Introducing a new approach for modeling stock market prices using the combination of jump-drift processes

IF 1.9 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Ali Asghar Movahed, Houshyar Noshad
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引用次数: 0

Abstract

The stock price data are sampled at discrete times (e.g., hourly, daily, weekly, etc). When data are sampled at discrete times, they appear as a sequence of discontinuous jump events, even if they have been sampled from a continuous process. On the other hand, distinguishing between discontinuities due to finite sampling of the continuous stochastic process and real jump discontinuities in the sample path is often a challenging task. Such considerations, led us to the question: Can discrete data (e.g., stock price) be modeled using only jump-drift processes, regardless of whether the sampled time series originally belongs to the class of continuous processes or discontinuous processes? To answer this question, we built a stochastic dynamical equation in the general form dyt=μ¯dt+i=1NξidJit, which includes a deterministic drift term (μ¯dt) and a combination of stochastic terms with jumpy behaviors (ξidJit), and used it to model the log-price time series yt. In this article, we first introduce this equation in its simplest form, including a drift term and a stochastic term, and show that such a jump-drift equation is capable of reconstructing stock prices in Black-Scholes diffusion markets. Afterwards, we extend the equation by considering two jump processes, and show that such a drift-jump-jump equation enables us to reconstruct stock prices in jump-diffusion markets more accurately than the old jump-diffusion model. To demonstrate the practical applications of the proposed method, we analyze real-world data, including the daily stock price of two different shares and gold price data with two different time horizons (hourly and weekly). Our analysis supports the practical applicability of the methodology. It should be noted that the presented approach is expandable and can be used even in non-financial research fields.
利用跳跃-漂移过程组合引入股市价格建模新方法
股价数据的采样时间是离散的(如每小时、每天、每周等)。当数据按离散时间采样时,即使它们是从连续过程中采样的,也会表现为一连串不连续的跳跃事件。另一方面,区分连续随机过程的有限采样导致的不连续性和采样路径中真正的跳跃不连续性往往是一项具有挑战性的任务。基于这些考虑,我们提出了一个问题:离散数据(如股票价格)能否只用跳跃漂移过程来建模,而不管采样的时间序列原本属于连续过程还是不连续过程?为了回答这个问题,我们建立了一个一般形式的随机动力学方程 dyt=μ¯dt+∑i=1NξidJit,其中包括一个确定性漂移项(μ¯dt)和一个具有跳跃行为的随机项组合(ξidJit),并用它来模拟对数价格时间序列 yt。在本文中,我们首先介绍该方程的最简单形式,包括一个漂移项和一个随机项,并证明这种跳跃-漂移方程能够重构布莱克-斯科尔斯扩散市场中的股票价格。之后,我们通过考虑两个跳跃过程来扩展该方程,并证明这种漂移-跳跃-跳跃方程能让我们比旧的跳跃-扩散模型更准确地重建跳跃-扩散市场中的股票价格。为了证明所提方法的实际应用,我们分析了现实世界的数据,包括两种不同股票的每日股价和两种不同时间跨度(每小时和每周)的黄金价格数据。我们的分析支持该方法的实际应用性。值得注意的是,所提出的方法是可扩展的,甚至可用于非金融研究领域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Frontiers in Physics
Frontiers in Physics Mathematics-Mathematical Physics
CiteScore
4.50
自引率
6.50%
发文量
1215
审稿时长
12 weeks
期刊介绍: Frontiers in Physics publishes rigorously peer-reviewed research across the entire field, from experimental, to computational and theoretical physics. This multidisciplinary open-access journal is at the forefront of disseminating and communicating scientific knowledge and impactful discoveries to researchers, academics, engineers and the public worldwide.
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