  The latter author, together with collaborators, proposed a numerical scheme
to calculate the price of barrier options. The scheme is based on a
symmetrization of diffusion process. The present paper aims to give a
mathematical credit to the use of the numerical scheme for Heston or SABR type
stochastic volatility models. This will be done by showing a fairly general
result on the symmetrization (in multi-dimension/multi-reflections). Further
applications (to time-inhomogeneous diffusions/ to time dependent boundaries/to
curved boundaries) are also discussed.
