Volatility refers to the tendency of prices to change unexpectedly, usually as a response to new information or changes in demand for the investment. Volatility can be defined as an investment's tendency to move up and down in price over the latest n periods.
A security with high volatility has bigger fluctuations in price compared to a security with low volatility. The more quickly a price changes up and down, the more volatile it is. As such, volatility is often used as a measure of risk.
For example: A stock whose price went up 10% yesterday and went down 25% today is more volatile than a stock which increased 2% in both days.
Historical volatility is calculated by looking at past changes in stock price. The standard deviation of percentage changes in price is used to calculate observed volatility within the considered timeframe.
Historical Volatility, which looks at the past, is distinct from Implied volatility, which represents expectations about future fluctuations in price and is calculated by looking at the prices of options on the underlying investment.