Can someone explain call and put option payoffs with diagrams?
I struggle to visualize option payoffs. I know a call gives the right to buy and a put gives the right to sell, but when I try to draw the payoff diagrams or calculate profit, I get confused. Help!
Option payoffs are best understood visually. Let me walk through all four basic positions.
Definitions first:
- Call option: Right (not obligation) to buy the underlying at the strike price
- Put option: Right (not obligation) to sell the underlying at the strike price
- Premium: The price paid to acquire the option
The four basic positions:
| Position | Payoff at Expiration | Max Gain | Max Loss |
|---|---|---|---|
| Long call | max(S - K, 0) | Unlimited | Premium paid |
| Short call | -max(S - K, 0) | Premium received | Unlimited |
| Long put | max(K - S, 0) | K - Premium | Premium paid |
| Short put | -max(K - S, 0) | Premium received | K - Premium |
Where S = stock price at expiration, K = strike price.
Worked example:
Consider Zenith Corp stock trading at $50. You buy a call option with:
- Strike price (K) = $52
- Premium = $3
Scenario analysis:
| Stock Price at Expiry | Payoff | Profit (Payoff - Premium) |
|---|---|---|
| $45 | max(45-52, 0) = $0 | $0 - $3 = -$3 |
| $52 | max(52-52, 0) = $0 | $0 - $3 = -$3 |
| $55 | max(55-52, 0) = $3 | $3 - $3 = $0 (breakeven) |
| $60 | max(60-52, 0) = $8 | $8 - $3 = +$5 |
| $70 | max(70-52, 0) = $18 | $18 - $3 = +$15 |
Breakeven for a long call = K + Premium = $52 + $3 = $55
Breakeven for a long put = K - Premium
Key relationships:
- Long call and short call are mirror images (zero-sum game)
- Long put and short put are mirror images
- Buying options = limited downside, potentially large upside
- Selling options = limited upside (premium), potentially large downside
Exam tip: Be able to calculate the payoff AND profit for any position given a stock price at expiration. Payoff ignores the premium; profit includes it. CFA Level I frequently tests this distinction.
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