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# Option time value

(Redirected from Time value of an option)

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", i.e. finishes out-the-money, its holder will simply "abandon the option" and it will expire worthless; the option will therefore never have a value less than zero.

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

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.

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.