When you buy a stock option, you are investing in the option to buy shares of a stock at a designated price up until a set expiration date, known as the expiry. As the name implies, you have an option, meaning you are in no way obligated to buy anything unless you find conditions favorable to do so. This comes at a price however, which includes a premium paid to the seller of the option, also known as the writer.
The main difference between stocks and options is that stocks are actual ownership of a company while options are merely contracts which allow the buyer to potentially buy shares of a stock from a seller if the price is right. If the price of the stock never goes above the buyers designated strike price, the buyer will choose not to exercise their option and will lose any premium paid to the seller of the option.
The price of an option is determined by the intrinsic value as well as an extrinsic value which is determined by how much time is remaining in the expiry period. The intrinsic value can be determined by subtracting the strike price from the current market value. If your option agreement is for $10 a share and the market value is $15 per share, your option has the intrinsic value of $5 per share.
Options with longer expiry periods have much more profit potential, as the stock has more time that it may go up in value. The longer the expiry period, the higher the extrinsic value will be. An option with a 5 year expiry can add an additional 25% to the intrinsic value to determine the price of an option. Options will shorter expiry periods will have extrinsic values proportionally less than 25%.
To determine the overall value, you can simply add the intrinsic and extrinsic values together to get a rough estimate. The actual formula to determine the price of an option is much more complex, and may be calculated somewhere online to get an exact figure.