Calculation of Historical Volatility of Daily Returns

In "Understanding Market Volatility" I have calculated the distribution of daily log returns for the GE stock price series downloaded from Yahoo!

In "Is the Distribution of Log Returns Normal?" I compared this distribution with the one from a series of random numbers with the same mean and standard deviation and noted how they are quite different.

Historical volatility is defined as the standard deviation of log returns over a certain period of time. Let's take this period of time to be 21 days, that is about one trading month, and calculate mean, standard deviation, skewness and kurtosis of GE daily log returns for 21 consecutive trading days. As I slide this window of 21 days from January 2, 1962 to today I get the following charts:



The second chart from the top is the historical volatility, the quantity normally used to estimate option's implied volatility, as it changed from the beginning of the historical period considered up to today.

Now I can create the histograms of the 21-day mean, standard deviation, skewness and kurtosis of GE daily log returns:



Categories: stock options, volatility
Technorati Tags: stock options, volatility