We present twenty-three transit light curves and seven occultation light curves for the ultra-short period planet WASP-43 b, in addition to eight new measurements of the radial velocity of the star. Thanks to this extensive data set, we improve significantly the parameters of the system. Notably, the largely improved precision on the stellar density (2.41 ± 0.08 ρ&sun;) combined with constraining the age to be younger than a Hubble time allows us to break the degeneracy of the stellar solution mentioned in the discovery paper. The resulting stellar mass and size are 0.717 ± 0.025 M&sun; and 0.667 ± 0.011 R&sun;. Our deduced physical parameters for the planet are 2.034 ± 0.052 MJup and 1.036 ± 0.019 RJup. Taking into account its level of irradiation, the high density of the planet favors an old age and a massive core. Our deduced orbital eccentricity, 0.0035-0.0025+0.0060, is consistent with a fully circularized orbit. We detect the emission of the planet at 2.09 μm at better than 11-σ, the deduced occultation depth being 1560 ± 140 ppm. Our detection of the occultation at 1.19 μm is marginal (790 ± 320 ppm) and more observations are needed to confirm it. We place a 3-σ upper limit of 850 ppm on the depth of the occultation at ~0.9 μm. Together, these results strongly favor a poor redistribution of the heat to the night-side of the planet, and marginally favor a model with no day-side temperature inversion. Based on data collected with the TRAPPIST and Euler telescopes at ESO La Silla Observatory, Chile, and with the VLT/HAWK-I instrument at ESO Paranal Observatory, Chile (program 086.C-0222).Tables 1 and 4 are available in electronic form at http://www.aanda.orgPhotometry is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/542/A4