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Heavy-tailed modeling of CROBEX

机译：CROBEX的重尾模型

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Classical continuous-time models for log-returns usually assume their independence and normality of distribution. However, nowadays it is widely accepted that the empirical properties of log-returns often show a specific correlation structure and deviation from normality, in most cases suggesting that their distribution is heavy-tailed. Therefore we suggest an alternative continuous-time model for logreturns, a diffusion process with Student's marginal distributions and exponentially decaying autocorrelation structure. This model depends on several unknown parameters that need to be estimated. The tail index is estimated by the method based on the empirical scaling function, while the parameters describing mean, variance and correlation structure are estimated by the method of moments. The model is applied to the CROBEX stock market index, meaning that the estimation of parameters is based on the CROBEX log-returns. The quality of the model is assessed by means of simulations, by comparing CROBEX log-returns with the simulated trajectories of Student's diffusion depending on estimated parameter values.
机译：经典的对数收益连续时间模型通常假定其独立性和分布正态性。然而，如今，人们普遍接受的是，对数收益率的经验特性通常显示出特定的相关结构和与正态性的偏差，在大多数情况下，这表明它们的分布是重尾的。因此，我们提出了对数返回的替代连续时间模型，具有学生边际分布和指数衰减自相关结构的扩散过程。该模型取决于需要估计的几个未知参数。尾部索引是通过基于经验比例函数的方法估算的，而描述均值，方差和相关结构的参数是通过矩的方法估算的。该模型应用于CROBEX股票市场指数，这意味着参数的估计基于CROBEX对数收益。通过将CROBEX对数收益与模拟的学生扩散轨迹（取决于估计的参数值）进行比较，通过模拟来评估模型的质量。

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