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Derivatives
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.
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Study aids
The errors candidates make on this topic, and what to carry into the exam.
Common mistakes
Exam tips