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 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.