Error estimates of the θ-scheme for backward stochastic differentialequations

In this paper, we study the error estimate of the θ-schemefor the backward stochastic differential equationyₜ=φ(WT)+∫ₜTf(s,yₛ)ds-∫ₜTzₛdWₛ. We show thatthis scheme is of first-order convergence in y for generalθ. In particular, for the case of θ=1/2 (i.e.,the Crank-Nicolson scheme), we prove that this scheme is ofsecond-order convergence in y and first-order in z. Somenumerical examples are also given to validate our theoreticalresults.