Understanding Market Volatility

In "How to Price American-Style Options" and "The Binomial Tree Formula" I made clear that a good estimate of market volatility is essential when pricing a derivative contract such as a stock option. I'm going to devote a few posts to a deeper study of volatility.

For the sake of concretness I am going to use General Electric stock price. Yahoo! Financial provides the daily price history from January 2, 1962. All what one has to do is to download a file and start working with the data.

The file contains 11118 records. First thing to do is to calculate stock returns over different periods.

The following charts to the left shows daily, weekly, monthly, quarterly and yearly returns. You must click on the thumbnail to see the full size chart, which is quite large.



Time on these charts goes right to left. That is, the most recent data are the left-most in the chart.

To have a better view at the way returns change going from the daily all the way to the yearly returns, I made these charts that show only the most recent one thousand days of data:



Now that we have the returns, we need to calculate the log returns, which are used in the definition of historical volatility. They must be annualized. This means that the daily log returns are the logarithm of the daily returns multiplied by 252, the number of trading days in one year. Similarly, the weekly log returns are the logarithm of the weekly returns multiplied by 52, etc.

Now that I have the daily log return, I can examine their statistics. For example, I can make a histogram, showing the frequency of a given log return over the entire period considered in the data:


If it is not clear what a histogram represents, check it out at Wikipedia.

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