Volatility: If an options market is highly volatile (i.e. if its daily price range is large), the premium will be higher, because the option has the potential to make more profit for the buyer. Conversely, if an options market is not volatile (i.e. if its daily price range is small), the premium will be lower. An options market's volatility is calculated using its long-term price range, its recent price range, and its expected price range before its expiration date, using various volatility pricing models.
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Puts are more or less the mirror image of calls. The put buyer expects the price to go down. Therefore, he pays a premium in the hope that the futures price will drop. If it does, he has two choices: (1) He can close out his long put position at a profit since it will be more valuable; or (2) he can exercise and obtain a profitable short position in the futures contract since the strike price will be higher than the prevailing futures price.

As an example, let's say an initial margin amount of $3,700 allows an investor to enter into a futures contract for 1,000 barrels of oil valued at $45,000—with oil priced at $45 per barrel. If the price of oil is trading at $60 at the contract's expiry, the investor has a $15 gain or a $15,000 profit. The trades would settle through the investor's brokerage account crediting the net difference of the two contracts. Most futures contracts will be cash settled, but some contracts will settle with the delivery of the underlying asset to a centralized processing warehouse.
The fee you are paying to buy the call option is called the premium (it's essentially the cost of buying the contract which will allow you to eventually buy the stock or security). In this sense, the premium of the call option is sort of like a down-payment like you would place on a house or car. When purchasing a call option, you agree with the seller on a strike price and are given the option to buy the security at a predetermined price (which doesn't change until the contract expires).