  We study the nonlinear conductance through a quantum dot, specifically its
dependence on the asymmetries in the tunnel couplings and bias voltages $V$, at
low energies. Extending the microscopic Fermi-liquid theory for the Anderson
impurity model, we obtain an exact formula for the steady current $I$ up to
terms of order $V^3$ in the presence of these asymmetries. The coefficients for
the nonlinear terms are described in terms of a set of the Fermi-liquid
parameters: the phase shift, static susceptibilities, and three-body
correlation functions of electrons in the quantum dots, defined with respect to
the equilibrium ground state. We calculate these correlation functions, using
the numerical renormalization group approach (NRG), over a wide range of
impurity-electron filling that can be controlled by a gate voltage in real
systems. The NRG results show that the order $V^2$ nonlinear current is
enhanced significantly in the valence fluctuation regime. It is caused by the
order $V$ energy shift of the impurity level, induced in the presence of the
tunneling or bias asymmetry. Furthermore, in the valence fluctuation regime, we
also find that the order $V^3$ nonlinear current exhibits a shoulder structure,
for which the three-body correlations that evolve for large asymmetries play an
essential role.
