Implied volatility is the amount of price variation the market is expecting
There isn’t a greek letter specifically tied to implied volatility, but you will almost always find implied volatility listed with the greeks in an options table. Often, the lower case greek letter sigma is used to represent implied volatility in formulas. Implied volatility is the expected percentage move in price of the underlying in the coming year, based on the market price of an option. Let’s break this down a bit, because the concept is a bit of a challenge to understand, yet it is the foundation of option pricing, so you need to grasp it.
Volatility is a statistical measure, usually thought of as the standard deviation of a data set. You can take a group of numbers and figure averages and standard deviation. From that you can say that most of the data is within one standard deviation from the average of the data. Looking back at stock prices, we can tell how much variation or volatility there was during any given time period in the past. It is just math and statistics.
However, the future is unknown. We can’t assume that the volatility we’ve seen in the past will translate into the future, or can we? Based on what happens in the news and in the price of an underlying, the options market will make assumptions about how much volatility to expect in the future- it will “imply” a volatility looking forward. How does it do this? By changing prices- what are buyers willing to pay, and what are sellers willing to accept? This process happens second by second and hour by hour with millions of market participants determining the market price at any given time.
But how do we imply volatility from a price? Since everything about an option is known except price and volatility- we know how far in or out of the money an option is, how long until it expires, when a dividend will be paid, what interest rates are, etc. So, if an option price is set, it implies a volatility, and if there is a certain expectation of volatility, then there is a price to reflect that. There are a series of complex formulas that factor all these things together and link option prices to an underlying implied volatility.
Implied volatility goes up as the market gets more uncertain. Big price drops will bring uncertainty to the market, as does future events that have unknown outcomes, like a meeting of the Federal Reserve, or a quarterly earnings announcement by an individual company, or a crop report for a agricultural commodity. Interestingly, big stock price increases tend to lower implied volatility.
There is another Greek that is used to quantify the impact of changes to Implied Volatility. Vega measures the change in option price for a 1% increase in Implied Volatility. This can be a helpful measure to determine how sensitive a combination of option positions are to changes in volatility.
