  We use data from five stellar occultations observed between 2013 and 2016 to
constrain Chariklo's size and shape, and the ring reflectivity. We consider
four possible models for Chariklo (sphere, Maclaurin spheroid, tri-axial
ellipsoid and Jacobi ellipsoid) and we use a Bayesian approach to estimate the
corresponding parameters. The spherical model has a radius $R=129\pm3$ km. The
Maclaurin model has equatorial and polar radii $a=b=143^{+3}_{-6}$ km and
$c=96^{+14}_{-4}$ km, respectively, with density $970^{+300}_{-180}$ kg
m$^{-3}$. The ellipsoidal model has semiaxes $a=148^{+6}_{-4}$ km,
$b=132^{+6}_{-5}$ km and $c=102^{+10}_{-8}$ km. Finally, the Jacobi model has
semiaxes $a$=157$\pm$4 km, $b$=139$\pm$ 4 km and $c$=86$\pm$1 km, and density
$796^{+2}_{-4}$ kg m$^{-3}$ . Depending on the model, we obtain topographic
features of 6-11 km, typical of Saturn icy satellites with similar size and
density. We constrain Chariklo's geometric albedo between 3.1\% (sphere) and
4.9\% (ellipsoid), while the ring $I/F$ reflectivity is less constrained
between 0.6\% (Jacobi) and 8.9\% (sphere). The ellipsoid model explains both
the optical light curve and the long-term photometry variation of the system,
giving a plausible value for the geometric albedo of the ring particles of
$10-15\%$. The derived Chariklo's mass of 6-8$\times10^{18}$ kg places the
rings close to the 3:1 resonance between the ring mean motion and Chariklo's
rotation period.
