Introduction to Volatility

To get the basic idea of what volatility is please read the article Putting volatility to
work written by Ravi Kant Jain and published in the Active Trader Magazine (April 2001).

Here we will provide a description of what volatility is, why it is important in option trading and how one can estimate it. Also, well we will briefly cover the most significant related parameters and indicators used in conjunction with volatility in options analysis.

Day-to-day market movements reflect the buying and selling decisions of millions of investors. Market prices change from one moment to the next. Volatility is defined as the variation of an asset's returns, and indicates the range of a return's movement. Large Volatility values mean that returns fluctuate in a wide range.

Usually increased volatility is associated with falling stock prices. See the chart below, which shows historical and implied volatility for the IBM, and the underlying's price. As you can see, as a rule, jumps in volatility correspond to a falling stock price. But fast rising markets also have a high level of volatility. There periods of quiet trading when volatility is low, and aggressive trading when volatility is high. Periods of high volatility are often caused by an emotionally driven market. Emotions, such as greed and fear, can cause stocks to move higher or lower, and change the level of volatility.

**Chart: Volatility and price of IBM**

**Note: those charts are available to Advanced Historical Data service subscribers.**

Increasing or falling volatility commonly is a result of changes in investor emotions and psychology in the marketplace. For example, corporations deliver earning results each quarter; when those earnings results disappoint investors, it can stimulate a landslide in a stock's price.

Fear and greed have an important effect on volatility, because they are two primary factors causing stock prices to change. When important and relevant new information arises in the markets, volatility tends to rise. When information is unexpected, it will have the greatest impact on stock prices, as a result, a stock jumps dramatically higher or lower. The impact of a news event will vary based on its relative importance and the degree to which it surprises investors.

Fundamental assumptions used in assets models are that returns follow a normal distribution and that underlying prices are lognormal distributed. For more information, see Price and Return's distribution.

Thus, in a return's distribution, Volatility is the deviation of returns from their mean. If we assume the mean of returnsto be zero, then 10% yearly Volatility represents that in one year returns will be within [-10%; +10%] with 68.3% probability; within [2*10%; 2*10%], with 95.4% probability, and within [-3*10%; +3*10], with 99.7% probability (according to a normal distribution).

The daily volatility for n-day term is calculated as deviation of daily returns, observed during n-day, from their mean, and can be normalized on any desired time interval (say, t day) by multiplying daily volatility by the square root from t. To compare volatilities calculated for different terms we can annualize them. The annualized n-day volatility is calculated from the daily volatility for n-day (i.e. calculated on the basis of n daily observations) by multiplying it by the square root of 252, since the average number of trading days in a year is 252. And vise versa to calculate daily volatility from the annualized volatility, you should to divide an annualized volatility by the square root of 252.

There are many methods of measuring Volatility. It can be done using historical data, or option pricing models, or using models of forecasting volatility based on recorded values. We will cover the following popular methods: Historical Volatility as standard deviation, Parkinson Historical Volatility based on extreme values, Implied Volatility and Implied Volatility Index, and a forecasting volatility model using weighted past volatilities to estimate future values.