The RBI website lists the Reserve Bank of India Act, 1934, the Banking Regulation Act, 1949, and the Foreign Exchange Management Act, 1999, among the laws it administers.
For derivatives, the RBI sets the rules for foreign exchange derivatives under the Foreign Exchange Management Act, and the rules for interest rate and credit derivatives under the Reserve Bank of India Act, through master directions and circulars. The individual rules are covered in the article on India.