On coordinate transformation and grid stretching for sparse grid pricing of basket options

AbstractWe evaluate two coordinate transformation techniques in combination with grid stretching for pricing basket options in a sparse grid setting. The sparse grid technique is a basic technique for solving a high-dimensional partial differential equation. By creating a small hypercube sub-grid in the ‘composite’ sparse grid we can also determine hedge parameters accurately. We evaluate these techniques for multi-asset examples with up to five underlying assets in the basket

Pricing of early-exercise Asian options under L\'evy processes based on Fourier cosine expansions

In this article, we propose a pricing method for Asian options with early-exercise features. It is based on a two-dimensional integration and a backward recursion of the Fourier coefficients, in which several numerical techniques, like Fourier cosine expansions, Clenshaw–Curtis quadrature and the Fast Fourier Transform (FFT) are employed. Rapid convergence of the pricing method is illustrated by an error analysis. Its performance is further demonstrated by various numerical examples, where we also show the power of an implementation on Graphics Processing Units (GPUs)

Stochastic grid bundling method for backward stochastic differential equations

In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations. The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving backward stochastic

Computing credit valuation adjustment for Bermudan options with wrong way risk

We study the impact of wrong way risk (WWR) on credit valuation adjustment (CVA) for Bermudan options. WWR is modeled by a dependency between the underlying asset and the intensity of the counterparty's default. Two WWR models are proposed, based on a deterministic function and a CIR-jump (CIRJ) model, respectively. We present a nonnested Monte Carlo approach for computing CVA-VaR and CVA-expected shortfall (ES) for Bermudan options. By varying correlation coefficients, we study the impact of credit quality and WWR on the optimal exercise boundaries and CVA values of Bermudan products. Stress testing is performed

On pre-commitment aspects of a time-consistent strategy for a mean-variance investor

In this paper, a link between a time-consistent and a pre-commitment investment strategy is established. We define an implied investment target, which is implicitly con- tained in a time-consistent strategy at a given time step and wealth level. By imposing the implied investment target at the initial time step on a time-consistent strategy, we form a hybrid strategy which may generate better mean-variance efficient frontiers than the time-consistent strategy. We extend the numerical algorithm proposed in Cong and Oosterlee (2016b) to solve constrained time-consistent mean-variance optimization pro- blems. Since the time-consistent and the pre-commitment strategies generate different terminal wealth distributions, time-consistency is not always inferior to pre-commitment

Pricing Bermudan options under Merton jump-diffusion asset dynamics

In this paper, a recently developed regression-based option pricing method, the Stochastic Grid Bundling Method (SGBM), is considered for pricing multidimensional Bermudan options.We compare SGBM with a traditional regression-based pricing approach and present detailed insight in the application of SGBM, including how to configure it and how to reduce the uncertainty of its estimates by control variates. We consider the Merton jump-diffusion model, which performs better than the geometric Brownian motion in modelling the heavy-tailed features of asset price distributions. Our numerical tests show that SGBM with appropriate set-up works highly satisfactorily for pricing multidimensional options under jump-diffusion asset dynamics