Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion [PDF]
Mathematics, 2021 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 ...
Vasile Brătian +4 more
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Geometric fractional Brownian motion model for commodity market simulation
Alexandria Engineering Journal, 2021 The geometric Brownian motion (GBM) model is a mathematical model that has been used to model asset price paths. By incorporating Hurst parameter to GBM to characterize long-memory phenomenon, the geometric fractional Brownian motion (GFBM) model was ...
Siti Nur Iqmal Ibrahim +2 more
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Applying the IR statistic to estimate the Hurst index of the fractional geometric Brownian motion
Lietuvos Matematikos Rinkinys, 2010 In 2010 J.M. Bardet and D. Surgailis [1] have introduced the increment ratio (IR) statistic which measures the roughness of random paths. It was shown that this statistic was applicable in the cases of diffusion processes driven by the standard Brownian ...
Dimitrij Melichov
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AIMS MathematicsConsidering the characteristics of long-range correlations in financial markets, the issue of valuing geometric average Asian options is examined, assuming that the variations of the underlying asset follow the mixed sub-fractional Brownian motion, and ...
Xinyi Wang, Chunyu Wang
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Geometrical optics of large deviations of fractional Brownian motion [PDF]
Physical Review E, 2022 9 pages, 7 ...
Meerson, Baruch, Oshanin, Gleb
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The evaluation of geometric Asian power options under time changed mixed fractional Brownian motion [PDF]
Journal of Computational and Applied Mathematics, 2018 The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion.
Foad Shokrollahi
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Evaluation of Geometric Asian Power Options under Fractional Brownian Motion
Journal of Mathematical Finance, 2014 Modern option pricing techniques are often considered among the most mathematical complex of all applied areas of financial mathematics. In particular, the fractional Brownian motion is proper to model the stock dynamics for its long-range dependence.
Zhijuan Mao, Zhian Liang
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Geometric Rough Paths above Mixed Fractional Brownian Motion [PDF]
This paper establishes a comprehensive theory of geometric rough paths for mixed fractional Brownian motion (MFBM) and its generalized multi-component extensions. We prove that for a generalized MFBM of the form $M_t^H(a) = \sum_{k=1}^N a_k B_t^{H_k}$ with $\min\{H_k\} > \frac{1}{4}$, there exists a canonical geometric rough path obtained as the ...
Lechiheb, Atef
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Simulating Rubber Prices under Geometric Fractional Brownian Motion with Different Hurst Estimators
Malaysian Journal of Fundamental and Applied Sciences, 2023 Natural rubber was a vital pillar of Malaysia's export-oriented economy throughout much of the twentieth century, according to the Economic History of Malaya (EHM) website, the worldwide demand for natural rubber is expected to expand at a CAGR of 4.8% in the future (2019–2023).
Balasubramaniam, Srivennila Sri +1 more
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Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach [PDF]
, 2017 The long-term dependence of Bitcoin (BTC), manifesting itself through a Hurst exponent $H>0.5$, is exploited in order to predict future BTC/USD price. A Monte Carlo simulation with $10^4$ geometric fractional Brownian motion realisations is performed as extensions of historical data. The accuracy of statistical inferences is 10\%.
Mariusz Tarnopolski
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