Distributions of Historic Market Data -- Relaxation and Correlations

Autor:	Moghaddam, M. Dashti, Liu, Zhiyuan, Serota, R. A.
Rok vydání:	2019
Předmět:	Quantitative Finance - Statistical Finance Quantitative Finance - Mathematical Finance
Zdroj:	Eur. Phys. J. B 94, 83 (2021)
Druh dokumentu:	Working Paper
DOI:	10.1140/epjb/s10051-021-00089-9
Popis:	We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. We derive closed-form expressions for the correlation functions and leverage for a general form of the stochastic term. We also discuss correlation functions and leverage for three specific models -- multiplicative, Heston (Cox-Ingersoll-Ross) and combined multiplicative-Heston -- whose steady-state probability density functions are Gamma, Inverse Gamma and Beta Prime respectively, the latter two exhibiting "fat" tails. For the Heston model, we apply the eigenvalue analysis of the Fokker-Planck equation to derive the correlation function -- in agreement with the general analysis -- and to identify a series of time scales, which are observable in relaxation of cumulants on approach to the steady state. We test our findings on a very large set of historic financial markets data. Comment: 17 pages, 8 figures, 3 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1907.05348 Zobrazit plný text záznamu Plný text ve formátu PDF