  In [5] the authors suggested a new algorithm for the numerical approximation
of a BSDE by merging the cubature method with the first order discretization
developed by [3] and [16]. Though the algorithm presented in [5] compared
satisfactorily with other methods it lacked the higher order nature of the
cubature method due to the use of the low order discretization. In this paper
we introduce a second order discretization of the BSDE in the spirit of higher
order implicit-explicit schemes for forward SDEs and predictor corrector
methods.
