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.

For example, if you believe the share price of a company currently trading for $100 is going to rise to $120 by some future date, you’d buy a call option with a strike price less than $120 (ideally a strike price no higher than $120 minus the cost of the option, so that the option remains profitable at $120). If the stock does indeed rise above the strike price, your option is in the money.
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.
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However, for put options (right to sell), the opposite is true - with strike prices below the current share price being considered "out of the money" and vice versa. And, what's more important - any "out of the money" options (whether call or put options) are worthless at expiration (so you really want to have an "in the money" option when trading on the stock market). 


According to Nasdaq's options trading tips, options are often more resilient to changes (and downturns) in market prices, can help increase income on current and future investments, can often get you better deals on a variety of equities and, perhaps most importantly, can help you capitalize on that equity rising or dropping over time without having to invest in it directly. 

When buying or selling options, the investor or trader has the right to exercise that option at any point up until the expiration date - so simply buying or selling an option doesn't mean you actually have to exercise it at the buy/sell point. Because of this system, options are considered derivative securities - which means their price is derived from something else (in this case, from the value of assets like the market, securities or other underlying instruments). For this reason, options are often considered less risky than stocks (if used correctly). 
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