The option price consists of time value and intrinsic value. For call options, the intrinsic value is defined as the maximum of two numbers - zero and forward price of the underlying minus strike, for put options - zero and strike minus forward price of the asset.
Intrinsic value (call) = max (0 ; F - X)
Intrinsic value (put) = max (0; X - F)
F - forward price
X - option exercise price
However, time value is of most interest to participants of the options market. The time value depends on the following parameters:
1) Time to expiration. The longer the time before the expiration date, the more likely it is that an option will be in-the-money, which increases the time value of the option.
2) Volatility in the price of the underlying asset. Higher volatility leads to a higher probability that the price of the underlying asset will make a big leap up or down. Consider a call option that is out of the money. Volatility increases the probability that the price of the asset will rise to a level significantly above the strike price. Volatility also increases the risk that the price of the asset will fall, but in case of a fall, the call option holder is not obliged to exercise the option. These two scenarios indicate the absolute advantage of the optionholder and represent a risk for the writer of the option. Therefore, the more volatile the price of the asset, the greater the time value of the option on the asset.
Thus, the time value must take into account
1) the advantages of owning an option for the holder and
2) the risks for the writer.
Components of Black-Scholes models
The cost of an option is determined using the following variables:
1) strike or strike price of the option;
2) price of the underlying asset;
3) time before expiration;
4) volatility of the underlying asset;
5) risk-free interest rate.
The figure below shows the fair value of an option with a strike of $100 (line with spaces) for different price levels of the underlying asset - a graph of how the option price depends on the price of the underlying asset in statics. We mean that the other variables, namely volatility, interest rate and time to expiration remain unchanged. The intrinsic value line (continuous line) of an option is also drawn on the chart. The difference between a continuous line and a line with spaces indicates the time value of the option.
Call option and underlying asset
When the option is deep out of the money, it has zero intrinsic value as well as a very low time value. The price of the underlying asset must rise significantly for the option to expire in-the-money. The probability of such an event is very small, but not equal to zero. Therefore, it has to be paid for with the time value.
Figure also shows that as the asset price approaches the strike, the time value increases, i.e. the probability that the option will expire in money increases. It should be noted that the intrinsic value reaches a maximum value when the price of the underlying asset is equal to the strike price.
Time value of the call option
As the option moves in the money area, the total value of the call option continues to grow as the intrinsic value increases along with the price of the asset. However, the time component falls slowly as the price of the asset increases. It follows that buying a call option deep in the money is almost equal to buying the underlying asset. The time value of ITM option is the additional amount that the investor is willing to pay, in addition to the intrinsic value, for the privilege of limited downside risk of the price of the underlying asset.
In contrast to owning the real asset, the loss from an option position is limited to the option premium. The deeper an option is in the money, the lower the time value - the less likely it is that the insurance that the option provides will be required.