Granularity in finance has different (and at time slightly different) meanings in different contexts. In relation to structured products/ instruments, it refers to the the actual number of obligations forming the overall product/ instrument. Granularity is the subdivision of a pool of underlying securitized assets into smaller pieces (tranches), with an aim to mitigate the credit risk of individual loans. Granularity may be determined ex-ante or post-facto. An entity may determine the level of subdivision, ex-ante.
For example, residential mortgage pools may be, by nature, highly granular (post-facto reality). However, pools consisting of commercial mortgages are generally less granular (less subdivided) (post-factor reality): involving of only a few number of loans.
Broadly speaking, granularity may also indicate the number and types of assets (underlying components) of a structure such as a securitized pool of mortgages, a portfolio (see: granular portfolio), etc.
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