Option price = intrinsic value + time value

Option price = intrinsic value + time value

The premium is the price at which the contract trades. The premium is the price of the option and is paid by the buyer to the writer, or seller, of the option. In return, the writer of the call option is obligated to deliver the underlying security to an option buyer if the call is exercised or buy the underlying security if the put is exercised. The writer keeps the premium whether or not the option is exercised.
The option price is constitued of 2 price components, the intrinsic value and the time value.
Option price = intrinsic value + time value
Intrinsic value:
The intrinsic value of an option is the difference between the actual price of the underlying security and the strike price of the option.
The intrinsic value of an option reflects the effective financial advantage which would result from the immediate exercise of that option.
The intrinsic value of an option reflects the effective financial advantage which would result from the immediate exercise of that option.

Condition

Call

Put

Strike price < underlying security price

In-the-money

Intrinsic value >0

Out-of-the-money

Intrinsic value = 0

Strike price > underlying security price

Out-of-the-money

Intrinsic value = 0

In-the-money

Intrinsic value >0

Strike price = underlying security price

At-the-money

Intrinsic value = 0

At-the-money

Intrinsic value = 0

The time value: It is determined by the remaining lifespan of the option, the volatility and the cost of refinancing the underlying asset (interest rates).
Time value = option price - intrinsic value

Examples
Option Strike

Option Premium

Stock

Intrinsic Value

Time Value

Call 3

$3

$29

$1

$2

Put 50

$4

$52

$2

$2

Call 25

$2

$25

$0

$2

Put 100

$6

$101

$1

$5

Call 15

$1

$16

$0

$1

Put 40

$18

$55

$15

$3

Notice in the above examples that the intrinsic value plus the time value equals the total premium of the option.

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