Time value, theta & gamma into expiry

Monday 10:00 ET: you buy an SPX 0DTE 6,000 call for $12, SPX at 5,998. By 13:00 SPX is at 6,002 — up, in your direction — and your call is worth $7. You were right and lost 40% in three hours. Nothing is broken. You just met the three forces that price every option on earth.

Premium = intrinsic + time value. Intrinsic (giá trị nội tại) = what the option is worth right now if exercised — for a call, max(0, spot − strike). Time value (giá trị thời gian, extrinsic) = everything else — the market’s price for possibility before expiry. Moneyness (trạng thái): ITM has intrinsic; ATM (strike ≈ spot) holds the most time value — maximum uncertainty about the outcome; OTM is pure time value, a lottery ticket.

Theta (suy giảm thời gian): the daily bleed. Long options pay theta every day; decay is non-linear — slow with 30 days left, a furnace in the final week. Weekends cost ~3 days of theta for zero trading. ATM options decay fastest (they hold the most time value).

Gamma (gia tốc): how fast delta (your directional exposure, 0–1) changes per point of underlying move. Gamma peaks ATM near expiry — a 0DTE ATM option’s delta can swing 0.2 → 1.0 on a 10-point SPX move. For buyers that’s convexity (small moves become big exposure fast — great if right, brutal theta cost if not). For dealers it’s the engine: typically short gamma, their hedge needs explode as spot moves, forcing the mechanical futures buying/selling from M8.06.

The single takeaway: every option’s price is a bet on the future; time value melts a little every day (theta) while positioning leverage concentrates (gamma). Buyers pay for time and need immediate, large moves; the closer to expiry, the more violent both forces get.

Figure: Two curves. Left: theta-decay curve — gentle slope at 30 days, cliff in the last 3 days (labeled “the furnace”). Right: gamma mountain — low and flat far from expiry, spiking ATM into 0DTE (labeled “delta goes 0.2 → 1.0 in minutes”). Caption: “Time melts; gamma concentrates.”

⚠️ Risk note: 0DTE long options can lose 50%+ in an hour on a quiet morning with no adverse move — theta plus midday IV fade combined. That’s the instrument working as designed, not a broken market.

Worked example: the hook, completed. 0DTE 6,000 call bought $12 at 10:00, SPX 5,998 → 6,002 by 13:00 (+4 points your way), call now $7 (−$5, −42%). Decompose: ~$3 of theta (3 hours of a 0DTE’s life is an eternity) + ~$2 of IV fade as midday uncertainty resolved. Contrast: the same $12 on a 30-day option loses maybe $1 in the same 3 hours. And the gamma side: had SPX ripped 15 points instead of drifting 4, that call’s delta would have exploded toward 1.0 — the buyer wasn’t wrong about the instrument, just about the move required. Short-dated long options demand immediacy and magnitude; drifts are losses wearing green underlyings.

Common mistake: “Waiting out” a losing long-option position — “it’ll come back.” Time is the buyer’s enemy, always: every day you wait, theta charges rent and the breakeven hurdle stays fixed. Futures can wait; long options cannot. If the thesis needed today and today is passing, the position is already decided.

Recap:

• Premium = intrinsic (worth now) + time value (price of possibility); ATM holds the most time value, OTM is pure time value.
• Theta bleeds buyers daily, non-linearly — the final week is a furnace; weekends charge ~3 days for nothing.
• Gamma peaks ATM into expiry: delta swings violently, which is buyer convexity — and the dealer’s hedging engine.

Quiz: Two traders each risk $1,200 on a bullish SPX view into Friday. A buys Friday’s 0DTE ATM call at Friday’s open; B buys a 30-day ATM call the prior Monday. SPX drifts up 0.3% into Friday’s close, never spiking. Who makes money, and which two forces explain it? Answer: B probably small-profit or breakeven; A likely loses most of the $1,200. Explanation: A’s 0DTE bled theta all session (~the entire time value) while gamma never got its spike — drift is the worst outcome for short-dated longs. B’s 30-day lost a week of gentle theta but delta did the work on a slow drift. The forces: theta (time decay, brutal on 0DTE) and gamma (needs sharp moves to pay; drift starves it). Same view, opposite results — the expiry, not the direction, decided.

Further reading:

• Options Vanna & Charm (SpotGamma) — the next two greeks, through a concrete SPX dealer: how time and vol mechanically move hedges.
• Predict the Market With the Dark Index and Gamma Exposure (financetldr) — the readable bridge from greeks to positioning context.

Connects to: M9.01 (the contracts) → M9.03 (IV: what the market expects the moves to be).

Educational content only — not financial advice. Futures trading involves substantial risk of loss.