Options and Volatility
Because the actual calculation, and sometimes even the discussions, of volatility involve some fearsome mathematics, novice options traders often forgo learning about it. Those traders are at a disadvantage compared to their more intrepid competitors. And unnecessarily so, since the concept is not only useful but simple to understand.
In essence, volatility is a measure of how much and how fast prices are likely to change. Will MSFT (Microsoft), currently at $27 increase to $28 in the next hour, or fall to $26? Does it continue to fluctuate like that for the day, or several days? Those are wide price swings in a short period  hence high volatility.
The issue is important since, if the price changes slowly, investors will have time to react. If the price changes by an extremely small amount, there is little to lose or gain. Both factors are important in measuring risk.
Mathematicians and options researchers being restless and curious people have naturally not stopped there. They've devised several different ways of defining and measuring volatility.
The most basic uses a statistical concept called 'standard deviation'. While the calculation is complex, the idea is simple. It's basically just a measure of how far from an average a certain amount differs (i.e. deviates). That calculation, carried out for data covering a year and then massaged a bit, becomes the figure shown in charts.
A variation on that number, called Implied Volatility (IV), uses factors you would intuitively expect: market price, strike price, expiration date, interest rate.
Why should a trader care?
One reason is that IV tends to increase when the market is bearish and decrease when the market is bullish. Common sense reveals why.
If it's August in the Northern Hemisphere, say New York, and the temperature is 80 degrees (Fahrenheit), how likely is it to deviate to below 40 at noon? If it's late February, 40 degrees at noon isn't at all unlikely, but in August it would be surprising.
That deviation from the norm, and the measurement of its likelihood forms the basis of betting on future movements. (In fact, there are optionlike derivatives known as Weather derivatives that do just that.)
If it were August in New York, traders would be bullish that it would rise above 70F. (It often does.)
How can a trader use volatility in evaluating trades?
Volatility is one common measure of risk and options are fundamentally about trading risk. One of the most widely used gauges of that volatility is VIX (Volatility Index). First developed by the CBOE (Chicago Board of Exchange), it's calculated using a weighted average of implied volatility. The data forming that average comes from a wide variety of strike prices for calls and puts from the S&P 500.
Traders use VIX to gauge market sentiment, with a range of 2025 indicating a probably selloff. VIX increases as the market goes down and decreases when the market moves up. Again, common sense suggests an obvious reason.
Since volatility implies uncertainty, traders tend to be less concerned about a rising stock market than a falling one. Though shorting certainly forms part of many trading strategies, most traders look to gain from higher prices, not lower.
The higher the perceived risk, the higher the implied volatility and the more expensive options become. As the market declines, puts become more popular. Since traders generally expect the trend to continue (at least in the short term), committing to buy at a lower price becomes a preferred position. Higher demand means higher prices  in this case, for puts.
Tracking volatility should form part of any trader's strategy. Fortunately, one doesn't have to be a mathematician to incorporate this tool. Software that calculates and tracks the common measures of volatility are readily available. Add it to your toolbox.
