  We give a classification up to equivalence of the fine group gradings by
abelian groups on the Jordan pairs and triple systems of types bi-Cayley and
Albert, under the assumption that the base field is algebraically closed of
characteristic different from $2$. The associated Weyl groups are computed. We
also determine, for each fine grading on the bi-Cayley and Albert pairs, the
induced grading on the exceptional simple Lie algebra given by the
Tits-Kantor-Koecher construction.
