The Black-Scholes Model is a standard model for calculating the price of an option. It considers the expected price of the underlying asset and the expected volatility. Consider a contract that pays out if the price of oil is above $100 on May 1. Suppose you think that the price of oil will be $95 with a standard deviation of $1. In that case, an option that pays off if the price of a barrel of oil will be above $100 is nearly useless, there would have to be a 5 SD event which occurs nearly 0% of the time. In contrast, if you think the price of oil will be $90 with a standard deviation of $10, then the probability that the price of oil will be above $100 is 30%. Thus even though the expected price was lower, the value of the option has risen.
There are few other calculations that one must take. For example, if one buys the option on January 1, one must lock up ones’ money for four months. Since one could easily earn positive returns in a risk-less environment by investing in Treasury bonds or other assets, the value of the option declines (since the money locked up in the option is not earning money like money invested in Treasuries are). One must also consider the structure of the contract: the price of the contract depends on how it pays out. The Black-Scholes Model usually models the price of a European call option, which gives the holder the right to purchase a security at a predetermined price at a predetermined time. However the same principles–if not the specific parameters–can apply to different option structures, such as American call options (which allows the holder to exercise the option any time) or binary options.