Option payoffs and four basic positions

Start with rights and obligations

A call buyer may buy the underlying at strike K; a put buyer may sell it at K. Long means buying the contract and paying a premium. Short means selling it, receiving a premium and accepting the corresponding obligation if exercised. Buying a put is still a long position, despite its right to sell the underlying.

Identify both the option type and your side of the contract before interpreting a graph. This lesson compares profit at a single expiry. The premium is not a refundable deposit, and expiry profit is different from the option's quoted value before expiry.

Why the four positions have different shapes

A long call gains intrinsic value when expiry price Sₜ exceeds K, then subtracts premium p. A long put gains intrinsic value below K. Either buyer may let the option expire and lose the premium paid. Reversing the cash flows gives the short position, so the two sides of the same contract have mirror-image profits.

Receiving a premium does not imply low risk. A naked short call has unbounded potential loss. With a nonnegative underlying price, a naked short put has a bounded but potentially large loss. A chart's finite price range is not a financial limit on that loss.

Compare all four positions with the same numbers

Assume K = 100, premium p = 5 per unit and multiplier M = 100, excluding costs and taxes. At expiry price 120, the long call earns (20 − 5) × 100 = 1,500 and the short call loses 1,500. The long put has no intrinsic value and loses 500; the short put earns 500.

At price 80, the long call loses 500 and the short call earns 500. The long put earns (20 − 5) × 100 = 1,500 and the short put loses 1,500. At exactly 100, both buyers lose 500 and both sellers earn 500. The multiplier scales contract cash amounts, not a rate of return.

The strike is not the break-even price

The call breaks even at K + p = 105; the put at K − p = 95. Strike 100 marks the change in the intrinsic-value slope, not necessarily zero profit. A long call expiring at 103 is in the money but still loses (3 − 5) × 100 = −200 after its premium.

Select each position and move the price from 80 to 120. Observe the kink, zero-profit crossing and slope. Switching long to short reverses profit and loss but leaves that contract's break-even price unchanged: reversing the trade does not alter its terms.

Separate expiry scenarios from today's valuation

The interaction asks what happens at a specified expiry price. It neither predicts that price nor determines a fair premium today. Before expiry, time remaining, volatility, rates and dividends also affect value; the option quote may change even when the underlying does not.

Actual trading involves bid–ask spreads, costs, margin and possible early exercise or assignment. These are outside a simple expiry graph. Use the graph to understand exposure, then assess funding and contract terms separately rather than comparing premiums received alone.

Scope and limitations

One contract, excluding fees, taxes, financing and pre-expiry time value; underlying price is nonnegative. This is expiry profit, not a Black-Scholes price or a margin requirement.