# Volatility Tutorials

This page is a summary of various resources and other pages on volatility, including topics such as historical volatility, implied volatility, volatility indices, volatility calculation, practical use, and volatility trading. Follow the links to see more details about individual topics.

## Historical Volatility

Historical volatility is the volatility that has been observed in the market. It is calculated from historical market data.

- Historical Volatility Start Page
- Historical Volatility Calculation
- Historical Volatility Excel Calculator + PDF guide

## Implied Volatility

Implied volatility is the volatility that is priced in option prices. It is derived from option prices, typically using an option pricing model.

Implied volatility is closely related to historical volatility, but the two can have hugely different values for the same security sometimes. While historical volatility is something that has already happened (and therefore it is certain and fully known), implied volatility reflects market’s expectations towards the future. Implied volatility is often different even on different options on the same underlying security.

- Implied Volatility Start Page
- Calculating Implied Volatility in Excel
- Black-Scholes Calculator + PDF Guide

## Volatility Indices and Derivatives

There has been a growing universe of volatility indices on various assets. The best known of the is the VIX (CBOE Volatility Index), which measures 30-day implied volatility of S&P500 options. Similar volatility indices exist for other equity indices, stocks, ETFs, and other securities around the world. Futures and options are available on some of the volatility indices.

- VIX (CBOE Volatility Index) Start Page
- What Is VIX?
- VIX Calculation
- VIX Futures
- VIX Options
- Trading the VIX

## Frequently Asked Questions about Volatility

The following are commonly asked questions about the basic properties of volatility.

### Volatility Calculation and Mathematical Meaning

Although there are different methods of its calculation and interpretation, volatility is commonly understood as standard deviation of returns. It is usually expressed in percent per annum. When transforming volatility to different time units, the square root of the time unit ratio must be used.

- Is Volatility Variance or Standard Deviation?
- Is Volatility the Same as Variance?
- Is Volatility and Standard Deviation the Same?
- Is Volatility Sigma or Sigma Squared?
- Is Volatility a Percentage?
- Why Is Volatility Proportional to the Square Root of Time?

### Volatility Value Range

Volatility can theoretically reach any value from zero to positive infinite. Most securities trading in real world have volatility between 0 and 100%, although volatility above 100% is far from uncommon. Zero volatility means that a security has constant price (doesn’t move at all).

- Is Volatility Constant?
- Can Volatility Be Negative?
- Can Volatility Be Zero?
- Can Volatility Be Greater than 1?
- Can Volatility Be Over 100?

### Using Volatility

While some people (including some academics and financial professionals) consider volatility an asset class, others don’t. It is believed that adding long volatility can improve risk adjusted return of a portfolio under some circumstances. Volatility futures, options, and exchange traded products (especially those on the VIX) have become popular also for short-term trading.

### Trading Volatility

Although volatility trading can be very rewarding, it is far from easy. As a trading vehicle, volatility has many specifics, especially a return distribution that is unlike any other asset class. While it is commonly believed that volatility is mean reverting (which it generally is), it is not necessarily true on all time horizons.