Optimal models of extreme volume-prices are time-dependent

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Rocha, Paulo^1 ; Raischel, Frank^2 ; Boto, João Pedro^1 ; Lind, Pedro G.^3

Centro de Matemática e Aplicações Fundamentals, Avenida Professor Gama Pinto 2, Lisboa

1649-003, Portugal^1

Instituto Dom Luiz, CGUL, University of Lisbon, Lisbon

1749-016, Portugal^2

For Wind and Institute of Physics, University of Oldenburg, Oldenburg

DE-26111, Germany^3

关键词: Best model;    Kullback-Leibler distance;    Large volumes;    Log-normal;    New York;    Optimal model;    Relative deviations;    Time dependent;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012148/pdf
DOI  :  10.1088/1742-6596/574/1/012148

来源: IOP

【 摘 要 】

We present evidence that the best model for empirical volume-price distributions is not always the same and it strongly depends in (i) the region of the volume-price spectrum that one wants to model and (ii) the period in time that is being modelled. To show these two features we analyze stocks of the New York stock market with four different models: Γ, Γ-inverse, log-normal, and Weibull distributions. To evaluate the accuracy of each model we use standard relative deviations as well as the Kullback-Leibler distance and introduce an additional distance particularly suited to evaluate how accurate are the models for the distribution tails (large volume-price). Finally we put our findings in perspective and discuss how they can be extended to other situations in finance engineering.