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Accumulated (integrated) interest and the square root process

Diandian Ma (Graduate School of Management, University of Auckland, Auckland, New Zealand)
Xiaojing Song (Newcastle University Business School, Newcastle upon Tyne, UK)
Mark Tippett (Business School, University of Sydney, Sydney, Australia)
Thu Phuong Truong (Victoria Business School, Victoria University of Wellington, Wellington, New Zealand)

Accounting Research Journal

ISSN: 1030-9616

Article publication date: 4 November 2019

118

Abstract

Purpose

The purpose of this study is to determine distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al. (1985) square root process.

Design/methodology/approach

The law of iterated (or double) expectations is used to determine the mean and variance of the accumulated rate of interest on a cash management (or loan) account when interest accumulates at the instantaneous rates of interest implied by the square root process.

Findings

This study demonstrates how the accumulated rate of interest does not satisfy the strong mixing conditions necessary for convergence in distribution to the normal density function.

Originality/value

This study has strong educational value in determining distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al. (1985) square root process and demonstrating how the accumulated rate of interest does not satisfy the strong mixing conditions necessary for convergence in distribution to the normal density function.

Keywords

Citation

Ma, D., Song, X., Tippett, M. and Truong, T.P. (2019), "Accumulated (integrated) interest and the square root process", Accounting Research Journal, Vol. 32 No. 4, pp. 678-691. https://doi.org/10.1108/ARJ-09-2017-0152

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited

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