Title: Modelling DAX by applying parabola approximation method

Authors: Meng-Rong Li; Daniel Wei-Chung Miao; Tsung-Jui Chiang-Lin; Yong-Shiuan Lee

Addresses: Department of Mathematical Sciences, National Chengchi University, Taipei, 116, Taiwan ' Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei, 106, Taiwan ' Graduate Institute of Finance, National Taiwan University of Science and Technology, Taipei, 106, Taiwan ' Department of Statistics, National Chengchi University, Taipei, 116, Taiwan

Abstract: Existing studies indicate that the nonlinear phenomenon occurs in the movement of stock prices (or returns) but few models provide the adequate explanations. We apply 'parabola approximation' as an inclusion of nonlinear explanatory variable to model German Deutscher Aktien IndeX (DAX) closing prices during 2 January 2006 to 12 June 2013. The empirical result shows accurate fits which means the model applied characterises DAX appropriately. As a result, the coefficients of the model meaningfully determine the movement of DAX. After examining the coefficients, unusual changes of the coefficients as a sign of approaching fluctuations in the DAX prices display right before the announcement of the bankruptcy of Lehman Brothers. In this way, we provide an instrument to detect the prompt structural changes and risks of the financial market.

Keywords: ordinary differential equation; ODE; nonlinear dynamic system; parabola approximation; stock index; DAX; Deutscher Aktien index; financial crisis.

DOI: 10.1504/IJCSM.2019.104024

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.6, pp.566 - 579

Received: 28 Apr 2017
Accepted: 22 Aug 2017
Published online: 09 Dec 2019 *

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