Options come in different styles, and while most traders will concentrate on basic vanilla options, understanding the different styles can help traders understand option pricing.

Most traders understand the basic definition of options: A contract that gives you the right, but not the obligation, to sell or buy an underlying stock or futures contract.

There are many kinds of options in the trading world. Vanilla options are the most common types of option contracts known to investors on the market. There are two kinds of vanilla options: European and American style options. European options are the most simple and basic form of option contracts used by equity market players. 

There are two general forms of every option contract: call and put options. A call gives you the right but not the obligation to buy an underlying at a certain price (the strike) and a put option gives you the right but not obligation to sell an underlying. 

Taking a long call position in a European option gives you the right to buy an underlying asset at a specified strike price on a specified date, known as the maturity date or expiration date. The payoff is the difference between the spot price of the underlying at maturity date, also known as the settlement price, and the strike price. 

Meanwhile, taking a short position in a European call means selling the option contract to receive a premium. Unlike option buyers who have an option to decide whether to exercise their rights, sellers of option contracts have an obligation to fulfill the contract if the counterparty demands it. Because of the premium received, you are obligated to sell the underlying instrument at the agreed strike price if the counterparty decides to exercise his right to buy regardless of the market price. 

Similarly, buying a European put gives you the right to sell at a specified price on its maturity date, while shorting a European put option is another way of buying the underlying asset for a specified price on the contracted date. However, in addition to locking the purchase price, a short put also allows you to receive a premium from selling the option contract. 

The trading of American options is almost the same as European ones, except for one rule. A European option can only be exercised at the end of its life and the payoff is the difference between its strike price and the spot price of the underlying asset at its maturity date. However, American options allow investors to exercise the option at any time between the purchase and the expiration date, meaning that payoff is dependent on any spot price of the underlying during that period of contracted time.

The advantage of American style contracts over European style contracts is the flexibility that they offer. When you own American style contracts, you have the right to exercise at any point up until the expiration date of the contract. 

The greater flexibility investors have in exercising American options results in greater implied volatility of the option contracts. Therefore, American options buyers are able to generate a potentially higher rate of return, while sellers are exposed to greater risks. This feature also increases the value of American style options over European style options.  

The flexibility that American options offer is an essential feature that makes them attractive to investors. As a result, the majority of the commonly traded options on the standardized equity options exchanges fall into the American style category. The Chicago Board Options Exchange (Cboe) and NYSE option exchanges offer standardized American option contracts. 

While American options usually trade on standardized equity options exchanges and are easily accessible to the public, European style option contracts are traded on certain options on futures (indexes and currencies) as well as over-the-counter options, and are tailored to the needs of individual investors. In some cases, there are a few European style options available on exchanges, such as the FLexible EXchange Options offered by Cboe. 

In addition to the vanilla options discussed previously, there are also options other than common European and American style options. They are classified as exotic options because of their difference in structure from vanilla options in terms of how or when a certain payoff is realized. An Asian option, also known as an average option, is one of them. 

The first Asian option was developed in 1987 when David Standish and Mark Spaughton first commercially used pricing formulas for options linked to the average price of crude oil. The contract was named as the Asian option because Standish and Spaughton were working for Bankers Trust in Tokyo when they developed their way of pricing average options.  

The intuition behind Asian options is quite similar to that of the vanilla options; the only difference is that the strike price or the settlement price of Asian options is determined by the average value of the underlying asset over a pre-contracted period. When the strike price is averaged rather than specified by the contract before purchase, such an option is called an average strike option. Similarly, when the settlement price is averaged, the contract is referred to as an average price option. 

Simply put, for average strike options, no one can know the strike price of the option contract until the expiration date. Payoff from such option contracts is the difference between the averaged strike price and the spot price of the underlying at expiration. However, for average price options, the payoff is the difference between a pre-determined strike price and the average value of the underlying over the contract time instead of the spot price of it at maturity. Either way, the payoff from Asian options is dependent on the average price of the underlying instrument over the contracted period. 

Investors with a position in Asian calls or puts are able to buy or sell at the average spot price of the underlying during the contracted period. Because of such features, Asian options are basically averaging the volatility of prices as well as the risks over a certain amount of time. Therefore, compared to vanilla options, Asian options tend to be less expensive, trade at lower premiums as a result of their lower implied volatility and hold less risk for option sellers.

Asian options are most useful for companies using commodities markets to hedge against price fluctuations. Businesses with an ongoing requirement for a specific commodity can lock in a relatively stable price at a lower premium using Asian options. 

Because the settlement price for Asian options can be calculated based on the average price of the underlying asset during a period, Asian options can protect investors from the risks of market manipulation of the underlying instrument at contract maturity.

Asian options are not as popular among the general investors as American options because of their relatively lower volatility and flexibility. They are exclusively traded over-the-counter and are mostly used by commodity firms to hedge ongoing business risks. “You can find people who can make the [Asian option] market for you,” says Dan Keegan, the founder of Optionthinker.com, commented. “But it is nowhere near a liquid market.”

While most traders will only utilize plain vanilla options, understanding how exotic options work and are priced can help you to better understand how options are valued.