There are also exotic options, which are exotic because there might be a variation on the payoff profiles from the plain vanilla options. Or they can become totally different products all together with "optionality" embedded in them. For example, binary options have a simple payoff structure that is determined if the payoff event happens regardless of the degree. Other types of exotic options include knock-out, knock-in, barrier options, lookback options, Asian options, and Bermudan options. Again, exotic options are typically for professional derivatives traders.
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.
Arbitrage arguments:  When the commodity has plentiful supply then the prices can be very well dictated or influenced by Arbitrage arguments. Arbitrage is basically buying in one market and simultaneously selling in another, profiting from a temporary difference. This is considered riskless profit for the investor/trader. For example, if the price of gold in delhi is INR 30,000 per 10 grams and in Mumbai gold price is INR 35,000 then arbitrageur will purchase gold in Delhi and sell in Mumbai
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. 
If there’s a company you’ve had your eye on and you believe the stock price is going to rise, a “call” option gives you the right to purchase shares at a specified price at a later date. If your prediction pans out you get to buy the stock for less than it’s selling for on the open market. If it doesn’t, your financial losses are limited to the price of the contract.
An option is a contract that allows (but doesn't require) an investor to buy or sell an underlying instrument like a security, ETF or even index at a predetermined price over a certain period of time. Buying and selling options is done on the options market, which trades contracts based on securities. Buying an option that allows you to buy shares at a later time is called a "call option," whereas buying an option that allows you to sell shares at a later time is called a "put option." 
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