The Biblical and Rabbinical obligation:
[Biblically the command to annul loans during Shemitah only applies during times that the Yovel cycle is in practice, which is when all the tribes are living in Eretz Yisrael.] In today’s times [however] the laws of Shemitas Kesafim [abolishing debts] during the year of Shemitah is [only] a Rabbinical enactment. This applies in both Eretz Yisrael, and in the Diaspora.
 Admur Hilchos Halva 34
 Michaber 67/1; Rambam Shemitah 2/9
Other Opinions: See Ramban brought in Urim Vetumim 67/1 that holds Shemitas Kesafim is a Biblical obligation even today, and even in the Diaspora.
 Rambam Shemitah 10/8
 Admur 34; Gittin ibid; Rambam 9/3; Michaber ibid
 Admur ibid; Michaber ibid