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A stock trades at 84. Three-month calls: the 80-strike is offered at 6.70, the 90-strike at 1.90. Split each premium into intrinsic value and time value. Which option carries more time value, and at what moneyness is time value greatest in general, and why?

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The split. Intrinsic value of a call is max(S - K, 0); time value is premium minus intrinsic. | Option | Premium | Intrinsic | Time value | |---|---|---|---| | 80-strike | 6.70 | 84 - 80 = 4 | mathbf2.70 | | 90-strike | 1.90 | 0 | 1.90 | The in-the-money 80-strike carries more time value here (2.70 vs 1.90), but notice how the composition differs: the 90-strike is pure optionality. Where time value peaks: at the money. Time value is the market price of not yet knowing which side of the strike you'll finish on. - Deep ITM: exercise is near-certain, the call is basically stock minus strike; optionality adds little. - Deep OTM: expiring worthless is near-certain; there is little hope to pay for. - ATM: a coin flip. Each dollar of movement matters one-for-one on one side and not at all on the other, that asymmetry is worth the most when the outcome is most uncertain. Formally, time value tracks the option's remaining convexity, which (like gamma and vega) is maximized near the strike. The trap: quoting "time value" as if it always decays smoothly to zero. It does for ATM options, but a deep-ITM European put can have negative time value when rates are positive (price below intrinsic), s

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