An Algorithmic Look at Financial Volatility
In this paper, we attempt to give an algorithmic explanation to volatility clustering, one of the most exploited stylized facts in finance. Our analysis with daily data from five exchanges shows that financial volatilities follow Levin’s universal distribution Kirchherr et al. (1997) once transforme...
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| Published in | Algorithms Vol. 11; no. 11; p. 185 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
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01.11.2018
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| ISSN | 1999-4893 1999-4893 |
| DOI | 10.3390/a11110185 |
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| Abstract | In this paper, we attempt to give an algorithmic explanation to volatility clustering, one of the most exploited stylized facts in finance. Our analysis with daily data from five exchanges shows that financial volatilities follow Levin’s universal distribution Kirchherr et al. (1997) once transformed into equally proportional binary strings. Frequency ranking of binary trading weeks coincides with that of their Kolmogorov complexity estimated by Delahaye et al. (2012). According to Levin’s universal distribution, large (resp. small) volatilities are more likely to be followed by large (resp. small) ones since simple trading weeks such as “00000” or “11111” are much more frequently observed than complex ones such as “10100” or “01011”. Thus, volatility clusters may not be attributed to behavioral or micro-structural assumptions but to the complexity discrepancy between finite strings. This property of financial data could be at the origin of volatility autocorrelation, though autocorrelated volatilities simulated from Generalized Auto-Regressive Conditional Heteroskedacity (hereafter GARCH) cannot be transformed into universally distributed binary weeks. |
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| AbstractList | In this paper, we attempt to give an algorithmic explanation to volatility clustering, one of the most exploited stylized facts in finance. Our analysis with daily data from five exchanges shows that financial volatilities follow Levin's universal distribution Kirchherr et al. (1997) once transformed into equally proportional binary strings. Frequency ranking of binary trading weeks coincides with that of their Kolmogorov complexity estimated by Delahaye et al. (2012). According to Levin's universal distribution, large (resp. small) volatilities are more likely to be followed by large (resp. small) ones since simple trading weeks such as "00000,, or "11111,, are much more frequently observed than complex ones such as "10100,, or "01011,,. Thus, volatility clusters may not be attributed to behavioral or micro-structural assumptions but to the complexity discrepancy between finite strings. This property of financial data could be at the origin of volatility autocorrelation, though autocorrelated volatilities simulated from Generalized Auto-Regressive Conditional Heteroskedacity (hereafter GARCH) cannot be transformed into universally distributed binary weeks. In this paper, we attempt to give an algorithmic explanation to volatility clustering, one of the most exploited stylized facts in finance. Our analysis with daily data from five exchanges shows that financial volatilities follow Levin’s universal distribution Kirchherr et al. (1997) once transformed into equally proportional binary strings. Frequency ranking of binary trading weeks coincides with that of their Kolmogorov complexity estimated byDelahaye et al. (2012). According to Levin’s universal distribution, large (resp. small) volatilities are more likely to be followed by large (resp. small) ones since simple trading weeks such as “00000” or “11111” are much more frequently observed than complex ones such as “10100” or “01011”. Thus, volatility clusters may not be attributed to behavioral or micro-structural assumptions but to the complexity discrepancy between finite strings. This property of financial data could be at the origin of volatility autocorrelation, though autocorrelated volatilities simulated from Generalized Auto-Regressive Conditional Heteroskedacity (hereafter GARCH) cannot be transformed into universally distributed binary weeks. |
| Author | Ma, Lin Delahaye, Jean-Paul |
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| Cites_doi | 10.1016/S0378-4371(00)00067-4 10.2307/2109850 10.1080/713665670 10.1016/0304-4076(86)90063-1 10.1086/294743 10.1016/j.physa.2008.01.025 10.3758/s13428-013-0416-0 10.1002/9780470644560 10.1007/BF03024407 10.1093/rfs/6.2.405 10.1111/j.1467-6419.2010.00666.x 10.1070/RM1970v025n06ABEH001269 10.1073/pnas.0409157102 10.1007/978-0-387-68441-3 10.1016/0304-4076(92)90067-2 10.1371/journal.pone.0096223 10.1086/294632 10.1093/rfs/5.3.473 10.1007/978-0-387-49820-1 10.1002/jae.800 10.1016/j.amc.2011.10.006 10.2307/1912773 |
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| SubjectTerms | Algorithms Autocorrelation Behavior Clustering Complexity Computers Econometrics kolmogorov complexity Normal distribution Quantitative Finance Simulation Stock exchanges Strings universal distribution Volatility volatility clustering |
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| Title | An Algorithmic Look at Financial Volatility |
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