## Definition of volatility in the stock market

Volatility is defined as the statistical measure of the dispersion of returns for a given security or market index.

In simpler words, volatility represents **how large an asset’s prices swing** around the mean price over a given span of time.

In general, it can be said that **the higher the volatility, the riskier** the security. The price of more volatile assets is expected to be less predictable.

Volatility is often measured from either the standard deviation or variance between returns from that same security or market index.

Volatility is a key variable in options pricing models like Black-Scholes. More volatile underlying assets will translate to higher options premiums because with volatility there is a greater probability that the options will end up in-the-money at expiration.

The most widely followed volatility indicator is the VIX Index, the indicator of the volatility of the S&P500 Index.

*Note: the standard deviation is the square root of the variance.*

## Types of Volatility

There are several types of volatility that are commonly used in finance and investing:

- Implied Volatility (IV): This is a measure of future volatility implied by the current market price of options on a financial instrument or market index. It is calculated by using a pricing model such as the Black-Scholes model to determine the implied volatility that would make the market price of the option equal to its observed market price.
- Historical Volatility (HV): This is a statistical measure of the past volatility of a financial instrument or market index. It is calculated by taking the standard deviation of the instrument’s return over a specific time period, typically using closing prices.
- Realized volatility (RV): This is similar to Historical Volatility but not exactly the same. It is calculated by taking the standard deviation of the natural logarithm of the instrument’s return over a specific time period, rather than using closing prices.
- Inter-market volatility: This is a measure of the volatility of the relationship between two different financial markets or instruments.
- Intra-market volatility: This is a measure of the volatility within a particular market or financial instrument.
- Inter-daily volatility: This is a measure of volatility from one day to the next.
- Inter-hourly volatility: This is a measure of volatility from one hour to the next.

It’s worth noting that volatility can be measured in different ways, and it’s important to understand the context and the specific metric being used when discussing volatility in any financial market.