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Stock exchanges do not decide the premium for Options. Option pricing models such as Black-Scholes or Binomial are used to calculate the premium on Options. The price of Options is also determined by market factors such as demand and supply.
The sum of intrinsic value and time value is what makes an Option premium. Call options have an intrinsic value that is determined as-
Intrinsic Value is equals to Strike Price - Spot Price
The intrinsic value of put options is calculated as follows:
Intrinsic Value is equals to Strike price - Spot price
It is the difference between intrinsic and premium value.
Time Value = Premium Intrinsic Value
The volatility of the underlying and the time until expiration of the option premium are factors that affect the time value of the option Premium.
There are many factors that go into determining the premium for an Option.