Maximum entropy distribution of stock price fluctuations
Maximum entropy distribution of stock price fluctuations
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DOI：
10.1016/j.physa.2012.11.048
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发表时间：
2013-04-01
影响因子：
3.3
通讯作者：
Bartiromo, Rosario
中科院分区：
文献类型：
--
作者：
Bartiromo, Rosario
本文提出在其熵解释中利用无套利机会原理，通过最大化其信息熵来获得股票价格波动的分布。我们表明，这种方法导致了对潜在动力学的物理描述，即随机漫步，其特征是随机扩散系数，并约束于给定的预期波动率值，以这种方式考虑到期权市场存在所提供的信息。通过与观测到的价格收益和扩散系数的分布进行综合比较，验证了模型的正确性。期望波动率是模型中唯一的参数，可以通过分析期权价格来获得。本文给出了价格收益的概率密度函数的解析表达式，该函数可用于从股票期权数据中提取期望波动率。(C) 2012 Elsevier B.V.版权所有
In this paper we propose to use the principle of absence of arbitrage opportunities in its entropic interpretation to obtain the distribution of stock price fluctuations by maximizing its information entropy. We show that this approach leads to a physical description of the underlying dynamics as a random walk characterized by a stochastic diffusion coefficient and constrained to a given value of the expected volatility, in this way taking into account the information provided by the existence of an option market. The model is validated by a comprehensive comparison with observed distributions of both price return and diffusion coefficient. Expected volatility is the only parameter in the model and can be obtained by analysing option prices. We give an analytic formulation of the probability density function for price returns which can be used to extract expected volatility from stock option data. (C) 2012 Elsevier B.V. All rights reserved.