Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation

DOI10.1007/s10444-015-9421-4zbMath1336.91086OpenAlexW611136723MaRDI QIDQ904258

Hans-Joachim Bungartz, Benjamin Peherstorfer, Pablo Gomez

Publication date: 13 January 2016

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1721.1/107122

zbMATH Keywords

option pricingproper orthogonal decompositionsparse gridsBlack-Scholes equation

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (2)

A parallel sparse grid construction algorithm based on the shared memory architecture and its application to flash calculations ⋮ Modulus-based successive overrelaxation iteration method for pricing American options with the two-asset Black-Scholes and Heston's models based on finite volume discretization

Uses Software

• Eigen

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Pricing of Options and Corporate Liabilities
• Option pricing with a direct adaptive sparse grid approach
• Sparse grid quadrature in high dimensions with applications in finance and insurance
• Dimension-wise integration of high-dimensional functions with applications to finance
• Calibration of options on a reduced basis
• On coordinate transformation and grid stretching for sparse grid pricing of basket options
• Dimension-adaptive tensor-product quadrature
• On multigrid for anisotropic equations and variational inequalities ``pricing multi-dimensional European and American options
• Hierarchical bases give conjugate gradient type methods a multigrid speed of convergence
• Principal component analysis.
• A note on the complexity of solving Poisson's equation for spaces of bounded mixed derivatives
• Space-time adaptive finite difference method for European multi-asset options
• Far Field Boundary Conditions for Black--Scholes Equations
• A Reduced Basis Method for the Simulation of American Options
• Nonlinear model order reduction based on local reduced-order bases
• A Reduced Basis for Option Pricing
• Reduced basis for vanilla and basket options
• Multilevel Monte Carlo Path Simulation
• Selected Recent Applications of Sparse Grids
• Option Pricing in Hilbert Space-Valued Jump-Diffusion Models Using Partial Integro-Differential Equations
• Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Certified real‐time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced‐basis a posteriori error bounds
• A highly parallel Black–Scholes solver based on adaptive sparse grids
• Analysis of linear difference schemes in the sparse grid combination technique
• Valuation of Structured Financial Products by Adaptive Multiwavelet Methods in High Dimensions
• Pricing Multi-Asset Options with Sparse Grids and Fourth Order Finite Differences
• Convergence Rates of the POD–Greedy Method
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods
• Localized Discrete Empirical Interpolation Method
• Efficient Hierarchical Approximation of High‐Dimensional Option Pricing Problems
• A highly accurate adaptive finite difference solver for the Black–Scholes equation

This page was built for publication: Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation