# Option time value

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Option time value

In finance, the time value (TV) (extrinsic or instrumental value) of an option is the premium a rational investor would pay over its current exercise value (intrinsic value), based on its potential to increase in value before expiring. This probability is always greater than zero, thus an option is always worth more than its current exercise value.[1] As an option can be thought of as ‘price insurance’ (e.g. an airline insuring against unexpected soaring fuel costs caused by a hurricane), TV can be thought of as the risk premium the option seller charges the buyer — the higher the expected risk (volatility • time), the higher the premium. Conversely, TV can be thought of as the price an investor is willing to pay for potential upside.

TV decays exponentially to zero at expiration, with a general rule that it will lose ⅓ of its value during the first half of its life and ⅔ in the second half. As an option moves closer to expiry, moving its price requires an increasingly larger move in the price of the underlying security.[2]

## Intrinsic value

The intrinsic value (IV) of an option is the value of exercising it now. If the option has a positive monetary value, it is referred to as being in-the-money, otherwise it is referred to as being out-of-the-money. If an option is out-of-the-money at expiration, its holder will simply abandon the option and it will expire worthless. Because no rational investor would choose to exercise out-of-the-money, an option can never have a negative value.[3]

Value of a call option: max[(SK),0], or (SK) +
Value of a put option: max[(KS),0], or (KS) +

As seen on the graph, the IV of a call option is positive when the underlying asset's spot price S exceeds the option's strike price K.

## Option value

Option Value

Option value (i.e. price) is estimated via a predictive formula such as Black-Scholes or using a numerical method such as the Binomial model. This price incorporates the expected probability of the option finishing "in-the-money". For an out-of-the-money option, 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; for an in-the-money option the chance of being in the money decreases; however the fact that the option cannot have negative value also works in the owner's favor. The sensitivity of the option value to the amount of time to expiry is known as the option's theta. The option value will never be lower than its IV.

As seen on the graph, the full call option value (IV + TV), at a given time t, is the red line.[4]

## Time value

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

`Time Value = Option Value - Intrinsic Value.`

More specifically, TV reflects the probability that the option will gain in IV — become (more) profitable to exercise before it expires.[5] An important factor is the option's volatility. Volatile prices of the underlying instrument can stimulate option demand, enhancing the value. Numerically, this value depends on the time until the expiration date and the volatility of the underlying instrument's price. TV cannot be negative (because the option value is never lower than IV), and converges to zero at expiration. Prior to expiration, the change in TV with time is non-linear, being a function of the option price.[6]

## References

1. ^ Note, however, that there is also a cost component of holding an option (or any asset), based on the time value of money.
2. ^ Understanding Option Pricing Hans Wagner
3. ^ Understanding Option Pricing Hans Wagner
4. ^ Note that the X axis is not time — the graph represents the relationship between price and value at a particular time. With more time left to expiration, the red curve would be higher; the closer to expiration, the more it would approach the blue intrinsic value line.
5. ^ Option premium valuation 22 August 2007
6. ^ Options: Time Value, wolfram.com

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