WSU

Loading chart library…

Loading chart library

Put Option Payoff Diagram: Long vs Short Put | EasyCFA | Wall Street Uni

Derivatives

Put Option Payoff at Expiration: Long vs Short

Interactive put option payoff diagram. Toggle between Long Put and Short Put to compare profit/loss profiles, break-even points, and maximum gain/loss at expiration.

Subtopic: Basics of Derivative Pricing and Valuation
Level: Fundamental
Status: Featured
Views: 417

Parameters

Position

viewModeView Mode

KStrike Price (K)$

10200

P0Premium (P₀)$

0.550

X-Axis Variable

S_T - Stock Price at Expiration

This variable varies across the chart from 0 to 200

Formula

\begin{aligned}\Pi_{\text{long}} &= \max(K - S_T,\,0) - P_0 \\ \Pi_{\text{short}} &= -\max(K - S_T,\,0) + P_0\end{aligned}

Interactive Chart

Long Put Option Profit/Loss

Position:Long Put

Strike (K):$50.00

Premium (P₀):$5.00

Break-even:$45.00

Formula:Π = max(50 - S_T, 0) - 5

Exercise when:S_T < K ($50)

Max Loss:$5.00|Max Gain:$45.00

Profit/Loss at Expiration

Position

Long Put

Strike Price

$50.00

Break-even

$45.00

Max Loss / Max Gain

$5.00/$45.00

A put option gives the holder the right, but not the obligation, to sell the underlying asset at the strike price K on or before the expiration date.

LONG PUT (BUYER) PAYOFF

The long put buyer pays premium P₀ upfront and profits when the stock price falls below the strike minus premium. The profit formula is:

Profit = max(K - S_T, 0) - P₀

When S_T ≥ K: The option expires worthless (out-of-the-money). The buyer loses the entire premium P₀. This is the maximum loss.

When S_T < K: The option is exercised (in-the-money). The buyer can sell at K while the stock trades at S_T, gaining K - S_T, minus the premium paid.

Break-even occurs at S_T = K - P₀. Below this price the position is profitable.

Maximum gain occurs when S_T = 0: Profit = K - P₀. Unlike calls, put gains are bounded because the stock price cannot go below zero.

SHORT PUT (SELLER/WRITER) PAYOFF

The short put writer receives premium P₀ upfront and has the obligation to buy the underlying at K if exercised. The profit formula is:

Profit = -max(K - S_T, 0) + P₀

The writer profits when the stock stays above the break-even (K - P₀) and faces maximum loss of K - P₀ if the stock falls to zero.

BREAK-EVEN ANALYSIS

Break-even stock price: S_BE = K - P₀

At this point, the intrinsic value exactly offsets the premium paid. Below this price the long put profits. Above this price the long put loses money.

Interactive charts are desktop only

The sliders, formulas and analytics view need more room than a phone screen can give them. Open this chart on a desktop or larger tablet to use the full interactive experience.

Study aids

Working with this chart

The errors candidates make on this topic, and what to carry into the exam.

Common mistakes

Wrong break-even direction: Put break-even is K - P₀ (below strike), not K + P₀. Students often add the premium to strike, which is the call break-even formula
Forgetting puts have bounded gain: Long put max gain = K - P₀, not unlimited. Stock cannot go below zero. Students who memorize "long options have unlimited gain" forget this only applies to calls
Confusing exercise condition: Puts are exercised when S_T < K (right to SELL high). Students sometimes think puts are exercised when stock rises, which is the call exercise condition
Mixing up the max function argument: For puts it is max(K - S_T, 0), for calls it is max(S_T - K, 0). Getting these reversed leads to completely wrong payoff calculations
Ignoring that short put loss is bounded: Unlike short calls (unlimited loss), short put maximum loss is K - P₀. Students sometimes say short put has unlimited loss, confusing it with short call
Wrong sign on premium for short position: Short put writer RECEIVES premium. Profit = -max(K - S_T, 0) + P₀. The premium is ADDED (received), not subtracted

Exam tips

Memorize put formulas: Long put profit = max(K - S_T, 0) - P₀. Short put profit = -max(K - S_T, 0) + P₀. Note K - S_T inside max (opposite of call)
Break-even shortcut: Put break-even = K - Premium (subtract). Call break-even = K + Premium (add). Opposite directions
Max gain/loss table: Long put: max loss = P₀, max gain = K - P₀. Short put: max gain = P₀, max loss = K - P₀
Key difference from calls: Both long and short put positions have BOUNDED payoffs. Long call and short call have unlimited components. This is because stock price has a floor at zero
Question type 1 - Calculate profit at specific S_T: Time 30 seconds. Apply max(K - S_T, 0), then add or subtract premium based on position
Question type 2 - Protective put: Time 1 minute. Combine stock payoff (S_T - purchase price) with put payoff. Show that total loss is capped
Question type 3 - Compare call vs put: Time 30 seconds. Same strike and premium. Call profits when stock rises, put profits when stock falls. Break-evens go in opposite directions
Common trap - "Value at expiration" vs "Profit": Value = max(K - S_T, 0) without premium. Profit includes premium adjustment. Read carefully