# Option time value

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Option Value

In finance, the value of an option consists of two components, its intrinsic value and its time value. Time value is simply the difference between option value and intrinsic value.

Intrinsic value is the difference between the exercise price of the option (strike price, K) and the current value of the underlying instrument (spot price, S). If the option does not have positive monetary value, it is referred to as out-the-money. If an option is out-the-money at expiration, its holder will simply "abandon the option" and it will expire worthless. Because of this fact, an option will never have a value less than zero, because the option owner will never choose to lose money by exercising it.

For a call option: value = Max [ (S – K), 0 ]
For a put option: value = Max [ (K – S), 0 ]

On the graph at right, the call option's intrinsic value begins when the underlying asset's spot price exceeds the option's strike price.

Option value (i.e. price) is found via a formula such as Black-Scholes. This price will reflect the "likelihood" of the option "finishing in-the-money ". The further in the future the expiration date - i.e. the longer the time to exercise - the higher the chance of this occurring, and thus the higher the option price. The sensitivity of the option value to the amount of time to expiry is known as the option's "theta"; see The Greeks. The option value will never be lower than its intrinsic value.

In the graph at right, the full option value (intrinsic and time value) is the red line.

Time value is, as above, the difference between option value and intrinsic value, i.e.

Time Value = Option Value - Intrinsic Value.

More specifically, an option's time value captures the possibility, however remote, that the option may increase in value due to volitiliy in the underlying asset. Numerically, this value depends on the time until the expiration date and the volatility of the option. The time value of an option is always positive and declines exponentially with time, reaching zero at the expiration date. At expiration, where the option value is simply its intrinsic value, time value is zero. Prior to expiration, the change in time value with time is non-linear, being a function of the option price. Note that theta does NOT reflect the sensitivity of the time value to the amount of time to expiry.

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