An option value that includes, in addition to the intrinsic value, the fair value of the forward underlying the option contract. In liquid markets, the forward value of a call option (a European call) is almost consistently above its intrinsic value (of course by the fair value of the forward) unless there is some sort of expected gains (like dividends) that the call holder would receive before expiration. The opposite is true for a put option (European put), i.e., its forward intrinsic value is almost invariably below its intrinsic value unless there are expected payments prior to expiration.
The forward intrinsic value is also known as parity plus basis or fair value premium.
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