If you are buying an option that is already "in the money" (meaning the option will immediately be in profit), its premium will have an extra cost because you can sell it immediately for a profit. On the other hand, if you have an option that is "at the money," the option is equal to the current stock price. And, as you may have guessed, an option that is "out of the money" is one that won't have additional value because it is currently not in profit.
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Volatility: If an options market is highly volatile (i.e. if its daily price range is large), the premium will be higher, because the option has the potential to make more profit for the buyer. Conversely, if an options market is not volatile (i.e. if its daily price range is small), the premium will be lower. An options market's volatility is calculated using its long-term price range, its recent price range, and its expected price range before its expiration date, using various volatility pricing models.
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.
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."