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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 the probability it will increase in value before expiry.
For an American option this value is always greater than zero in a fair market, thus an option is always worth more than its current exercise value.
For a European option, the extrinsic value can be negative.
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.

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