Volatility, in the broader financial sense, is a measure of the extent to which the price of an asset moves in a given time frame. Traders will generally focus on two distinct, quite different types of volatility; historical and implied. The former, as its name suggests, refers to an asset's recorded price action in the past. The latter is a forward-looking measure derived from observable prices in the options market.
Option pricing models generally utilise six parameters in their formulae; the asset's spot and strike prices, the prevailing risk-free interest rate and the cost of carry, the time left to expiry, and the asset's volatility. Except for volatility, all other parameters are either known or directly observable in the market.
This essentially means that the model can either be solved for the option value, by using an arbitrary future volatility assessment, or alternatively it can be solved for volatility itself, by using live option prices from the market as inputs. In the latter case, the asset's volatility is said to be implied from the market with the use of the option pricing model, giving rise to the term "Implied Volatility".
The calculator uses the Black-Scholes formula for European options and the Barone-Adesi And Whaley pricing model for American options. Implied volatility can only be calculated with options that have a suitable vega value.
This direct relationship between an option's value and its implied volatility is so important that markets are quite often quoted in terms of the latter rather than the former. In other words, quotes of bid and offer option prices are often replaced by those of their corresponding bid and offer implied volatilities. Indeed, a valid argument can be made that this is a more efficient way to quote options, since actual option premia will fluctuate with changing price levels of the underlying asset, and are thus meaningless without the use of the underlying spot as a reference.
In summary, implied volatility is usually the most important factor determining the price of an option. Traders therefore need to understand what it represents and to be aware of the levels of implied volatility they trade.
The calculator is for education purposes only - use at your own risk