Volatility is a metric that measures the magnitude of the change in prices in an asset. The major types of volatility measures include: Actual Volatility, Historical Volatility, Realized Volatility, Future Volatility, and Forecast Volatility.
Actual Volatility refers to the volatility of the underlying asset reflected in the market. Yet, the actual volatility does not exist in calculations due to various limitations such as availability of data, the space and time barriers of calculating the data. Hence, actual volatility is only a theoretic being, investors are not able to obtain the perfectly accurate actual volatility.
Historical volatility is a statistical measurement of the dispersion of returns for a given security or market index over a given period. Generally, this measure is calculated by determining the average deviation from the historical average price of a financial instrument in the given period.
Realized volatility is the assessment of variation in returns for an investment product by analysing its historical returns within a defined period.
Future volatility refers to the volatility of the underlying asset in the future, typically the volatility between the current point in time and the expiration date of options. We can always make the right investment decisions if we get to know what the future volatility will be. Yet, there is no crystal ball that we can gaze into to foresee the future. Thus, it all comes down to the forecasting.
Forecast volatility as an estimate to future volatility, it plays a vital role in making option investment decisions. Hence, there are many volatility forecast models created by various academics and investment professionals over the years trying to forecast volatility.
The Black-Scholes model is the most widely used methodology for pricing options. It requires five key elements: the strike price of an option, the current price of the underlying asset, the expiration date, the risk-free rate, and the volatility. Given the strike price, risk-free rate and the expiration date are known and constant, you can simply key in the parameters into the model to determine the fair price of the option.
Nevertheless, one should notice this is only an estimation and there is also a certain limitation of the Black-Scholes model so the forecasted pricing does often has a deviation from the market price.
The fair price is only an idealized state in which both market and models try to converge. The reason being that there are many man-made assumptions behind the model to hinder its accuracy. For instance, the model assumes volatility remains constant over the option's life, which is not the case because volatility constantly fluctuates with the supply and demand in the market.
Implied volatility is an estimation of the future volatility of the underlying asset of the options contract. Investors can use it to project future moves, its demand and supply, and often employ it to price options contracts i.e. high implied volatility results in options with higher premiums and vice versa.
One of the inventors of the Black-Scholes Model has once illustrated the model with a vivid example: A trader living in Chicago is deciding whether to wear a coat on a morning in June. According to historical data, Chicago in June was not that cold to wear a coat (historical volatility); he then turns on the radio and it is 32℃ according to the weather forecast. In this case, he only needs to wear short sleeves (forecast volatility); To play safe, he opens the window to observe the pedestrians outside and finds out that they were all wearing coats and carrying umbrellas, so he should also be wearing a coat and bring an umbrella with him (implied volatility).