How to estimate volatility?
It is important for companies to estimate the expected volatility carefully since it provides much of the value of options--especially relatively short-term options. Even for longer term options such as most employee stock options, the level of expected volatility accounts for a significant part of the difference in the values of options on different stocks.
Volatility Definition
First, we need to agree on definition of volatility. It's basically the variation from the average value over a measurement period. If a price varies a great deal from day to day, the volatility will be high, and conversely if the day to day variation is low, the value of volatility will be low as well.
While it get pretty complicated in a hurry when you burrow into the statistics, and you factor in things like log normal returns, and stationary processes, it can be approximated by saying that if the volatility is calculated by the standard deviation of the asset prices, then approximately 2/3 of the time the price will be within one standard deviation of the average price over time.
Why Do We Care About Volatility?
One of the areas that volatility takes on greater importance is in the area of options pricing. Not to go into great detail, but an example would be call option, or the option to buy a stock or some other asset in some future period, say the next few months. If a stock price has a history of relatively large price swings, then it becomes more likely that it can exceed the "strike price" of the potentially triggering the buyer to exercise the option, or to buy and sell the stock at a profit, even though the long term average price of the stock hasn't changed. So the option seller will price the option higher for a volatile stock to compensate for this possibility.
