This depends if you are getting a Conforming or FHA loan. Conforming does require 2 years of employment and there is no exception.
However, FHA requires only 2 consecutive pay stubs if you have started a new job or a profession. All of the other compensating factors like Debt ratio, FICO etc must be met regardless.
Another out happens when the borrower has been finishing post-graduate school i.e. MD, MBA etc. In this case, they will allow a letter of employment along with first months 2 pay stubs to qualify you for conforming loans.
Length of employment can be a very sensitive issue to the underwriting, do not take it lightly if you are employed less than 2 years.
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This question was initially answered in Quora by our co-founder and mortgage ninja Kevin. View in Quora