dorsal/arxiv
View SchemaAre volatility correlations in financial markets related to Omori processes occurring on all scales?
| Authors | Philipp Weber, Fengzhong Wang, Irena Vodenska-Chitkushev, Shlomo Havlin, H. Eugene Stanley |
|---|---|
| Categories | |
| ArXiv ID | physics/0611093 |
| URL | https://arxiv.org/abs/physics/0611093 |
| DOI | 10.1103/PhysRevE.76.016109 |
Abstract
We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period is characterized by the Omori law, which describes the decay in the rate of aftershocks of a given size with time t by a power law with exponent close to 1. A shock followed by such a power law decay in the rate is here called Omori process. Studying several aftercrash time series, we show that the Omori law holds not only after significant market crashes, but also after ``intermediate shocks''. Moreover, we find self-similar features in the volatility. Specifically, within the aftercrash period there are smaller shocks that themselves constitute Omori processes on smaller scales, similar to the Omori process after the large crash. We call these smaller shocks subcrashes, which are followed by their own aftershocks. We also find similar Omori processes after intermediate crashes in time regimes without a large market crash. By appropriate detrending we remove the influence of the crashes and subcrashes from the data, and find that this procedure significantly reduces the memory in the records. Our results are consistent with the hypothesis that the memory in volatility is related to Omori processes present on different time scales.
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"abstract": "We analyze the memory in volatility by studying volatility return intervals,\ndefined as the time between two consecutive fluctuations larger than a given\nthreshold, in time periods following stock market crashes. Such an aftercrash\nperiod is characterized by the Omori law, which describes the decay in the rate\nof aftershocks of a given size with time t by a power law with exponent close\nto 1. A shock followed by such a power law decay in the rate is here called\nOmori process. Studying several aftercrash time series, we show that the Omori\nlaw holds not only after significant market crashes, but also after\n``intermediate shocks\u0027\u0027. Moreover, we find self-similar features in the\nvolatility. Specifically, within the aftercrash period there are smaller shocks\nthat themselves constitute Omori processes on smaller scales, similar to the\nOmori process after the large crash. We call these smaller shocks subcrashes,\nwhich are followed by their own aftershocks. We also find similar Omori\nprocesses after intermediate crashes in time regimes without a large market\ncrash. By appropriate detrending we remove the influence of the crashes and\nsubcrashes from the data, and find that this procedure significantly reduces\nthe memory in the records. Our results are consistent with the hypothesis that\nthe memory in volatility is related to Omori processes present on different\ntime scales.",
"arxiv_id": "physics/0611093",
"authors": [
"Philipp Weber",
"Fengzhong Wang",
"Irena Vodenska-Chitkushev",
"Shlomo Havlin",
"H. Eugene Stanley"
],
"categories": [
"physics.soc-ph",
"q-fin.ST"
],
"doi": "10.1103/PhysRevE.76.016109",
"title": "Are volatility correlations in financial markets related to Omori processes occurring on all scales?",
"url": "https://arxiv.org/abs/physics/0611093"
},
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