Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major...

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Autores principales:	Vasile Brătian, Ana-Maria Acu, Camelia Oprean-Stan, Emil Dinga, Gabriela-Mariana Ionescu
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	geometric Brownian motion geometric fractional Brownian motion efficient market hypothesis fractal market hypothesis Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ad6e754a33394e229605d0b22c9695ca
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spelling	oai:doaj.org-article:ad6e754a33394e229605d0b22c9695ca2021-11-25T18:17:47ZEfficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion10.3390/math92229832227-7390https://doaj.org/article/ad6e754a33394e229605d0b22c9695ca2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2983https://doaj.org/toc/2227-7390In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar.Vasile BrătianAna-Maria AcuCamelia Oprean-StanEmil DingaGabriela-Mariana IonescuMDPI AGarticlegeometric Brownian motiongeometric fractional Brownian motionefficient market hypothesisfractal market hypothesisMathematicsQA1-939ENMathematics, Vol 9, Iss 2983, p 2983 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	geometric Brownian motion geometric fractional Brownian motion efficient market hypothesis fractal market hypothesis Mathematics QA1-939
spellingShingle	geometric Brownian motion geometric fractional Brownian motion efficient market hypothesis fractal market hypothesis Mathematics QA1-939 Vasile Brătian Ana-Maria Acu Camelia Oprean-Stan Emil Dinga Gabriela-Mariana Ionescu Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
description	In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar.
format	article
author	Vasile Brătian Ana-Maria Acu Camelia Oprean-Stan Emil Dinga Gabriela-Mariana Ionescu
author_facet	Vasile Brătian Ana-Maria Acu Camelia Oprean-Stan Emil Dinga Gabriela-Mariana Ionescu
author_sort	Vasile Brătian
title	Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
title_short	Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
title_full	Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
title_fullStr	Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
title_full_unstemmed	Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
title_sort	efficient or fractal market hypothesis? a stock indexes modelling using geometric brownian motion and geometric fractional brownian motion
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/ad6e754a33394e229605d0b22c9695ca
work_keys_str_mv	AT vasilebratian efficientorfractalmarkethypothesisastockindexesmodellingusinggeometricbrownianmotionandgeometricfractionalbrownianmotion AT anamariaacu efficientorfractalmarkethypothesisastockindexesmodellingusinggeometricbrownianmotionandgeometricfractionalbrownianmotion AT cameliaopreanstan efficientorfractalmarkethypothesisastockindexesmodellingusinggeometricbrownianmotionandgeometricfractionalbrownianmotion AT emildinga efficientorfractalmarkethypothesisastockindexesmodellingusinggeometricbrownianmotionandgeometricfractionalbrownianmotion AT gabrielamarianaionescu efficientorfractalmarkethypothesisastockindexesmodellingusinggeometricbrownianmotionandgeometricfractionalbrownianmotion
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Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion

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