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Interactive call option payoff diagram. Toggle between Long Call and Short Call to compare hockey-stick profit/loss profiles, break-even points, and risk exposure at expiration.
Position
X-Axis Variable
S_T - Stock Price at Expiration
This variable varies across the chart from 0 to 200
A call option gives the holder the right, but not the obligation, to buy the underlying asset at the strike price K on or before the expiration date.
The long call buyer pays premium C₀ upfront and profits when the stock price rises above the strike plus premium. The profit formula is:
When S_T ≤ K: The option expires worthless (out-of-the-money). The buyer loses the entire premium C₀. This is the maximum loss.
When S_T > K: The option is exercised (in-the-money). The buyer receives S_T - K from exercise and subtracts the premium paid. Break-even occurs at S_T = K + C₀.
When S_T > K + C₀: The position is profitable. Maximum gain is theoretically unlimited as the stock price can rise without bound.
The short call writer receives premium C₀ upfront and has the obligation to sell the underlying at K if exercised. The profit formula is:
This is the mirror image of the long call. The writer profits when the stock stays below the break-even (K + C₀) and faces unlimited loss if the stock rises significantly.
At this point, the intrinsic value exactly offsets the premium paid. Below this price the long call loses money. Above it the long call profits.
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.
Avoid these frequent errors
Confusing payoff with profit: Payoff = max(S_T - K, 0) ignores premium. Profit = Payoff - Premium. Students calculate payoff and forget to subtract the premium paid
Forgetting premium for the short side: Short call writer RECEIVES premium. Their profit = -max(S_T - K, 0) + C₀. The plus sign on C₀ is because they received it
Wrong break-even direction: For calls, break-even is K + C₀ (above strike). Students sometimes subtract premium from strike, which is the put break-even formula
Thinking OTM options are worthless before expiration: An OTM option still has time value before expiration. This chart only shows expiration payoff where time value is zero
Ignoring that max loss for long call equals premium: Students sometimes think long call can lose more than the premium. The premium IS the maximum loss regardless of how far the stock falls
Confusing call and put exercise conditions: Call is exercised when S_T > K (right to BUY cheap). Put is exercised when S_T < K (right to SELL high). Mixing these up leads to wrong payoff calculations
Strategic insights for success
Memorize the four core formulas: Long call profit = max(S_T - K, 0) - C₀, Short call profit = -max(S_T - K, 0) + C₀. Same pattern for puts with K - S_T inside the max function
Break-even shortcut: Call break-even = K + Premium. Put break-even = K - Premium. This appears frequently in multiple choice questions
Max loss/gain table: Long call: max loss = C₀, max gain = unlimited. Short call: max gain = C₀, max loss = unlimited. Memorize this 2x2 table
Calculator approach: No calculator needed for option payoff. Use max(a, 0) which means "if negative, use zero." Mental math is faster than BA II Plus for these
Question type 1 - Calculate profit at specific S_T: Time 30 seconds. Plug into formula, apply max function, subtract/add premium
Question type 2 - Identify break-even: Time 15 seconds. K + C₀ for calls, K - P₀ for puts
Question type 3 - Compare long vs short: Time 30 seconds. Remember they are mirror images. One's max gain = other's max loss
Common trap - "Value at expiration" vs "Profit": Value = max(S_T - K, 0) without premium. Profit = Value - Premium. Read question carefully
Common trap - Per share vs per contract: If question says "contract" (100 shares), multiply by 100. Default is per share unless stated otherwise