With respect to an option, this cost is known as the premium. It is the price of the option contract. In our home example, the deposit might be $20,000 that the buyer pays the developer. Let’s say two years have passed, and now the developments are built and zoning has been approved. The home buyer exercises the option and buys the home for $400,000 because that is the contract purchased.
The price you pay for an option, called the premium, has two components: intrinsic value and time value. Intrinsic value is the difference between the strike price and the share price, if the stock price is above the strike. Time value is whatever is left, and factors in how volatile the stock is, the time to expiration and interest rates, among other elements. For example, suppose you have a $100 call option while the stock costs $110. Let’s assume the option’s premium is $15. The intrinsic value is $10 ($110 minus $100), while time value is $5.

American options can be exercised at any time between the date of purchase and the expiration date. European options are different from American options in that they can only be exercised at the end of their lives on their expiration date. The distinction between American and European options has nothing to do with geography, only with early exercise. Many options on stock indexes are of the European type. Because the right to exercise early has some value, an American option typically carries a higher premium than an otherwise identical European option. This is because the early exercise feature is desirable and commands a premium.

The less time there is until expiry, the less value an option will have. This is because the chances of a price move in the underlying stock diminish as we draw closer to expiry. This is why an option is a wasting asset. If you buy a one-month option that is out of the money, and the stock doesn’t move, the option becomes less valuable with each passing day. Since time is a component to the price of an option, a one-month option is going to be less valuable than a three-month option. This is because with more time available, the probability of a price move in your favor increases, and vice versa.
When a trader buys an options contract (either a Call or a Put), they have the rights given by the contract, and for these rights, they pay an upfront fee to the trader selling the options contract. This fee is called the options premium, which varies from one options market to another, and also within the same options market depending upon when the premium is calculated. The option's premium is calculated using three main criteria, which are as follows:

So, call options are also much like insurance - you are paying for a contract that expires at a set time but allows you to purchase a security (like a stock) at a predetermined price (which won't go up even if the price of the stock on the market does). However, you will have to renew your option (typically on a weekly, monthly or quarterly basis). For this reason, options are always experiencing what's called time decay - meaning their value decays over time.