Geometric fractional Brownian motion model for commodity market simulation

Ibrahim, Siti Nur Iqmal; Misiran, Masnita; Laham, Mohamed Faris

doi:10.1016/j.aej.2020.10.023

Cited by 15 publications

(8 citation statements)

References 28 publications

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“…To summarize, our findings after evaluating the S&P500 and Stoxx Europe 600 stock indexes confirm the conclusions presented in the current literature, which point in general favor of the fractional Brownian motion of stock markets. In one case [50], for example, the authors analyze the accuracy of the GBM and GFBM in modeling Malaysia's crude palm oil price simulation, as well as the presentation of persistent or anti-persistent behavior over time. The results demonstrated that the GFBM model outperformed the GBM model in simulating the future price path for the provided dataset.…”

Section: Discussionmentioning

confidence: 99%

“…Since then, authors have used the GBM to simulate stock price pathways and examine whether the simulated stock prices match the actual market returns [48,49]. While the majority of these studies focus on stock prices, others have discovered that commodity prices, such as crude palm oil [50], petroleum products and natural gas [51], gold [52], and other commodities, exhibit randomness that can be explained mathematically using the GBM model.…”

Section: Introductionmentioning

confidence: 99%

“…Geometric fractional Brownian motion has been studied extensively, with many studies identifying potential applications in the context of neuronal models [58]. It was validated by a rigorous statistical test with added white Gaussian noise based on the autocovariance function [59] and has been applied in studies both for stock indexes [60] and for the price of financial securities [61], in the case of cryptocurrencies [62], in the case of modeling epidemic diseases, such as coronavirus [63], and for the price of goods [50]. Furthermore, the GFBM has been utilized in a great deal of literature research to evaluate derivative titles (options) [64][65][66][67].…”

Section: Introductionmentioning

confidence: 99%

“…Ibrahim, Misiran, and Laham [50] conducted similar analyses but on commodity price modeling. Moreover, in a recent study of 26 international stock market indexes, Dittrich and Srbek [72] concluded that Brownian motion cannot be perceived as a norm for describing stock market behavior, challenging the assumption of a random walk of stock prices.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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“…Based on the obtained MAPE value, the GBM model produced very accurate prediction results, resulting from the return value, which was usually distributed (Ibrahim et al 2021). Several previous studies applied the GBM.…”

Section: Variable Mean (µ) Volatility (σ)mentioning

confidence: 99%

Price Index Modeling and Risk Prediction of Sharia Stocks in Indonesia

et al. 2022

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This study aimed to predict the JKII (Jakarta Islamic Index) price as a price index of sharia stocks and predict the loss risk. This study uses geometric Brownian motion (GBM) and Value at Risk (VaR; with the Monte Carlo Simulation approach) on the daily closing price of JKII from 1 August 2020–13 August 2021 to predict the price and loss risk of JKII at 16 August 2021–23 August 2021. The findings of this study were very accurate for predicting the JKII price with a MAPE value of 2.03%. Then, using VaR with a Monte Carlo Simulation approach, the loss risk prediction for 16 August 2021 (one-day trading period after 13 August 2021) at the 90%, 95%, and 99% confidence levels was 2.40%, 3.07%, and 4.27%, respectively. Most Indonesian Muslims have financial assets in the form of Islamic investments as they offer higher returns within a relatively short time. The movement of all Islamic stock prices traded on the Indonesian stock market can be seen through the Islamic stock price index, namely the JKII (Jakarta Islamic Index). Therefore, the focus of this study was predicting the price and loss risk of JKII as an index of Islamic stock prices in Indonesia. This study extends the previous literature to determine the prediction of JKII price and the loss risk through GBM and VaR using a Monte Carlo simulation approach.

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Towards a Better Understanding of Fractional Brownian Motion and Its Application to Finance

Zhuang

Song

2023

Bull. Malays. Math. Sci. Soc.

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The aim of this work is to first build the underlying theory behind fractional Brownian motion and applying fractional Brownian motion to financial market. By incorporating the Hurst parameter into geometric Brownian motion in order to characterize the long memory among disjoint increments, geometric fractional Brownian motion model is constructed to model S &P 500 stock price index. The empirical results show that the fitting effect of fractional Brownian motion model is better than ordinary Brownian motion.

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Geometric fractional Brownian motion model for commodity market simulation

Cited by 15 publications

References 28 publications

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

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

Price Index Modeling and Risk Prediction of Sharia Stocks in Indonesia

Towards a Better Understanding of Fractional Brownian Motion and Its Application to Finance

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