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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
doaj +4 more sources
Geometrical Brownian Motion Driven by Color Noise [PDF]
arXiv, 2007 The evolution of prices on ideal market is given by geometrical Brownian motion, where Gaussian white noise describes fluctuations. We study the effect of correlations introduced by a color noise.
Ryszard Zygadło
arxiv +6 more sources
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
doaj +2 more sources
An optimal polynomial approximation of Brownian motion [PDF]
SIAM Journal on Numerical Analysis, vol. 58, no. 3, pp. 1393-1421,
2020, 2020 In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the expansion of Brownian motion in this polynomial basis are independent ...
Foster, James +2 more
core +4 more sources
Large deviations for rough paths of the fractional Brownian motion [PDF]
, 2004 Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$ given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric rough paths ...
Millet, Annie, Sanz-Solé, Marta
core +6 more sources
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
doaj +2 more sources
Multi-purpose binomial model: Fitting all moments to the underlying geometric Brownian motion [PDF]
arXiv, 2016 We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model is used to resolve a discontinuity problem in option pricing.
Young Shin Kim +3 more
openalex +2 more sources
Integral representations of some functionals of fractional Brownian motion [PDF]
arXiv, 2011 We prove change of variables formulas [It\^o formulas] for functions of both arithmetic and geometric averages of geometric fractional Brownian motion. They are valid for all convex functions, not only for smooth ones.
Tikanmäki, Heikki
core +4 more sources
Asymptotics for the discrete-time average of the geometric Brownian motion and Asian options [PDF]
Advances in Applied Probability, Volume 49, Issue 2, 446-480
(2017), 2017 The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps.
Dan Pirjol, Lingjiong Zhu
arxiv +4 more sources
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
doaj +3 more sources