Call option is a type of options contract whose value is directly proportional to the movement in the price of the underlying asset. You buy a cal option when you expect the price of the underlying to go up.
Put option is a type of options contract whose value is inversely proportional to the movement in the price of the underlying asset. You buy a put option when you expect the price of the underlying to go down.
Price of the premium is decided based on the underlying stock price in relation to the strike price (intrinsic value), the length of time until the option expires (time value) and how much the price fluctuates (volatility value).
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