Far Field Boundary Conditions for Black--Scholes Equations
SIAM Journal on Numerical Analysis
Computational Methods for Option Pricing (Frontiers in Applied Mathematics) (Frontiers in Applied Mathematics 30)
Efficient Hierarchical Approximation of High-Dimensional Option Pricing Problems
SIAM Journal on Scientific Computing
Numerical Valuation of European and American Options under Kou's Jump-Diffusion Model
SIAM Journal on Scientific Computing
On coordinate transformation and grid stretching for sparse grid pricing of basket options
Journal of Computational and Applied Mathematics
Multilevel Monte Carlo Path Simulation
Operations Research
Multi- and many-core data mining with adaptive sparse grids
Proceedings of the 8th ACM International Conference on Computing Frontiers
A comparison study of ADI and operator splitting methods on option pricing models
Journal of Computational and Applied Mathematics
Many-core architectures boost the pricing of basket options on adaptive sparse grids
WHPCF '13 Proceedings of the 6th Workshop on High Performance Computational Finance
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We present an adaptive sparse grid algorithm for the solution of the Black-Scholes equation for option pricing, using the finite element method. Sparse grids enable us to deal with higher-dimensional problems better than full grids. In contrast to common approaches that are based on the combination technique, which combines different solutions on anisotropic coarse full grids, the direct sparse grid approach allows for local adaptive refinement. When dealing with non-smooth payoff functions, this reduces the computational effort significantly. In this paper, we introduce the spatially adaptive discretization of the Black-Scholes equation with sparse grids and describe the algorithmic structure of the numerical solver. We present several strategies for adaptive refinement, evaluate them for different dimensionalities, and demonstrate their performance showing numerical results.