Long Call: max(0, Stock − Strike) − Premium. Long Put: max(0, Strike − Stock) − Premium. Short positions are the inverse — you collect the premium and lose if the option goes in-the-money. The calculator handles all four legs (long/short × call/put) and shows P&L at expiration.

Delta = price sensitivity to underlying ($Δ option per $1 underlying move). Gamma = rate of change of delta. Theta = time decay per day (always negative for long options). Vega = sensitivity to implied volatility. Together they describe how the option's value changes as time passes, the stock moves, or volatility shifts. Critical for managing positions, not just opening them.

A pricing model that gives the theoretical value of European-style options based on stock price, strike, time to expiry, risk-free rate, and implied volatility. It assumes log-normal price distribution and constant volatility. The Greeks are derivatives of the Black-Scholes formula. Real markets deviate from its assumptions, but it's the universal language for quoting options.

Time decay (theta). An option's value has two components: intrinsic (in-the-money amount) and extrinsic (time value). The extrinsic value erodes faster as expiration nears — accelerating in the final 30 days. ATM options decay fastest in absolute terms; OTM options decay fastest in relative terms.

Almost never — usually it's better to sell the option to capture both intrinsic and remaining extrinsic value. Exception: for American calls on stocks paying a large dividend, early exercise just before ex-dividend date can be optimal. The calculator's profit-at-expiration view shows when assignment becomes profitable.

Long means you BUY the option (pay premium). Max loss = premium paid. Theoretically unlimited profit on calls. Short means you SELL the option (collect premium). Max profit = premium collected. Potentially unlimited loss on uncovered (naked) calls. Short positions earn from time decay; long positions fight against it.