Volatility
Stock market volatility is probably one of the most arguable financial concepts. It often has a negative meaning for investors because it is quite risky. However, it can still be profitable for experienced and patient investors.
What Is Volatility?
It is the most important financial indicator and concept in financial risk management that defines the degree of variation of a trading price series. To calculate this indicator, a standard selective deviation is used, allowing investors to determine the risk of acquiring a financial instrument. Most often, the average annual volatility is calculated. It is expressed as absolute (for example: $100± $5) or relative to the initial value (for example: 100% ± 5%).
Types of Volatility
There are the following volatility types:

Historical – the standard deviation of the yield of a financial instrument for a given period of time, calculated on the basis of historical data regarding its value.

Implied – the calculation based on the current value of a financial instrument assuming that the market value of a financial instrument reflects the expected risks.

Historical implied volatility  a "chronicle" of the implied volatility predictions.
How to Calculate Historical Volatility
The average annual volatility σ is proportional to the standard deviation σ SD of the financial instrument yield and inversely proportional to the square root of the time period:
σ = σ SD/P,
where σ SD is the standard deviation of the financial instrument yield and P is the time period in years.
The σ T for the time interval T (expressed in years) is calculated based on the average annual volatility as follows:
σ T = σ.
For example, if the standard deviation of a financial instrument's return during the day is 0.01, and there are 252 trading days in a year (that is, the time period is 1 day = 1/252 years), then the average annual volatility will equal:
σ annual = 0.01 = 0.1587.
The monthly volatility (that is, T = 1/12 years) will equal:
σ month = 0.1587 = 0.0458.
Implied Volatility
The implied volatility depends on the following factors:

Historical data  the higher it is at present, the higher expectations for future volatility will probably be.

Political and economic situation (elections, the promulgation of economic indicators, etc.).

Liquidity (supply/demand) of the market  if supply exceeds demand, prices fall, and vice versa.

The day of the week.
Volatility in Long Term Trading
Long term traders use a strategy called buyandhold, wherein stock is purchased and then held for an extended period, often many years, to profit the company's cumulative growth. This strategy is based on the assumption that while there may be a fluctuation in the market, it generally produces returns in the long run. In this case, low volatility can actually mean greater profits. As the price changes, it gives investors an opportunity to buy stock in a solid company when the price is very low, and then wait for incremental growth.
Volatility in Short Term Trading
For shortterm traders, volatility is even more important. Day traders monitor even the smallest changes and profit from them. As price fluctuates, shortterm traders can various technical indicators to benefit from those highs and lows. The highly volatile stock also provides a lot of opportunities to swing traders. They work with longer time frames than short traders, typically days or weeks against minutes and seconds, but their strategy is still based on market volatility.
Summary
Volatility is a financial indicator that refers to the fluctuation of prices on the market. It can be historical, implied, and combined (historical + implied). Both the long and shortterm traders can benefit from market volatility in a variety of ways.