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Option pricing with a direct adaptive sparse grid approach

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Volume
236
Issue
15
Identifiers
DOI: 10.1016/j.cam.2011.09.024
Keywords
  • Black–Scholes Equation
  • Option Pricing
  • Sparse Grids
  • Finite Elements
  • Adaptivity
Disciplines
  • Computer Science

Abstract

Abstract 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.

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