Long Put, Short Put, and Moneyness Explained with Examples
Long put payoff is max(K-ST,0) minus premium. Short put is the exact negative. Includes moneyness (ITM/ATM/OTM) for calls and puts, stock split adjustments, and a full risk ranking of all four option positions.
Call option profits increase when the stock rises above the strike. Put options work in the opposite direction.
The equation changes in exactly one place: ST minus K becomes K minus ST. Everything else, the max() function, the premium subtraction, the mirror-image relationship between long and short, stays exactly the same.
Long Put Payoff
The Decision at Expiry
You enter a put contract. The underlying is stock XYZ. The strike price is $100. Three months.
At expiry, the market offers $110 per share. Your option gives you the right to sell at $100. Selling at $110 in the market is better. You do not execute the contract.
At expiry, the market offers $90 per share. Your option gives you the right to sell at $100. You exercise. You sell at $100 while the market would have paid only $90. Profit: $100 minus $90 = $10 per share.
Put options profit when the stock falls below the strike. Call options profit when it rises above. This is the exact reversal.
The Equation
The long put payoff formula is max(K - ST, 0) - premium, where K is the strike price and ST is the stock price at expiry.
The max() function captures the same choice logic as the call. If K is above ST, you exercise and earn K - ST. If K is below ST (stock rose above strike), you walk away and the exercise value is zero.
In both cases, the premium was paid upfront and is always subtracted.
Long Put: K = $95, Premium = $1
| ST | max(95 - ST, 0) | Payoff (- $1 premium) |
|---|---|---|
| $90 | 5 | +$4 |
| $91 | 4 | +$3 |
| $92 | 3 | +$2 |
| $93 | 2 | +$1 |
| $94 | 1 | $0 |
| $95 | 0 | -$1 |
| $96 | 0 | -$1 |
| $97 | 0 | -$1 |
| $98 | 0 | -$1 |
| $99 | 0 | -$1 |
| $100 | 0 | -$1 |
From $95 to $100, the holder does not exercise. Payoff is flat at -$1.
At $94, payoff is exactly $0. This is the break-even point.
Below $94, payoff increases by $1 for every dollar the stock falls.
Break-even = K - premium = $95 - $1 = $94.
Long Put Shape
The long put diagram is the mirror image of the long call, but flipped horizontally:
- Flat at -premium for all prices above the strike
- Rising as the price falls below the break-even
Limited loss. Limited profit. The loss is capped at the premium paid (-$1). The profit grows as the stock falls, but it is bounded: a stock can only fall to $0. Maximum profit = K - premium = $94 per share.
This is the key difference from the long call. Long call has unlimited upside (stock can rise indefinitely). Long put has large but limited upside (stock can only fall to zero).
Short Put Payoff
Short Put Equation
The short put payoff is the exact negative of the long put: premium - max(K - ST, 0).
Whatever the long put holder earns, the short put seller loses. The seller received premium upfront (positive), but must pay out if the buyer exercises.
Short Put: K = $95, Premium = $1
| ST | max(95 - ST, 0) | Payoff ($1 - above) |
|---|---|---|
| $90 | 5 | -$4 |
| $91 | 4 | -$3 |
| $92 | 3 | -$2 |
| $93 | 2 | -$1 |
| $94 | 1 | $0 |
| $95 | 0 | +$1 |
| $96 | 0 | +$1 |
| $97 | 0 | +$1 |
| $98 | 0 | +$1 |
| $99 | 0 | +$1 |
| $100 | 0 | +$1 |
From $95 to $100, the buyer does not exercise. The seller keeps the full premium at +$1.
At $94, payoff hits $0 (break-even).
Below $94, the seller starts losing: $1 for every dollar the stock falls.
Short Put Shape
Flat at +premium above the strike. Falling as the price drops below the break-even.
Limited profit. Limited loss. The seller earns at most the premium received (+$1). The loss grows as the stock falls, but is bounded: the stock can only reach $0, so maximum loss = K - premium = $94 per share.
This is different from short call, where losses are unlimited. Short put has limited (though potentially large) downside. Short call has unlimited downside.
Use the explorer below to try Long Put and Short Put. Notice how raising the strike price shifts the entire floor -- and how a larger premium shrinks the profit window.
Interactive Option Payoff Explorer
Profit Formula
max(ST − 95, 0) − 1.0
Break-even Price
$96.0
Max Profit
Unlimited
Max Loss
-$1.0
Moneyness
Moneyness describes the relationship between the current stock price and the strike price of an option. It tells you whether the option would generate profit if exercised right now.
Three states exist: in the money, at the money, and out of the money.
In the money (ITM): the option has positive exercise value. Money is coming in.
At the money (ATM): exercise value is exactly zero. No profit, no loss from exercising.
Out of the money (OTM): exercise value is zero (you would walk away). Money is going out, through the premium already paid.
One important rule: premium is not counted when calculating moneyness. Moneyness is purely the relationship between ST and K.
Moneyness for Call Options
A call option profits when ST is above K (the holder can buy cheap and sell high). So:
| State | Condition | What it means |
|---|---|---|
| In the money (ITM) | ST > K | Exercising generates profit |
| At the money (ATM) | ST = K | No gain from exercising |
| Out of the money (OTM) | ST < K | Would not exercise |
Moneyness for Put Options
A put option profits when ST is below K (the holder can sell above market). The direction reverses:
| State | Condition | What it means |
|---|---|---|
| In the money (ITM) | ST < K | Exercising generates profit |
| At the money (ATM) | ST = K | No gain from exercising |
| Out of the money (OTM) | ST > K | Would not exercise |
The memory rule: for put options, just reverse the inequality signs from call. ITM for a call means ST > K. ITM for a put means ST < K. Everything else follows.
Moneyness applies at any point during the option's life for American options (since they can be exercised early). For European options, it is most relevant at maturity.
How Stock Splits Affect Option Contracts
Companies occasionally announce a stock split. A 3-for-1 split means every existing share becomes 3 shares. The price per share drops accordingly, but the total market value of the company does not change overnight.
When a stock split occurs, the exchange automatically adjusts the terms of any open option contracts on that stock.
The rule: divide the strike price by the split ratio, multiply the number of shares per contract by the same ratio.
Example before the split: you hold a call option with a strike of $90. One contract covers 100 shares.
After a 3-for-1 split:
| Term | Before split | After split |
|---|---|---|
| Strike price (K) | $90 | $30 (divided by 3) |
| Shares per contract | 100 | 300 (multiplied by 3) |
| Total contract value | $9,000 | $9,000 |
The total contract value is unchanged: 90 times 100 equals 9,000, and 30 times 300 also equals 9,000. The adjustment preserves the economic value of the position.
The option holder does not need to do anything. The exchange updates the contract automatically.
The same logic applies to other split ratios. A 4-for-1 split: divide strike by 4, multiply shares by 4. Value remains the same.
Risk Ranking: Most to Least Dangerous
Comparing all four positions by the size of possible losses:
1. Short call -- most dangerous. Profit is capped at the premium received. But if the stock rises, losses have no ceiling. This is the only position with truly unlimited risk.
2. Short put -- high risk, but bounded. Profit is capped at the premium received. If the stock falls to zero, the maximum loss is K minus premium. Large, but not infinite.
3. Long call -- limited risk, unlimited profit. The buyer loses at most the premium paid. Profit potential is unlimited as the stock rises.
4. Long put -- limited risk, large but bounded profit. The buyer loses at most the premium paid. Profit is bounded because the stock can only fall to zero.
From a pure loss perspective, long call and long put carry identical maximum downside: just the premium. The difference is in the upside: long call has unlimited upside while long put has a theoretical ceiling (stock reaching zero).
The Four Positions at a Glance
| Position | Expectation | Payoff Equation | Max Profit | Max Loss |
|---|---|---|---|---|
| Long call | Bullish | max(ST - K, 0) - P | Unlimited | P (premium) |
| Short call | Bearish | P - max(ST - K, 0) | P (premium) | Unlimited |
| Long put | Bearish | max(K - ST, 0) - P | K - P | P (premium) |
| Short put | Bullish | P - max(K - ST, 0) | P (premium) | K - P |
The Essentials
- Long put payoff = max(K - ST, 0) - premium. The put profits when the stock falls below the strike. Break-even is K minus premium. Maximum profit is K minus premium (if the stock reaches zero).
- Short put is the exact negative of long put. It earns the premium when the stock stays above the strike, and loses when it falls below break-even. Losses are large but bounded.
- Moneyness measures the relationship between ST and K, not the premium. For calls: ITM when ST > K. For puts: ITM when ST < K. The direction is reversed.
- Stock splits automatically adjust option contracts. Strike price divides by the split ratio; shares per contract multiply by the same ratio. Total contract value is preserved.
- Short call carries unlimited risk. Of the four positions, it is the only one where losses have no ceiling. Short put has limited but potentially large risk. Long positions lose at most the premium.
The concepts covered across these posts (what options are, the four positions, payoff equations, moneyness) form the foundation. The next layer covers the Greeks: Delta, Gamma, Vega, Theta, and Rho. These measure how sensitive an option's price is to changes in the underlying price, time, volatility, and interest rates.
Further Reading
- Book: Options, Futures, and Other Derivatives by John C. Hull
- Wikipedia: Put option · Moneyness · Stock split · Option (finance)
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