Autocorrelations of Stock Price and Volatility

Continuing the line of thought into a possible time-dependence of stock market volatility, it is worthwile to use a statistical tool known as autocorrelation. In fact, the autocorrelation of a data series can tell how long it will take to a signal to disappear from the data. In other words, one can measure the duration of the memory effect in the data.

First of all, I take the following log-normal computer generated price series with the same mean and standard deviation of GE stock prices:



Superficially, the computer generated series does not look that different from the "real thing":



The following picture shows the autocorrelation of the historical volatility (red curve) and of the price (black curve):



Both autocorrelations fall down very quickly to zero, signifying that there is no memory effect whatsoever in both price and volatility, as it should be.

This picture shows the historical volatility calculated from the GE prices:



The autocorrelation of GE historical volatility (thick red curve) does not fall off right away. In fact, it is well approximated by an exponential decay with life-time of about 175 trading days (thin red curve). On the other hand GE price autocorrelation (black curve) shows no memory effect just like the random walk:



Categories: stock options, volatility
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