Payoff at expiry
Profit or loss at settlement across a band of prices around your strikes. The two break-evens and the two strikes are marked; between the strikes a long strangle sits at its full loss and a short strangle at its full profit.
| Price at expiry | P&L ($) | Zone |
|---|
Wide, cheap, and honest about the tails
A strangle is the volatility trade for people who do not want to pay at-the-money prices. Buy the out-of-the-money call and the out-of-the-money put and you own a position that profits from a big move in either direction for less than a straddle costs — the price of that discount is a wider dead zone your move has to clear. Sell them instead and you collect a credit for betting price sits quietly between two far strikes, with a wide margin for error and a capped reward hanging over an uncapped loss. The seller's high win rate is the seductive part and the uncapped loss is the part that ends accounts, so this tool always shows the probability of profit next to what you can make and what you can lose. If you want the tighter, more expensive at-the-money version, use the straddle calculator; to cap the short strangle's runaway risk by buying wings, price it as an iron condor; and to watch delta and theta move each leg before expiry, open the greeks calculator.
The math
Call the put strike Kp, the call strike Kc, and the total premium P — the sum of the two legs' prices. A strangle has two break-evens: an upper break-even at Kc + P and a lower break-even at Kp − P. The distance between them is the width of the dead zone.
For a long strangle (you buy both legs) the premium P is your maximum loss, taken in full if price finishes anywhere between the two strikes. Profit is uncapped: above Kc you make S − Kc − P, below Kp you make Kp − S − P, so a large move on either side pays. For a short strangle (you sell both legs) the credit P is your maximum profit, kept if price finishes between the strikes; your loss is uncapped beyond the break-evens. Risk/reward for the short is the capped credit over the loss at a reference move.
The probability of profit comes from a one-standard-deviation move σ$ = S · (IV ÷ 100) · √(days ÷ 365), where S is the underlying price and Φ the standard normal CDF. A long strangle profits outside the break-evens, so POP = Φ((S − BEup) ÷ σ$) + Φ((BElo − S) ÷ σ$); a short strangle profits inside them, so POP = Φ((BEup − S) ÷ σ$) − Φ((BElo − S) ÷ σ$). It assumes a driftless, roughly normal return — a first-order estimate that understates the fat tails of real crypto, so it is mildly pessimistic for long strangles and mildly optimistic for short ones.