S Lima Leonardo
Departamento de Física, Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG 30510-000, Brazil.
Entropy (Basel). 2019 May 25;21(5):530. doi: 10.3390/e21050530.
The stochastic nonlinear model based on Itô diffusion is proposed as a mathematical model for price dynamics of financial markets. We study this model with relation to concrete stylised facts about financial markets. We investigate the behavior of the long tail distribution of the volatilities and verify the inverse power law behavior which is obeyed for some financial markets. Furthermore, we obtain the behavior of the long range memory and obtain that it follows to a distinct behavior of other stochastic models that are used as models for the finances. Furthermore, we have made an analysis by using Fokker-Planck equation independent on time with the aim of obtaining the cumulative probability distribution of volatilities P ( g ) , however, the probability density found does not exhibit the cubic inverse law.
提出了基于伊藤扩散的随机非线性模型作为金融市场价格动态的数学模型。我们结合金融市场的具体典型事实来研究这个模型。我们研究波动率长尾分布的行为，并验证某些金融市场所遵循的反幂律行为。此外，我们得到了长程记忆的行为，并发现它与用作金融模型的其他随机模型的行为不同。此外，我们使用与时间无关的福克 - 普朗克方程进行了分析，目的是获得波动率的累积概率分布P(g)，然而，所发现的概率密度并未表现出立方反比定律。
