Modeling Stock Price of Transnational companies using Brownian motion

IF 2.2 3区 工程技术 Q1 SOCIAL SCIENCES, INTERDISCIPLINARY Jasss-The Journal of Artificial Societies and Social Simulation Pub Date : 2022-01-01 DOI:10.18254/s207751800019525-6
Ivan Kucherov
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Abstract

This article is concerned with creating a model for stock price using the Brownian motion. At first, we consider the notion of a discrete time stochastic process, simple random walk, and then move on to its continuous analogue, the Brownian motion. Next we identify the problem with using regular Calculus for stochastic differential equations and derive Ito’s Lemma. After that we derive a model for stock prices and use lognormal distribution to determine its expected value and variance. Finally, we use sample volatility to make predictions for Apple and Gazprom stock prices.
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跨国公司股票价格的布朗运动模型
本文讨论的是利用布朗运动建立股票价格模型。首先,我们考虑离散时间随机过程的概念,简单随机游走,然后转向它的连续类比,布朗运动。接下来,我们用正则微积分来识别随机微分方程的问题,并推导出伊藤引理。在此基础上,推导出股票价格的模型,并利用对数正态分布确定其期望值和方差。最后,我们利用样本波动率对苹果公司和俄罗斯天然气工业股份公司的股价进行预测。
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来源期刊
CiteScore
7.40
自引率
9.50%
发文量
16
审稿时长
21 weeks
期刊介绍: The Journal of Artificial Societies and Social Simulation is an interdisciplinary journal for the exploration and understanding of social processes by means of computer simulation. Since its first issue in 1998, it has been a world-wide leading reference for readers interested in social simulation and the application of computer simulation in the social sciences. Original research papers and critical reviews on all aspects of social simulation and agent societies that fall within the journal"s objective to further the exploration and understanding of social processes by means of computer simulation are welcome.
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