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Fisher Black, Myron Scholes and Robert Merton were the three academics that developed the much acclaimed option pricing model now called Black and Scholes.
The Black and Scholes option pricing model was the result of the educational paper called Real Options, written by these academics in 1973. The model was so highly praised that they were awarded the prestigious Noble Prize in 1997.
The Black and Scholes model has spawned a family of other pricing variations since then, although the Black and Scholes still remains the foundation model for pricing options today.
Five key components are needed to correctly calculate a theoretical price for an option contract;
Of these inputs, the first four are a given, i.e. we know with certainty what the exercise price is, how many days until the option expires, where the underlying instrument is currently trading and we also know what interest rates currently are. However, we do not know what volatility the underlying will experience between the time of trade and the expiry date. That is why volatility is so important when it comes to option pricing - the volatility of an option really determines how likely that contract will be in, at or out-of-the-money by the expiration date.
As well as calculating the fair value for an option contract, option pricing models also calculate what-if values, referred to as The Greeks - Delta, Gamma, Vega, and Theta. The importance of these calculations are covered under The Greeks link above.
An important assumption in the Black-Scholes option pricing model is a statistical concept known as the Normal Distribution. The Black-Scholes model uses the volatility input to calculate the probability of the underlying price expiring in the money before the option's maturity date. The higher the volatility the more likely it is that the underlying price will be above the exercise price before the maturity date and hence the option will then have a higher premium. If the volatility of the underlying instrument is expected to be low then there is less chance that the option will be profitable and will have a lower expected option value.
You can download the Option Trading Workbook spreadsheet and examine how the option price varies when certain inputs are changed.