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Generalised Geometric Brownian Motion: Theory and Applications to Option Pricing [PDF]
Entropy, 2020 Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics, due to ...
Viktor Stojkoski +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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Entropy corrected geometric Brownian motion [PDF]
Scientific ReportsThe geometric Brownian motion (GBM) is widely used for modeling stochastic processes, particularly in finance. However, its solutions are constrained by the assumption that the underlying distribution of returns follows a log-normal distribution.
Rishabh Gupta +3 more
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Geometric Brownian Motion (GBM) of Stock Indexes and Financial Market Uncertainty in the Context of Non-Crisis and Financial Crisis Scenarios [PDF]
Mathematics, 2022 The present article proposes a methodology for modeling the evolution of stock market indexes for 2020 using geometric Brownian motion (GBM), but in which drift and diffusion are determined considering two states of economic conjunctures (states of the ...
Vasile Brătian +3 more
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E-Jurnal Matematika, 2015 The aim of this research was to measure the risk of the IHSG stock data using the Value at Risk (VaR). IHSG stock index data typically indicates a jump. However, Geometric Brownian Motion (GBM) model can not catch any of the jumps.
I GEDE ARYA DUTA PRATAMA +2 more
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Physical Review ResearchThe translational motion of anisotropic or self-propelled colloidal particles is closely linked with the particle’s orientation and its rotational Brownian motion.
Felix Höfling, Arthur V. Straube
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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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JTAM (Jurnal Teori dan Aplikasi Matematika)Exchange rate fluctuations are critical in ensuring economic stability and shaping foreign investment, while foreign currencies serve as asset and wealth diversification instruments.
Siti Masitah +2 more
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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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An Empirical Analysis of Price Jump and Asymmetric Information in Tehran Stock Exchange [PDF]
راهبرد مدیریت مالی, 2016 Deep understanding aboutthe impact of news and information on stock market is vital for analyzing and forecasting stock return. For this purpose, stochastic differential equations, such as geometric Brownian motion, geometric Brownian motion with jump ...
Saber Molaei +2 more
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