We propose a new method for the numerical solution of backward stochastic differential equations (BSDEs) which finds its roots in Fourier analysis. The method consists of an Euler time discretization of the BSDE with certain conditional expectations expressed in terms of Fourier transforms and...

The implementation of the convolution method for the numerical solution of backward stochastic differential equations (BSDEs) presented in Hyndman and Oyono Ngou (arXiv:1304.1783, 2013) uses a uniform space grid. Locally, this approach produces a truncation error, a space discretization error...

We provide explicit solutions of certain forward-backward stochastic differential equations (FBSDEs) with quadratic growth. These particular FBSDEs are associated with quadratic term structure models of interest rates and characterize the zero-coupon bond price. The results of this paper are...

We consider a forward-backward stochastic differential equation associated with the bond price for the Cox-Ingersoll-Ross interest rate model and prove an existence and uniqueness result. This technique is generalizable to multidimensional affine term structure models.