# Implied volatility

Implied volatility is a theoretical value designed to represent the expected annualized fluctuation ("volatility") of a security, be looking at the prices of options contracts that underlie the security. It is the market's prediction of future volatility. It can be seen as the difference between an option's theoretical price -- as calculated based on the current price of the security, the option's strike (contract) price, time to expiration and other known variables -- and the option's actual trading price.

In equity markets, implied volatility tends to increase when the market is bearish and decrease when the market is bullish, because bearish markets are seen as more risky.

## Calculating Implied Volatility

Calculating implied volatility requires the use of an options pricing model such as the Black-Scholes Model:

The formula basically states that the theoretical value of a call option (C) is worth a fraction of the price of the underlying security - a stock, a futures contract, a bond, etc. - based on five factors:

• the current price of the security (S)
• the exercise price (or "strike price" of the option (K)
• the risk-free rate of return (r) (if the underlying security is a stock, stock index or other dividend-paying security, the rate also includes an adjustment for dividends paid during the life of the option)
• the time left until the option's expiration (T)
• the annualized standard deviation of the security (σ) - essentially a measure of the security's price fluctuations over a year's time or its volatility.

Since we know all of these variables, except its volatility, and we know where the call option is currently valued by the marketplace, we can plug the current call price, current security price, the strike price, interest rate and time to expiration into the formula and solve for σ.

This is the level of volatility implied by the market or its "implied volatility."

## VIX

One of the most widely recognized uses of implied volatility is the CBOE Volatility Index, or "VIX."

The VIX, introduced in 1993, measures the market’s expectation of future volatility implied by a basket of options on the S&P 500 stock index (SPX). In other words, VIX Index uses options pricing as a way to measure perceived market risk and uncertainty. The VIX Index is a 30-day risk forecast of stock market volatility and typically has an inverse relationship with the S&P benchmark as it tracks option prices that investors are willing to pay as a protection on the underlying stocks.