Geometrical Brownian Motion Driven by Color Noise
Ryszard Zygad{\l}o
TL;DR
This paper investigates how introducing color noise, which has correlations, affects the evolution of prices modeled by geometrical Brownian motion, traditionally driven by uncorrelated Gaussian white noise.
Contribution
It explores the impact of correlated color noise on geometric Brownian motion, extending the classical model to include realistic noise correlations.
Findings
Color noise introduces correlations that alter price dynamics.
Correlated noise affects the statistical properties of the model.
The study provides insights into more realistic market fluctuation modeling.
Abstract
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.
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Taxonomy
TopicsComplex Systems and Time Series Analysis · Stochastic processes and financial applications · Financial Risk and Volatility Modeling