Appendix: Recursive Marginal Quantization of Higher-Order Schemes

9 Pages Posted: 17 Nov 2017

See all articles by Thomas McWalter

Thomas McWalter

University of Cape Town (UCT); University of Johannesburg

Ralph Rudd

The African Institute of Financial Markets and Risk Management

Joerg Kienitz

University of Wuppertal - Applied Mathematics; University of Cape Town (UCT); Quaternion Risk Management

Eckhard Platen

University of Technology, Sydney (UTS) - Finance Discipline Group; University of Technology Sydney, School of Mathematical and Physical Sciences; Financial Research Network (FIRN)

Date Written: November 14, 2017

Abstract

This document serves as the online appendix to McWalter et al. [2017]. It provides efficient matrix implementations for both vector quantization and the generalized recursive marginal quantization, which allows for the implementation of the higher-order discretization schemes presented in the main paper. It includes graphical examples of how the higher-order discretization schemes reduce the error in the implied marginal distributions for both the geometric Brownian motion process (GBM) and its generalization, the constant elasticity of variance (CEV) process. It concludes with an example of the effect of modelling the CEV process with an absorbing or reflecting boundary at zero.

The full-text version of this paper can be found at http://ssrn.com/abstract=2894753.

Suggested Citation

McWalter, Thomas and Rudd, Ralph and Kienitz, Joerg and Platen, Eckhard, Appendix: Recursive Marginal Quantization of Higher-Order Schemes (November 14, 2017). Available at SSRN: https://ssrn.com/abstract=3071201 or http://dx.doi.org/10.2139/ssrn.3071201

Thomas McWalter (Contact Author)

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Ralph Rudd

The African Institute of Financial Markets and Risk Management ( email )

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Joerg Kienitz

University of Wuppertal - Applied Mathematics ( email )

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University of Cape Town (UCT) ( email )

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Eckhard Platen

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