Long and short call option profit formula
At expiration, a call's intrinsic value per share is max(stock price minus strike price, zero). A purchased call's profit is intrinsic value minus premium paid. A written call reverses that amount. The result is multiplied by the number of contracts and 100 shares per standard contract.
Before expiration, the calculator substitutes a Black-Scholes theoretical value for intrinsic value, then compares that estimate with the entered premium. This preserves time value in the today and midpoint chart lines.
- Long call P&L = (call value - premium) x contracts x 100
- Short call P&L = (premium - call value) x contracts x 100
Long and short put option profit formula
At expiration, a put's intrinsic value per share is max(strike price minus stock price, zero). A purchased put subtracts the premium, while a written put receives the premium and subtracts intrinsic value. Contract quantity and the 100-share multiplier are applied after the per-share result.
Stock prices are bounded at zero, so a long put has finite theoretical upside. An uncovered short put can lose up to roughly strike price minus premium per share if the underlying falls to zero.
- Long put P&L = (put value - premium) x contracts x 100
- Short put P&L = (premium - put value) x contracts x 100
Multi-leg options strategy profit and break-even calculation
A strategy is the sum of its independent option and stock legs minus entered commissions. A long stock leg contributes stock price minus entry price times shares; a short stock leg reverses that amount. Legs may use different strikes, premiums, quantities, types, and expirations.
The default analysis horizon is the earliest option expiration. This makes same-expiry strategies an expiration payoff while correctly retaining Black-Scholes time value in later-dated calendar, diagonal, and poor man's covered call legs. A custom analysis day can be selected from today through that first expiration.
The break-even solver samples P&L from a zero stock price through a broad upper range and identifies every point where total P&L changes sign. It interpolates within each crossing. Complex strategies may have multiple break-even prices, while some positions may not cross zero in the modeled range.
Options probability of profit and expected move calculation
The probability of profit estimate treats the underlying price on the analysis date as lognormally distributed. It uses the entered stock price, default annualized volatility, risk-free rate, dividend yield, and time horizon, then adds the risk-neutral probability mass inside every price interval where the modeled strategy P&L is positive.
Expected move is stock price times annualized volatility times the square root of time in years. Both values are model outputs, not forecasts. They do not include volatility skew, jumps, earnings events, liquidity, assignment, or a real-world risk premium.
Black-Scholes option price and Greeks methodology
The Black-Scholes calculation uses underlying price, strike, time in years, annualized volatility, a continuously compounded risk-free rate, and continuous dividend yield. Call and put values use the cumulative normal distribution. Delta, gamma, theta, vega, and rho follow the analytical derivatives of the same formula.
Theta is reported per calendar day. Vega is reported for one volatility percentage point, and rho for one interest-rate percentage point. Net strategy Greeks multiply per-share values by long or short direction, contract quantity, and 100 before summing.
Implied volatility solver and convergence
Implied volatility is solved numerically because volatility cannot be isolated in a simple closed-form rearrangement of Black-Scholes. The site uses a binary search between a near-zero annualized volatility and 500 percent, repeatedly choosing the half whose theoretical price is closer to the entered option price.
Observed prices below intrinsic value or above practical bounds can produce extreme results. The solver reports the mathematical match within its search range and does not validate the quote.
Options calculator risk disclosure and model limits
Options involve risk and can expire worthless. Uncovered short positions may create losses greater than the credit received, and a naked short call has unlimited theoretical loss. A modeled probability does not represent a guaranteed outcome, trade quality, liquidity, assignment risk, or personal suitability.
Black-Scholes assumes a lognormal diffusion, constant volatility and rates, continuous trading, and European exercise. Real markets have volatility skew, jumps, discrete dividends, early exercise, bid-ask spreads, fees, taxes, margin rules, and contract-specific settlement. Use outputs for education and arithmetic review only, not as investment advice.