We have performed an ab initio calculation of the hyperfine, P-odd and P, T-odd constants for the YbF molecule using a recently developed technique which allows us to take into account correlations and polarization in the outer-core region. The ground state (²Σ_1/2) electronic wavefunction of the YbF molecule is found with the help of the relativistic effective core potential method followed by the restoration of molecular four-component spinors in the core region of ytterbium within the framework of a non-variational procedure. Core polarization effects are included with the help of atomic many-body perturbation theory for the Yb atom. Our calculation of the isotropic hyperfine constant A agrees at the 3% level with the experimental value. The dipole constant A_d (which is much smaller in magnitude), though better than in all previous calculations, is still underestimated by almost 23%. This error is reduced to 8% after a semiempirical correction for perturbation of the 4f-shell in the core of Yb due to the chemical bonding made. Our value for the effective electric field on the unpaired electron is 4.9 au = 2.5 × 10¹⁰ V cm^-1.