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 ...
Baruch Meerson, Gleb Oshanin
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A Geometric Drift Inequality for a Reflected Fractional Brownian Motion Process on the Positive Orthant [PDF]
Journal of Applied Probability, 2011 We study a d-dimensional reflected fractional Brownian motion (RFBM) process on the positive orthant S = ℝ+d, with drift r0 ∈ ℝd and Hurst parameter H ∈ (½, 1). Under a natural stability condition on the drift vector r0 and reflection directions, we establish a geometric drift towards a compact set for the 1-skeleton chain Ž̆ of the RFBM process Z ...
Chihoon Lee
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Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus [PDF]
Bernoulli, 2010 We approximate the solution of some linear systems of SDEs driven by a fractional Brownian motion $B^H$ with Hurst parameter $H\in(\frac{1}{2},1)$ in the Wick--It sense, including a geometric fractional Brownian motion. To this end, we apply a Donsker-type approximation of the fractional Brownian motion by disturbed binary random walks due to ...
Christian Bender, Peter Parczewski
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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).
Srivennila Sri Balasubramaniam +1 more
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The fractional Brownian motion property of the turbulent refractive within Geometric Optics
, 2003 28 pages, no ...
Darı́o G. Pérez
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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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