We describe and present results from a finite-volume (FV) parallel computer code for forward modelling the Maxwell viscoelastic response of 3-D, self-gravitating, elastically compressible Earth to an arbitrary surface load. implement conservative, control volume discretization governing equations using tetrahedral grid in Cartesian geometry low-order, linear interpolation. The basic starting honours all major radial discontinuities Preliminary Reference Model (PREM), models are permitted...

Abstract A new collocation method based on quadratic splines is presented for second order two‐point boundary value problems. First, O ( h 4 ) approximations to the first and derivative of a function are derived using quadratic‐spline interpolant u. Then these used define an perturbation given problem. Second, perturbed problem approximation at interval midpoints which optimal 3‐J global estimate j th error derived. Further, 4‐J bounds obtained certain superconvergence points. It should be...

SUMMARY We develop highly efficient parallel PDE‐based pricing methods on graphics processing units (GPUs) for multi‐asset American options. Our approach is built upon a combination of discrete penalty the linear complementarity problem arising because free boundary and GPU‐based alternating direction implicit approximate factorization technique with finite differences uniform grids solution algebraic system from each iteration. A timestep size selector implemented efficiently GPUs used to...

Space–time adaptive and high-order methods for valuing American options using a partial differential equation (PDE) approach are developed in this paper. The linear complementarity problem that arises due to the free boundary is handled penalty method. Both finite difference element considered space discretization of PDE, while classical differences, such as Crank–Nicolson, used time discretization. based on an optimal collocation method, main computational requirements which solution one...

We study a parallel implementation on Graphics Processing Unit (GPU) of Alternating Direction Implicit (ADI) time-discretization methods for solving time-dependent parabolic Partial Differential Equations (PDEs) in three spatial dimensions with mixed derivatives variety applications computational finance. Finite differences uniform grids are used the discretization PDEs. As examples, we apply GPU-based to price European rainbow and basket options, each written assets. Numerical results...

SUMMARY We present a graphics processing unit (GPU) parallelization of the computation price exotic cross‐currency interest rate derivatives via partial differential equation (PDE) approach. In particular, we focus on GPU‐based parallel pricing long‐dated foreign exchange (FX) hybrids, namely power reverse dual currency (PRDC) swaps with Bermudan cancelable features. consider three‐factor model FX volatility skew, which results in time‐dependent parabolic PDE three spatial dimensions. Finite...

We propose a general framework for efficient pricing via Partial Differential Equation (PDE) approach of crosscurrency interest rate derivatives under the Hull–White model. In particular, we focus on long-dated foreign exchange (FX) hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features. formulate problem in terms three correlated processes that incorporate FX skew local volatility function. This formulation results time-dependent parabolic PDE spatial...

In this paper, we discuss efficient pricing methods via a partial differential equation (PDE) approach for long-dated foreign exchange (FX) interest rate hybrids under three-factor multicurrency model with FX volatility skew. The emphasis of paper is on power-reverse dual-currency (PRDC) swaps popular exotic features, namely knockout and target redemption (FX-TARN). Challenges in these derivatives PDE arise from the high dimensionality as well complexities handling especially case FX-TARN...

We present a Graphics Processing Unit (GPU) parallelization of the computation price exotic cross-currency interest rate derivatives via Partial Differential Equation (PDE) approach. In particular, we focus on GPU-based parallel pricing long-dated foreign exchange (FX) hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features. consider three-factor model FX volatility skew which results in time-dependent parabolic PDE three spatial dimensions. Finite...

We propose a general framework for efficient pricing via Partial Differential Equation (PDE) approach of cross-currency interest rate derivatives under the Hull-White model. In particular, we focus on long-dated foreign exchange (FX) hybrids, namely Power Reverse Dual Currency (PRDC) swaps with Bermudan cancelable features. formulate problem in terms three correlated processes that incorporate FX skew local volatility function. This formulation results time dependent parabolic PDE spatial...

We discuss efficient pricing methods via a Partial Differential Equation (PDE) approach for long dated foreign exchange (FX) interest rate hybrids under three-factor multi-currency model with FX volatility skew. The emphasis of the paper is on Power-Reverse Dual-Currency (PRDC) swaps popular exotic features, namely knockout and Target Redemption (FX-TARN). Challenges in these derivatives PDE arise from high-dimensionality PDE, as well complexities handling especially case FX-TARN provision,...

We develop highly efficient parallel pricing methods on Graphics Processing Units (GPUs) for multi-asset American options via a Partial Differential Equation (PDE) approach. The linear complementarity problem arising due to the free boundary is handled by penalty method. Finite difference uniform grids are considered space discretization of PDE, while classical finite differences, such as Crank-Nicolson, used time discretization. discrete nonlinear penalized equations at each timestep solved...