I'm sorry I didn't notice this question until now. "Nat cat" is an established short form of "natural catastrophe" (hurricanes, earthquakes, etc.), a standard term in insurance.

"In 1992, Hurricane Andrew in Florida was insurers' most expensive natural catastrophe to date, at 25 billion US dollars. Andrew pushed insurers to the limits of their risk bearing capacity, and triggered new developments in every segment: new disaster simulations and risk models were developed, more data was gathered and analyzed, risks were spread and better diversified, reinsurance capacity was expanded, and the capital market began to be tapped with what came to be known as "Nat Cat" (natural catastrophe) bonds."
https://www.allianz.com/en/press/news/business/insurance/new...

"Our client, a successful and growing reinsurance firm, is looking to expand their Natural Catastrophe team with an experienced Nat Cat Modeller for the European market - ideally within Earthquake."
http://www.theactuaryjobs.com/job/14340/natural-catastrophe-...