摘要翻译:
本文研究了金融工具价格变化的重尾概率密度分布的微观成因。我们将标准的对数正态过程扩展到在所谓的随机波动率模型中包含另一个随机分量。我们在一个类似于Born-Oppenheimer近似的假设下研究这些模型,在这个假设中,波动率已经放松到其均衡分布,并作为价格过程演化的背景。在这个近似下,我们证明了所有的随机波动模型在零漂移修正对数收益的时滞上都应该表现出一个标度关系。我们验证了道琼斯工业平均指数确实遵循了这一比例。然后我们重点讨论了两个流行的随机波动率模型,Heston模型和Hull-White模型。特别地,我们证明了在Hull-White模型中,在这种近似下得到的对数收益的概率分布对应于Tsallis(T-Studenter)分布。Tsallis参数是根据微观随机波动模型给出的。最后,我们证明了道琼斯指数30年数据的对数收益符合Tsallis分布,得到了相关参数。
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英文标题:
《Microscopic Origin of Non-Gaussian Distributions of Financial Returns》
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作者:
T. S. Biro and R. Rosenfeld
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最新提交年份:
2007
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分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Statistical Finance 统计金融
分类描述:Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类:Physics 物理学
二级分类:Other Condensed Matter 其他凝聚态物质
分类描述:Work in condensed matter that does not fit into the other cond-mat classifications
在不适合其他cond-mat分类的凝聚态物质中工作
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一级分类:Physics 物理学
二级分类:Physics and Society 物理学与社会
分类描述:Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体(人类或其他)的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统(如能源网、运输网络)的物理和工程。
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英文摘要:
In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters.
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PDF链接:
https://arxiv.org/pdf/0705.4112