Difference between Implied, Realized and Historical Volatility

This page explains the differences between types of volatility – implied, realized, historical. There are other types and terms which we will also explain, including forecast volatility, future volatility, and statistical volatility.

How They Differ

Volatility, typically expressed as a percentage and interpreted as standard deviation of returns, measures how much a security moves over a certain period. The individual types of volatility differ mainly in two things:

  1. What that period is (historical volatility is for some period in the past, while future or forecast volatility is forward looking).
  2. How we find or calculate the volatility (implied volatility is calculated from option prices, while realized volatility is calculated from underlying price changes).

Implied vs. Realized Volatility

Volatility is particularly important for option traders, because it affects options prices (or option values?). In general, higher volatility makes options more valuable, and vice versa.

The subtle difference between an option’s price and its value is key to understanding the difference between implied and realized volatility.

Price is what you pay. Value is what you get.

To make a profit you must buy high value for low price (or sell low value for high price). This is true when trading options like it is when trading stocks (or anything else).

Implied volatility is what you pay – it is the volatility implied (contained or reflected) in an option’s price.

Option pricing models such as the Black-Scholes model can calculate exact option price for a particular level of volatility (assuming we also know the other factors, such as the option’s strike price, time to expiration, or underlying price). They can also be reversed to find the exact volatility that is implied in a particular option price. This is how we calculate implied volatility – from option prices. Therefore, implied volatility is the future volatility expected by the options market. This expectation may be correct, or it may not.

Realized volatility is what you get – it is the volatility actually realized in the underlying market. It can be calculated from underlying price moves (e.g. daily stock price changes). Although there are various approaches, the most common way is to calculate realized volatility as standard deviation of daily logarithmic returns. This is why realized volatility is sometimes called statistical volatility.

Option prices don’t affect realized volatility in any way.

In fact, you can calculate realized volatility even for securities without any options on them. On the contrary, there is no implied volatility without options. At the same time, when there are multiple options listed on the same underlying and same expiration (calls and puts, different strikes), each of these options can have different implied volatility (this is in fact very common and known as volatility skew or smile).

Historical vs. Future Volatility

While implied volatility is always forward looking (it is the expected volatility from now until the option’s expiration), realized volatility can relate either to the past (then it is called historical volatility) or the future (then it is called future realized volatility).

Another important characteristic of realized volatility (historical or future) is the length of the period over which it is measured. For example, “20-day historical volatility” measures realized volatility over last 20 days (it is typically calculated as standard deviation of last 20 daily price changes).

Future vs. Forecast Volatility

When talking about future volatility, we must distinguish between our opinion (before it happens) or prediction of what the future volatility will be – this is often called forecast volatility – and the reality, which we will only know after it happens – the future realized volatility.

Our ability to forecast volatility (not an easy task!) is essential for successful option trading – we want our forecast volatility (what we think will happen) to be as close as possible to the future realized volatility (what actually happens). If we can do that consistently, we only need to buy options which are underpriced relative to our expectation (the option’s implied volatility is lower than our forecast volatility) or sell options which are overpriced (implied volatility is higher than our forecast volatility). This won’t guarantee that we make a profit on one particular trade (besides volatility there are other factors affecting option prices, including particularly underlying price direction, though these can be hedged). However, it should make us profitable in the long run, over a large number of trades.

Summary

We have explained the differences between individual types of volatility:

Implied volatility is calculated from an option’s price. It is the volatility that the buyers and sellers of this particular option expect to be realized in the period from now until the option’s expiration. Different options can have different implied volatilities, even when they are on the same underlying and with the same expiration date.

Realized volatility is calculated from underlying price changes over a certain period (exact calculation explained here). If this certain period is in the past, we call it historical volatility. If it is in the future, we call it future realized volatility.