Option payoff diagrams
Build an options strategy and watch its payoff at expiry draw itself. Prices come from the Black-Scholes formula using your parameters, so the premium you pay or receive is consistent with the strike, maturity and volatility you chose. Combine up to four option legs with a position in the underlying, or start from a classic strategy and pull it apart.
Black-Scholes parameters
Greeks for these parameters
| Call | Put | |
|---|---|---|
| Price | 5.43 | 4.45 |
| Delta | 0.556 | -0.444 |
| Gamma | 0.0318 | 0.0318 |
| Vega (per 1% vol) | 0.196 | 0.196 |
| Theta (per day) | -0.033 | -0.022 |
| Rho (per 1% rate) | 0.124 | -0.120 |
Greeks curves
Curves use the parameters set above.
How to read a payoff diagram
A payoff diagram shows the profit or loss of a position at expiry for every possible price of the underlying. The horizontal axis is the underlying price at expiry; the vertical axis is profit or loss including the premium paid or received. Where the line crosses zero is a breakeven point (marked in gold above). A long call loses at most its premium and gains without limit above the strike plus premium; a short put keeps at most the premium and loses down to the strike below the breakeven.
Why the premium comes from Black-Scholes
The shape of a payoff at expiry depends only on the strikes and premiums, but for the diagram to be honest the premiums have to be plausible. This tool prices each leg with the Black-Scholes formula at the moment you add it, so a straddle bought at-the-money really does cost two premiums, and the profit region shrinks as you raise volatility or maturity. Open the Greeks panel to see delta, gamma, vega, theta and rho for the current parameters, straight from the closed-form derivatives.
The classic strategies
- Long straddle — a call and a put at the same strike. Profits from a large move in either direction; loses both premiums if the price stays put.
- Long strangle — the same idea with the strikes spread apart, cheaper to open but needing a bigger move.
- Bull call spread — buy a call, sell a higher-strike call. Caps both the cost and the maximum profit.
- Butterfly — long two outer strikes, short two at the middle. A cheap bet that the price finishes near the centre strike.
- Covered call — hold the share, sell a call against it. Income now in exchange for capped upside.
- Protective put — hold the share, buy a put as insurance below the strike.
Studying CM2, SP5 or the CFA? These payoffs and the Black-Scholes results behind them are exactly what the exams test. Memori is a flashcard app built by actuarial students, with ready-made sets for CM2 and SP5 that include the formulas above rendered in proper notation. Join the beta or see the formula guide.
This tool is for education only. It prices European options under the standard Black-Scholes assumptions (no dividends, constant volatility and rates) and is not investment advice.