P/L charts and the chance of profit
Every options strategy, from one call to a six-legged condor, can be drawn as one picture: its profit or loss against the stock price. Read well, the P/L chart says where a trade makes and loses money, how much, and, with implied volatility, how likely each outcome is.
The expiry line
At expiration an option is worth only its intrinsic value, so a strategy's P/L at expiry is made of straight segments with a kink at each strike. A long call is flat at minus the premium below its strike, then rises dollar for dollar above it. Add legs and the kinks add up: a spread is flat on both sides, a condor a plateau with slopes down to either side.
The curve before expiry
Before expiry the options still hold time value, so the P/L is a smooth curve rather than straight lines, valued with Black-Scholes at the legs' implied volatilities. It sits closer to zero than the expiry line and bends toward it as the days pass: that sagging is theta, and how the curve shifts when IV changes is vega.
Breakevens, max profit, max loss
- Breakevens are where the expiry line crosses zero: strike plus premium for a long call, strike minus premium for a long put, one each side for a straddle or a condor.
- Max profit and max loss are the line's highest and lowest points. When a line keeps rising or falling, a naked short call above the stock for one, the loss is unlimited.
- Capital at risk is the max loss, the figure a trade's return should be measured against.
The chance of profit
The chance of profit is the probability that the stock ends where the expiry line is above zero. It is worked out from the same model that prices the options: the stock's price at expiry is taken as lognormal, its spread set by the expiry's at-the-money implied volatility, and the probability added up over every stretch of prices where the strategy makes money.
chance of profit = P(stock at expiry lies where the expiry P/L > 0), price lognormal with the ATM IV
Two cautions. The odds are the market's, not a forecast: if implied volatility runs above what the stock will actually move, as it usually does, the true odds of a premium sale are somewhat better and of a purchase somewhat worse. And real stocks make large moves more often than the lognormal allows, so the tails, where the big losses of a short option live, are underweighted.
Probability against payoff
A high chance of profit is easy to buy: sell a far out-of-the-money option and you will keep the premium most of the time. But the losses, when they come, are many times the typical win. What matters is both together, the chance and the size of what is won and lost. A 90% chance of making $50 and a 10% chance of losing $450 is no edge at all. Compare strategies by their return on the capital at risk alongside their chance, never the chance alone.
In Options Meerkat
A strategy's P/L page (p on a symbol's detail page) draws the expiry line and a curve for any date before it, and gives the max profit and loss, the breakevens, the chance of profit, and the net Greeks. , and . move the date line, v and V scale every leg's IV down and up, H turns it into a heatmap of P/L by price and date, and w saves the strategy as a trade to follow. The templates (n) build more than fifty strategies at the money, and the optimizer (O) ranks them for a price target by an expiry, blending each one's return on its capital at risk with its chance of profit, priced at the natural fill (buying at the ask, selling at the bid).