan, different for each loan, allows assessing the price of losses to be in the ballpark for both fixed-rate and ARM groups of CW0708. Using a few same paths for each loan leads to a large error.
Exhibit 1. Monte-Carlo convergence (price of losses using +0.7% HPI equilibrium rate)
This few-paths-random-seeds method benefits from error diversification - much like investing in many independent stocks. It also suggests that a typical senior management’s dream of seeing every position priced “consistently” against the same set of paths will likely reduce accuracy in risk measurements, without benefits. When measuring duration, convexity and other Greeks, we must keep the initial seed unchanged, but should change it going from one position to another.
