Discretization Methods

Abstract

This chapter describes various important discretization methods. The chapter discusses convergence issues and presents four processes that are used as illustrations. Ito-Taylor schemes in Q-dimensions and the forms taken by them in 1-dimension are presented. The predictor–corrector schemes are introduced and the approximations are applied to two of the illustrative processes, which benchmarks with the geometric Brownian motion (GBM) and Vasicek processes. All the Ito-Taylor based schemes in the benchmark cases work well and higher order convergence is achieved. The Euler discretization usually works for processes met in finance but converges only slowly with possibly high error. However, higher order Ito–Taylor schemes are complex and they can work well when they work at all.

Cite this paper

@misc{anon2012discretization,
  title = {{Discretization Methods}},
  pages = {399--416},
  year = {2012},
  doi = {10.1002/9781119206149.ch25}
}

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