A regression-based numerical scheme for backward stochastic differential equations

Based on Fourier cosine expansion, two approximations of conditional expectations are studied, and the local errors for these approximations are analyzed. Using these approximations and the theta-time discretization, a new and efficient numerical scheme, which is based on least-squares regression, for forward–backward stochastic differential equations is proposed. Numerical experiments are done to test the availability and stability of this new scheme for Black–Scholes call and calls combination under an empirical expression about volatility. Some conclusions are given.