Options Profit Calculator

The model

call = S·N(d₁) − K·e^−rT·N(d₂)
put = K·e^−rT·N(−d₂) − S·N(−d₁)
d₁ = [ln(S/K) + (r + σ²/2)T] ÷ σ√T  ·  d₂ = d₁ − σ√T

Standard Black-Scholes. At the reference case every textbook uses, spot 100, strike 100, one year, 5% rate and 20% volatility, it returns a call at 10.4506 and a put at5.5735, and the two satisfy put-call parity exactly: C − P = S − K·e^−rT. That identity is worth knowing because it is a genuine arbitrage relationship rather than a modelling assumption, so any pricing tool that violates it is broken.

A worked example

Take the default: a long call at the money, spot 100, 30 days, 25% volatility. The model prices it at about 3.02, so the position risks 3.02 per unit and breaks even around 103.02 at expiry. Being right about direction is not enough; the stock has to move roughly 3% in a month simply to return the premium. That gap between "the stock went up" and "the option made money" is the most common way new options traders lose, and the payoff diagram shows it as the flat loss region stretching all the way to the breakeven.

Now switch to the bull call spread. Selling the higher strike cuts the cost substantially, so the breakeven moves closer and the trade profits on a smaller move, at the price of a hard cap on the upside. That is the real trade being made whenever a strategy involves selling an option: you are exchanging unlimited upside for a lower cost and a nearer breakeven. Neither is better; they suit different views about how far price will travel.

Why the model is not the market

Black-Scholes assumes European exercise, no dividends, and one constant volatility for every strike. Real listed equity options are American, many underlyings pay dividends, and the market prices a volatility skew, with out-of-the-money puts typically carrying higher implied volatility than calls because crash protection is in demand. The model is still the right starting point, it is how the greeks are defined and how the market itself quotes volatility, but a difference between the number here and your broker's screen is usually the market being right about something the model omits, not an error.

Whatever the strategy, the sizing question is unchanged: how much of the account is at risk if the position expires worthless. Options make that easy to answer, because for long positions the maximum loss is the premium, and theposition size calculatorturns that into a number of contracts for a fixed percentage of capital. If you are selling options, the max loss figure above is the one to size against, and for undefined-risk strategies it is not bounded at all.