  We present our preliminary results for three-point correlation functions
involving the operators entering the $\Delta{S}=1$ effective Hamiltonian with
an active charm quark, obtained using overlap fermions in the quenched
approximation. This is the first computation carried out for valence quark
masses small enough so as to permit a matching to Quenched Chiral Perturbation
Theory in the $\epsilon$-regime. The commonly observed large statistical
fluctuations are tamed by means of low-mode averaging techniques, combined with
restrictions to individual topological sectors. We also discuss the matching of
the resulting hadronic matrix elements to the effective low-energy constants
for $\Delta{S}=1$ transitions. This involves (a) finite-volume corrections
which can be evaluated at NLO in Quenched Chiral Perturbation Theory, and (b)
the short-distance renormalization of the relevant four-quark operators in
discretizations based on the overlap operator. We discuss perturbative
estimates for the renormalization factors and possible strategies for their
non-perturbative evaluation. Our results can be used to isolate the
long-distance contributions to the $\Delta I=1/2$ rule, coming from physics
effects around the intrinsic QCD scale.
