Stan Freifeld comes to us from the Floor of the American Stock Exchange where he traded options for his own account from 1994-2001. He was a Market Maker for the options on several popular equities including Dupont, Schering Plough, Walgreen's, CBS, U.S. Surgical and Biovail.When he is not trading or thinking about trading, Stan relieves his stress by playing competitive squash, competing in local road rallies with his Ferrari Cabriolet and tutoring local high school students for the SAT's. The bottom line is that Stan, a long time MENSA member, is an engaging teacher with an extraordinary background in options trading and risk management. He is helpful and patient by nature and equally at ease with all levels of traders, from complete novices to advanced pros and academics. He'll be happy to teach you to trade!

Calculation Details: Historical Volatility

As many of you know, I approach things from a mathematical point of view. Actually, I have no choice. My background and training as a mathematician and actuary are well ingrained, and it has become a part of who I am. I remember when I bought my first car (1963 Chevy Impala) asking the salesman how many miles to the gallon did it get? He said it didn't matter, "when it runs out of gas, you fill it up." Well that didn't fly in my world years ago, and with gas prices where they are now, it still wouldn't be acceptable today. Everyone looks at things differently based on the tools they have available; I have numbers.

Anyway, I've kept the mathematics in my articles relatively basic thinking that's what the majority of you would want. Recently, a number of readers and students have asked me to explain in detail how some of the calculations are made. I'm sure they want to program their own calculations using an Excel spreadsheet or some other more advanced programming language. As a compromise to most of the readers who are happy to use one of the options calculators that are readily available on the internet, I only plan on doing two such articles (although my arm can be twisted!). This week, I'll go through the steps of calculating historical volatility and I'll do another giving step by step details and instructions as to how to calculate an options' theoretical value using the Black-Scholes formula.

In a previous article, Getting To Know Volatility, I defined volatility as the rate at which a security moves up or down, or more precisely as the annualized standard deviation of the daily price changes in the security. Historical (also called statistical or actual) volatility is easy to measure and the results shouldn't vary much based on who does the calculations. Keep in mind, that when we're talking about historical volatility, we're talking about the volatility of the security, not the options. It's typical to see 10 day, 20 day, 50 day, 100 day or 200 day historical volatility, but they all are annualized numbers so that valid comparisons can be made. Depending on what the volatility numbers are being used for, sometimes a moving average is also computed, such as a 20 day moving average of 50 day historical volatility.

There actually are a number of different ways to do the calculations. One method was developed in 1980 by the physicist, Michael Parkinson and is based on the daily high and low prices of a security. When calculated in this fashion the volatility is referred to as the Parkinson number. A more common method utilizes the ratio of close to close prices and that is what will be illustrated here.

Let's get on to the calculations. We'll calculate a current 10 day historical volatility for a stock we're all familiar with, Apple Inc. (AAPL). Our approach will be to calculate the standard deviation (sd) based on 10 days and then annualize it. That result will yield the historical volatility. The formula for calculating the standard deviation of a set of N data points is

Here is the AAPL data:

As always, if you have any questions about my articles, have suggestions for future topics, or want more information about our options mentoring program, feel free to email me at: sfreifeld@tradingacademy.com or call me at: (888) OTA-2580 ext. 2010.

11. Know Thy Options!

DISCLAIMER:
This newsletter is written for educational purposes only. By no means do any of its contents recommend, advocate or urge the buying, selling or holding of any financial instrument whatsoever. Trading and Investing involves high levels of risk. The author expresses personal opinions and will not assume any responsibility whatsoever for the actions of the reader. The author may or may not have positions in Financial Instruments discussed in this newsletter. Future results can be dramatically different from the opinions expressed herein. Past performance does not guarantee future results.

Reprints allowed for private reading only, for all else, please obtain permission.