## 11 December 2006

### Volatility

Perhaps the most neglected, yet most important aspects of options trading is in the area of volatility, its analysis, and consideration when trading. Intrinsic in using volatility in option trading, is an understanding of the greeks. This is why volatility is often ignored or misunderstood, because of the difficulty in grasping what the greeks are all about and how they affect every option trade you undertake.

Yet they are really not that hard to grasp individually, and it is only a matter of practice to consider all the greeks together when analyzing a trade.

So why am I banging on about greeks when the title of this article is volatility. It's because volatility also has a greek name, so therefore should be considered amongst them. That greek name is "sigma".

Sigma is the measure of 1 standard deviation of price movement, annualized and expressed as a percentage.

What is volatility?

Expressed in the most simple terms, volatility is how much a stock moves around in price. We can say that a stock that moves in a range of \$70 to \$75 over a period of months would be considered as a low volatility stock. Its movement is relatively quiet and sedate. Another stock that moves in a range from \$35 to \$90 in the same time period would be considered a lot more volatile. This would be a high volatility stock.

Technicians have various methods of measuring volatility; average true range, standard error, standard deviation plus a few others. But in the option world there is a specific formula for measuring and annualizing volatility. This web page explains the mathematics, or, if you have a charting package it can be plotted as an indicator.

This formula is known in the options trading world as "Statistical Volatility" or "Historical" Volatility. The two terms mean the same thing and are interchangeable

If you have Metastock or Amibroker, the formula for 30 day statistical volatility is as follows:

(StDev(log(C/Ref(C,-1)),30)*sqrt(252))*100

What is meant by "30 day" volatility is that the last 30 days volatility is measured and converted to give an annualized percentage figure; "sigma". Lets have a look at Statistical Volatility on a chart.

As you can see this measure of volatility varies as the retrospective period of 30 days is moving. So it can be viewed in a similar way as a moving average... sort of. But what you can see is that volatility varies. Typically a stock will oscillate from a period of relative low volatility to periods of relative high volatility. This information is useful for evaluating the value of options and for the timing of trades.

Questions are welcome.

Next we look at Implied Volatility.