Option Payoff vs Profit, Margin Calls, and Position Limits
Payoff excludes premium; profit includes it. Covers stock dividend contract adjustments, the 250,000-contract position and exercise limits, and the Hull gold futures margin call case study.
Every worked example in the last two posts subtracted the premium from the max() function. Those were profit calculations, not payoff calculations.
The terminology matters more than it sounds.
Payoff Is Not Profit
Payoff is what the option contract delivers at expiry, treating the premium as if it never existed.
Profit is the net result after accounting for what you paid to buy (long positions) or received to write (short positions) the contract.
One word separates them: premium. Remove the premium from any profit equation and you get the payoff. Add it back and you return to profit.
| Position | Payoff Equation | Profit Equation |
|---|---|---|
| Long call | max(ST - K, 0) | max(ST - K, 0) - premium |
| Short call | -max(ST - K, 0) | premium - max(ST - K, 0) |
| Long put | max(K - ST, 0) | max(K - ST, 0) - premium |
| Short put | -max(K - ST, 0) | premium - max(K - ST, 0) |
The payoff column has no premium. The profit column adds or subtracts it depending on the position.
How the Two Diagrams Differ
The shapes of the payoff and profit diagrams are identical. Only the vertical position shifts.
For a long call with a $1 premium, the profit line sits exactly $1 below the payoff line at every stock price. Left of the strike, the payoff is flat at $0 while the profit is flat at -$1. Right of the strike, both lines rise with the same slope, always $1 apart.
Payoff diagrams always start from zero at the strike. Profit diagrams start from negative premium (long) or positive premium (short). The kink in both diagrams is at K. But the profit line crosses zero at the break-even point, which is K + premium for calls and K - premium for puts. The payoff line crosses zero right at K itself.
Use the explorer below -- switch between Long Call and Short Call and watch how the dashed payoff line and solid profit line sit exactly one premium apart. Raise the premium slider and that gap widens.
Interactive Option Payoff Explorer
Profit Formula
max(ST − 95, 0) − 1.0
Break-even Price
$96.0
Max Profit
Unlimited
Max Loss
-$1.0
The dashed line is payoff (no premium). The solid line is profit (premium included). Both share the same slope right of K -- only their vertical position differs by the premium.
The zero-sum nature of derivatives holds in payoff as much as in profit. At ST = $90 with K = $95, the long call payoff is +$5 and the short call payoff is -$5. Whatever value the buyer receives, the seller gives up exactly that amount. Payoff is just profit with the premium removed -- the mirror-image relationship between positions never breaks.
Stock Dividends and Option Contracts
Post 07 covered how stock splits adjust option contracts. Stock dividends follow the same logic but arrive differently.
A stock dividend means the company issues new shares to existing shareholders rather than paying cash. The formula for any stock dividend: divide 100 by the dividend percentage to find how many existing shares earn one new share.
A 20% stock dividend gives 100 / 20 = 5 -- one new share for every 5 owned. A 25% stock dividend gives 100 / 25 = 4 -- one new share for every 4 owned.
A 25% stock dividend is equivalent to a 5-for-4 split. Before the dividend, you held 4 shares and receive 1 more, ending with 5.
Consider a put option: the right to sell 100 shares at a strike price of $15. The company announces a 25% stock dividend.
| Term | Before dividend | After 25% stock dividend |
|---|---|---|
| Shares per contract | 100 | 125 (x 5/4) |
| Strike price | $15 | $12 ($15 x 4/5) |
| Total contract value | $1,500 | $1,500 |
The total is preserved: 100 x $15 = $1,500; 125 x $12 = $1,500. The exchange adjusts the contract automatically.
Cash dividends are different. When a company pays cash to shareholders, it does not issue new shares. Option contracts are not adjusted for cash dividends. Only stock dividends (and splits) trigger contract term changes.
The standard Black-Scholes model does not account for dividends at all. The Black-Scholes-Merton extension adds a dividend term to handle dividend-paying stocks.
Position Limits and Exercise Limits
Regulators impose two hard caps on option market participants to prevent price manipulation and liquidity crises.
Position limit: the maximum number of option contracts a single investor or entity can hold on the same side of the market for a given security. "Same side" means same directional expectation: bullish (long call + short put combined) or bearish (short call + long put combined). In the US, this limit is 250,000 contracts.
Exercise limit: the maximum number of contracts that can be exercised over any five consecutive business days. This is also 250,000 contracts. One contract covers 100 shares, so 250,000 contracts represent 25 million shares. That volume is enough to move a market, which is exactly why a ceiling exists.
Both limits are set by regulatory bodies. Different countries have different numbers. The 250,000 figure applies to US markets.
Margin Requirements for Futures
When you open a futures position, you do not pay the full contract value upfront. Instead you deposit a smaller amount with your broker as collateral. Three concepts govern how this works.
Margin account: the account you maintain with your broker for all futures trading. All deposits and daily gains or losses flow through here.
Initial margin: the minimum amount required to open a position. It typically ranges from 2% to 12% of the contract's total value, depending on how volatile the underlying asset is. Because futures are marked to market daily, any losses are deducted from this account every evening.
Maintenance margin: the floor your account balance must stay above. If the balance falls below this level, the broker sends a margin call.
Margin call: a notification that your balance has dropped below the maintenance margin. You must deposit additional funds to bring the account back up to the initial margin level. The deposit amount is called the variation margin.
The direction of the rule matters: you must restore the account to the initial margin level, not just to the maintenance margin level.
The Hull Gold Futures Case Study
This example comes from John C. Hull's Options, Futures, and Other Derivatives, and it is the clearest illustration I have seen of how margin calls actually work in practice.
A trader buys two December gold futures contracts. The current futures price is $1,250 per ounce. Each contract covers 100 ounces, so the total position is 200 ounces.
- Initial margin: $6,000 per contract, totaling $12,000
- Maintenance margin: $9,000
- Expiry: 16 days away
Because this is a futures contract, it is marked to market every single day. Each price change directly hits the margin account.
Day 1: price falls by $9 per ounce. Daily loss = $9 x 200 = $1,800. Balance drops from $12,000 to $10,200. No margin call (still above $9,000).
Day 2: price falls to $1,238.30. Additional loss = $540. Balance: $9,660. Cumulative loss: $2,340. Still above the maintenance margin.
Day 3: price rises. The trader gains $1,260. Balance climbs to $10,920.
Day 8: the balance falls below $9,000, landing at approximately $7,980. Margin call issued. Variation margin = $12,000 - $7,980 = $4,020. After depositing, balance returns to $12,000.
A second margin call occurs later in the 16-day window when the price falls again.
One nuance worth noting: if there is a price gain on the same day the variation margin deposit is made, the balance after deposit is not exactly $12,000 but initial margin plus that day's gain. In the Hull example, one day shows a balance of $12,180 after a margin call -- because the trader deposited enough to reach $12,000 and the price also moved in their favor by $180 that day.
The variation margin always targets the initial margin, not the maintenance margin. When the account hits $7,980, the trader does not deposit just enough to clear $9,000. They deposit $4,020 to return to the full $12,000.
Forwards vs Futures on Margin
The entire margin discussion above applies to futures only.
Forward contracts are settled at maturity. There is no daily mark-to-market, no margin account, and no margin calls during the life of the contract. The gain or loss is calculated once at expiry -- comparing the original price to the final price and multiplying by the quantity.
Futures settle every day. Forwards settle once. This daily discipline makes futures cleaner for clearing houses (counterparty risk is bounded each day) but operationally heavier for traders who must manage margin balances continuously.
The Essentials
- Payoff = max() with no premium. Profit = payoff adjusted for premium. Long positions subtract premium (they paid it). Short positions add premium (they received it). The diagrams have identical shapes but different vertical positions -- always separated by exactly the premium amount.
- Stock dividends adjust option contracts the same way splits do. A 25% dividend = a 5-for-4 split. Shares per contract multiply by 5/4; strike price multiplies by 4/5. Total contract value is unchanged. Cash dividends do not affect option contracts.
- Position limit and exercise limit are both 250,000 contracts in the US. Position limit caps what you can hold on one side of the market. Exercise limit caps what you can exercise in any 5 consecutive business days. Both exist to block price manipulation.
- Initial margin is the required deposit to open a futures position (2-12% of contract value). If the balance falls below the maintenance margin, a margin call requires you to deposit the variation margin -- the exact amount needed to restore the account to the initial margin level, not just above the maintenance floor.
- Forwards are settled at maturity; futures are marked to market daily. Daily settlement means futures margin accounts fluctuate every evening, while forward contracts have no interim cash flows.
Further Reading
- Book: Options, Futures, and Other Derivatives by John C. Hull -- the gold futures case study is from Chapter 2
- Wikipedia: Payoff diagram -- Stock dividend -- Margin (finance) -- Margin call
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