Distributions of Historic Market Data -- Relaxation and Correlations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866929309602545664 |
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| author | Moghaddam, M. Dashti Liu, Zhiyuan Serota, R. A. |
| author_facet | Moghaddam, M. Dashti Liu, Zhiyuan Serota, R. A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_05348 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Distributions of Historic Market Data -- Relaxation and Correlations Moghaddam, M. Dashti Liu, Zhiyuan Serota, R. A. Statistical Finance Mathematical Finance 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. |
| title | Distributions of Historic Market Data -- Relaxation and Correlations |
| topic | Statistical Finance Mathematical Finance |
| url | https://arxiv.org/abs/1907.05348 |