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.
However, unless soybeans were priced at $15 per bushel in the market on the expiration date, the farmer had either gotten paid more than the prevailing market price or missed out on higher prices. If soybeans were priced at $13 per bushel at expiry, the farmer's $15 hedge would be $2 per bushel higher than the market price for a gain of $2,000,000. On the other hand, if soybeans were trading at $17 per bushel at expiry, the $15 selling price from the contract means the farmer would have missed out on an additional $2 per bushel profit.
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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.
The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium." When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price. The price you are paying for that bet is the premium, which is a percentage of the value of that asset.