Warranty is a statement or representation that the goods and/or services will perform as promised in the agreement; a guaranty. For example, a License Agreement relating to a database of samples of musical compositions may contain a Warranty that the Licensor has obtained permission from the composers and performers of the individual musical works to provide access to the database to the Licensee.

Since this is some sort of assurance, I feel that it can be translated as per one of the three alternatives mentioned hereinabove. Of course, there is no harm in its transliteration either as it is quite common in Hindi.

When we give warranty for a product, we take some responsibility towards its performance.
Taking responsibility = Jimmedaari

when we say this item has three months warranty, we easily understand that there is a written document for replacement or repair the item.

If one want to go more precise then प्राधिकृत बाध्यता is more appropriate otherwise वारंटी will do.
Warranty is an undertaking by the manufacturer for the services & quality of the product sold. It gives a sense of legal binding on the manufacturer's part.