Can you correctly predict a price rise and still lose money? Consider a call option with a strike of one hundred and a premium of six dollars per underlying unit. At expiry, its payoff is zero below the strike and rises dollar for dollar above it. But payoff leaves out what you paid to buy the option.

Shift the payoff curve down by the six dollar premium to get profit. At an expiry price of one hundred and four, the call pays four but loses two overall. Break even is one hundred and six. A long put reverses the direction: its payoff grows below the strike. With the same premium, its break even is ninety four.

Before expiry, an option has a curved value function, not just a kinked payoff. This illustrative European call uses the Black Scholes model with zero interest, no dividends and constant volatility. The tangent slope is delta: sensitivity to a small underlying price change. Gamma measures how that slope changes. Both are local sensitivities, not promises about future prices.

Watch the extra value fade as time remaining shrinks, holding everything else fixed. Time and implied volatility can offset a favorable underlying move. The Greeks help separate these effects; they do not predict them. Our numbers are per unit, so apply the actual contract multiplier. A purchased option can lose its full premium. Selling uncovered calls can create unlimited losses. Shape, timing and price all matter.