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.

Options belong to the larger group of securities known as derivatives. A derivative's price is dependent on or derived from the price of something else. As an example, wine is a derivative of grapes ketchup is a derivative of tomatoes, and a stock option is a derivative of a stock. Options are derivatives of financial securities—their value depends on the price of some other asset. Examples of derivatives include calls, puts, futures, forwards, swaps, and mortgage-backed securities, among others.
The currency market, or foreign exchange market ("forex"), was created to facilitate the exchange of currency that becomes necessary as the result of foreign trade. That is, when an entity in one country sells something to an entity in another country, the seller earns that foreign currency. When China sells t-shirts to Walmart, for example, China earns US dollars. When Toyota wants to build a factory in the US, it needs dollars. It may get those from its local bank, which in turn will obtain them in the international currency market. This market exists to facilitate these types of exchanges.
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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).