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The SPV is the owner of the pool in case 1. A financial institution or SPV may own the pool in 2.
Other gaps we noticed include the definition of Fannie Mae, Freddie Mac, and Ginnie Mae. They are government agencies (instrumentalities) that should be covered.
Elisa will work figuring out the relationships between a pool and its owner - based on the patterns we have for ownership. In this case ownership is transitive - if the SPV or institution owns the pool they also own the individual instruments that are part of that pool.