Is Volatility Time Dependent?

In the previous posts "Weekly Volatility", "Monthly Volatility", "Quarterly Volatility" and "Yearly Volatility", I have calculated the historical volatility of GE stock price using returns over an increasing time period from weekly returns to yearly returns and compared them with the corresponding quantities for a random walk. It may be worthwile to show all these results together to better see the effect of time on the calculation of volatility.

These are the histograms of the 21 day mean of GE annualized log returns going from daily returns to yearly returns, compared with the corresponding normal distributions:



And these are the histograms of the 21 day volatility for the same time periods, compared with the corresponding random walk distributions:



It seems clear that the discrepancy between the stock price statistics and the random walk statistics is concentrated at the shortest time horizons. The longer the period used to calculate the returns, the less the discrepancy. That could mean that there is a "memory effect" that fades away with time, being the strongest considering daily returns and being almost gone when we reach the yearly returns.


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