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 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...

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 propose Quantum Majorization as a way of comparing and ranking correlation matrices, with the aim of assessing portfolio risk in a unified framework. Quantum majorization is a partial order in the space of correlation matrices, which are evaluated through their spectra. We discuss the...

This paper enhances a well-known dynamic portfolio management algorithm, the BGSS algorithm, proposed by Brandt, Goyal, Santa-Clara and Stroud (Review of Financial Studies, 18, 831-873, 2005). We equip this algorithm with the components from a recently developed method, the Stochastic Grid...

The regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio, is computed based on the portfolio exposure over its lifetime. Usually the future portfolio exposure is approximated using Monte Carlo simulation, as the portfolio value can be driven by...

This paper describes an American Monte Carlo approach for obtaining fast and accurate exercise policies for pricing of callable LIBOR Exotics (e.g., Bermudan swaptions) in the LIBOR market model using the Stochastic Grid Bundling Method (SGBM). SGBM is a bundling and regression based Monte Carlo...