$L_2$-variation of Lévy driven BSDEs with non-smooth terminal conditions

We consider the $L_2$-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a L\'evy process $(X_t)_{t \in [0,T]}.$ The terminal condition may be a Borel function of finitely many increments of the L\'evy process which is not necessarily Lipschitz but only satisfies a fractional smoothness condition. The results are obtained by investigating how the special structure appearing in the chaos expansion of the terminal condition is inherited by the solution to the BSDE.