Simulation of Stochastic Geometric Brownian Motion of Stock Market Using R Programming

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.

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Fuzzy Time Series and Geometric Brownian Motion in Forecasting Stock Prices in Bursa Malaysia

Jurnal Intelek ◽

10.24191/ji.v14i2.241 ◽

2019 ◽

Vol 14 (2) ◽

pp. 240-250

Author(s):

Nor Hayati Shafii ◽

Nur Ezzati Dayana Mohd Ramli ◽

Rohana Alias ◽

Nur Fatihah Fauzi

Keyword(s):

Time Series ◽

Brownian Motion ◽

Stock Market ◽

Stock Prices ◽

Stock Exchange ◽

Investment Decisions ◽

Geometric Brownian Motion ◽

Fuzzy Time Series ◽

Good Information ◽

The Mean

Every country has its own stock market exchange, which is a platform to raise capital and is a place where shares of listed company are traded. Bursa Malaysia is a stock exchange of Malaysia and it is previously known as Kuala Lumpur Stock Exchange. All over the world, including Malaysia, it is common for investors or traders to face some loss due to wrong investment decisions. According to the conventional financial theory, there are so many reasons that can lead to bad investment decisions. One of them is confirmation bias where an investor has a preconceived notion about an investment without a good information and knowledge. In this paper, we study the best way to provide good information for investors in helping them make the right decisions and not to fall prey to this behavioral miscue. Two models for forecasting stock prices data are employed, namely, Fuzzy Time Series (FTS) and Geometric Brownian Motion (GBM). This study used a secondary data consisting of AirAsia Berhad daily stock prices for a duration of 20 weeks from January 2015 to May 2015. The 16-weeks data from January to April 2015 was used to forecast the stock prices for the 4-weeks of May 2015. The results showed that FTS has the lowest values of the Mean Absolute Percentage Error (MAPE) and the Mean Square Error (MSE), which are 1.11% and MYR20.0011, respectively. For comparison, for GBM, the MAPE is 1.53% and the MSE is MYR2 0.0017. The findings imply that the FTS model provides a more accurate forecast of stock prices. Keywords: Forecasted values, stock market, Fuzzy Time Series, Geometric Brownian Motion

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Analysing the Nepali Stock Market with Stochastic Models

Nepalese Journal of Management Science and Research ◽

10.53056/njmsr-2016.001.1 ◽

2016 ◽

Vol 1 (1) ◽

Author(s):

Karan Singh Thagunna ◽

Radal M Lochowski

Keyword(s):

Brownian Motion ◽

Stock Market ◽

Diffusion Model ◽

Stock Prices ◽

Jump Diffusion ◽

Efficient Market Hypothesis ◽

Geometric Brownian Motion ◽

Brownian Motion Model ◽

Jump Diffusion Model ◽

Daily Returns

In this article we analyse the behaviour of the Nepali stock market and movements of stock prices of selected companies using (i) Efficient Market Hypothesis (EMH) (ii) geometric Brownian motion model (gBm) and (iii) Merton’s jump-diffusion model. Using the daily returns of the NEPSE index and the daily returns of stock prices of selected companies we estimate the geometric Brownian motion model and Merton’s jump-diffusion model. Further, we compare both models to identify the best fit for the Nepali stock market data. Keywords: Black-Scholes model, Efficient Market Hypothesis, geometric Brownian motion, Merton’s jump-diffusion Model, Variance Ratio Test

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Use of geometric Brownian motion to forecast stock market scenario using post covid-19 NEPSE index

BIBECHANA ◽

10.3126/bibechana.v18i2.31180 ◽

2021 ◽

Vol 18 (2) ◽

pp. 50-60

Author(s):

Prabin Thapa ◽

Binil Aryal

Keyword(s):

Stochastic Process ◽

Brownian Motion ◽

Stock Market ◽

Geometric Brownian Motion ◽

Forecasting Accuracy ◽

Python Programming ◽

Random Nature

Stock market is one of the fields where the randomness is prominent factor to be considered. Although many stochastic process deals which the randomness found in nature through the interdisciplinary subject like Econophysics, many of them exhibits cumbersome trends. So, Geometric Brownian motion (GBM) is used to analyze the market scenario of Nepal on the basis of the parameter; NEPSE Index along with the prediction of indices through python programming platform. Python simulation was carried out to check the consistency by implying it to the stable market timeline 2003/2004. And after the verification of the model proposed in the stable market year, the model (GBM) is employed to the unstable timeline; pandemic situation by COVID-19 in 2020. Mapping of Nepal stock market through GBM was found to be consistent with the standard forecasting accuracy making GBM one of the flexible and consistent to predict stock market scenario of Nepal accounting the random nature. BIBECHANA 18 (2) (2021) 50-60

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Geometric brownian motion: an alternative to high-frequency trading for small investors

Independent Journal of Management & Production ◽

10.14807/ijmp.v11i3.1114 ◽

2020 ◽

Vol 11 (3) ◽

pp. 1434

Author(s):

Eder Oliveira Abensur ◽

Davi Franco Moreira ◽

Aline Cristina Rodrigues De Faria

Keyword(s):

Brownian Motion ◽

Stock Market ◽

Financial Management ◽

High Frequency ◽

Prediction Models ◽

Risk Measure ◽

High Volume ◽

Geometric Brownian Motion ◽

High Frequency Trading ◽

Small Investors

High-frequency trading (HFT) involves short-term, high-volume market operations to capture profits. To a large extent, these operations take advantage of early access to information using fast and sophisticated technological tools running on supercomputers. However, high-frequency trading is inaccessible to small investors because of its high cost. For this reason, price prediction models can substitute high-frequency trading in order to anticipate stock market movements. This study is the first to analyze the possibility of applying Geometric Brownian Motion (GBM) to forecast prices in intraday trading of stocks negotiated on two different stock markets: (i) the Brazilian stock market (B3), considered as a low liquidity market and (ii) the American stock market (NYSE), a high liquidity market. This work proposed an accessible framework that can be used for small investors. The portfolios formed by Geometric Brownian Motion were tested using a traditional risk measure (mean-variance). The hypothesis tests showed evidences of promising results for financial management.

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