When Fourier techniques are employed to specific option pricing cases from computational finance with non-smooth functions, the so-called Gibbs phenomenon may become apparent. This seriously impacts the efficiency and accuracy of the pricing. For example, the Variance Gamma asset price process...

We develop three numerical methods to solve coupled forward-backward stochastic differential equations. We propose three different discretization techniques for the forward stochastic differential equation. A theta-discretization of the time-integrands is used to arrive at schemes with...

We develop a Fourier method to solve backward stochastic differential equations (BSDEs). General theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier-cosine series expansions, relying on the availability...

We develop a Fourier method to solve rather general backward stochastic differential equations (BSDEs) with second-order accuracy. The underlying forward stochastic differential equation (FSDE) is approximated by different Taylor schemes, such as the Euler, Milstein, and Order 2.0 weak Taylor...