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BoolQ / can the time value of an option be negative

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can the time value of an option be negative
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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.. 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 ⋅ (\displaystyle \cdot ) 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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