Option price = Intrinsic value + Time value
Time value is one component of the total option value, which depends on the time before expiration and the implied volatility. Time to expiration and volatility are directly proportional to the time value of the option.
The intrinsic value depends on 1) strike, 2) forward price and 3) interest rate. The time value depends on 1) the time before the expiration and 2) the implied volatility.
Fig. 1. Call with strike $50
Fig. 2. Time value
The cost of the option is called time value.
Intrinsic value – the maximum value between zero and the value of the option, if it had been exercised now. The intrinsic value indicates the position of the forward price of the asset relative to the strike price of the option.
Intrinsic value (call) = Max (0; Spot - Strike)
Intrinsic value (put) = Max (0; Strike - Spot)
Only in-the-money options have intrinsic value, while intrinsic value for out of the money and at-the-money options is zero.