Options contracts & payoff
Learning objectives
- Define calls, puts, strike, expiry, and premium; diagram the four basic payoffs.
- Explain why option buyers face defined risk while sellers need margin and respect.
Model Dealer Gamma by Strike, Under Two Assumed Dealer Signs
ModelSPX at 6,000. You buy one 6,050 call for $18. You pay $1,800. At expiry SPX closes at 6,040 — and your $1,800 is gone, even though you were right about direction. This is the first options lesson and the most important: options are not stock with leverage. They are bets on direction and magnitude and timing — get two of three right and you still lose.
The contract (hợp đồng quyền chọn): a call (quyền chọn mua) = the right, not the obligation, to buy at the strike (giá thực hiện). A put (quyền chọn bán) = the right to sell at the strike. Expiry (ngày đáo hạn) = when the right dies. Premium (phí quyền chọn) = what the right costs.
Buyer vs seller: the buyer pays premium, holds rights, can lose at most the premium. The seller collects premium, takes obligations, posts margin — and can lose far more than the premium (a naked short call’s loss is theoretically unlimited). This asymmetry is the whole game.
The four payoffs (hockey sticks):
- Long call: flat below strike, rising above — profit when spot > strike + premium
- Long put: mirror image — profit when spot < strike − premium
- Short call / short put: the inverses — capped gains, open-ended risk
- Breakeven = strike ± premium paid
SPX options are European-style and cash-settled — no early exercise, no shares change hands. Options on ES futures are American-style (exercisable early). For your purposes: SPX is the clean index-options laboratory.
Expirations: monthlies (third Friday), weeklies, and 0DTE — expiring the same day (full lesson M9.06).
Why this matters for a futures trader — the replication intuition: every option can be replicated by trading the underlying dynamically (buying as it rises, selling as it falls). That’s what dealers do — and that replication is the hedging flow that moves your ES chart (M8.06). Options aren’t a separate market; they’re a machine for generating futures orders.
Figure: Payoff diagrams. Long 6,050 call at $18: flat line at −$1,800 from 0 to 6,050, then rising 1-for-1, breakeven marked at 6,068. Caption: “Right on direction (6,040), wrong on magnitude — still a full loss.”
⚠️ Risk note: buying options looks “safe” (defined loss) but most expire worthless — the premium is the full risk and it decays (M9.02). Selling options for income without understanding margin is how accounts blow up; never a beginner trade.
Worked example: SPX 6,000. Buy one 6,050 call at $18 → pay $1,800 (18 × $100 multiplier), maximum loss. Breakeven: 6,068. SPX closes 6,100: intrinsic = 50 pts × $100 = $5,000 − $1,800 = +$3,200. SPX closes 6,040: −$1,800, expired worthless — right on direction, wrong on magnitude and timing. The asymmetry: defined prepaid risk for leveraged upside, at the cost of needing all three — direction, distance, and deadline.
Common mistake: “Calls are bullish, so buying calls is how you trade a rally.” A long call is bullish plus long-magnitude plus long-time — if the rally is slow or small, theta and the breakeven hurdle eat you while the futures trader next to you profits. Match the instrument to the shape of your view, not just its direction.
Recap:
- Call = right to buy, put = right to sell at the strike; premium is the maximum a buyer can lose, while sellers face margin and open-ended risk.
- Breakeven = strike ± premium; SPX options are European cash-settled — the clean laboratory.
- Options are direction + magnitude + timing; every option implies dynamic hedging — the replication machine behind dealer flows.
Quiz: You buy a 5,950 put for $22 with SPX at 6,000. (a) Max loss? (b) Breakeven? (c) P&L if SPX closes at 5,900? Answer: (a) $2,200 (22 × $100) — the premium is the entire risk. (b) 5,928 (5,950 − 22). (c) Intrinsic = 28 × $100 = $2,800 − $2,200 = +$600. Explanation: the put profits only below strike-minus-premium — at 5,900 you’re 28 points ITM but paid 22 points of premium, so the net is 6 points. This is the magnitude hurdle in action: being “right” that SPX fell wasn’t enough; it had to fall past your premium.
Further reading:
- The Beauty of Options (Moontower) — replication and arbitrage-pricing intuition: the mental model for why dealer positioning moves futures.
- Gamma, Vanna, Charm and How Options Influence the Market (Brent Kochuba) — video primer: from basic contracts to dealer flows in one sitting.
Connects to: M8.06 (the dealer preview) → M9.02 (what the premium is actually made of).
Educational content only — not financial advice. Futures trading involves substantial risk of loss.
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