Spot at 90 or 110 (the wings)
Outside or on the outer strikes the structure decays to the net debit. That 5 is the most a long fly can lose on these quantities.
- Expiry P&L
- −5
- Max loss (long)
- 5
Butterfly Calculator
A 1-2-1 fly around a body strike. Long, you want spot near the body; short, you want a larger move. Both sides are defined-risk if the sizes stay 1 / 2 / 1.
Defaults are 90 / 100 / 110 calls priced 20, 10, and 5. Click Calculate, then slide spot, days, and each implied vol. Figures are theoretical and for information only.
Type a symbol, then Load or leave the field. Spot, ~30-day historical realized vol, and a US risk-free proxy are filled when the ticker is found. Strikes and target are recentered near the new spot.
Delayed/free data. Historical realized vol is not implied vol from an options chain. Not investment advice.
New Option 1 Price:
New Option 2 Price:
New Option 3 Price:
How the butterfly P&L is calculated
A long call butterfly buys one lower-strike call, sells two middle-strike calls, and buys one higher-strike call (puts work the same way). You want spot near the body at expiry. A short butterfly flips the signs and wants a larger move.
Expiry P&L = d × [Q(max(S − K, 0) − V) − Q2(max(S − K2, 0) − V2) + Q3(max(S − K3, 0) − V3)]
- d — +1 long butterfly, −1 short
- K, K2, K3 — low, body, and high strikes (defaults 90 / 100 / 110)
- The chart uses call intrinsic even when you select puts; live P&L still reprices the chosen type via Black-Scholes
Default premiums 20 / 10 / 5 imply 37.04%, 23.97%, and 21.03%. Net debit on the long fly is 20 − 2×10 + 5 = 5.
Worked examples
Long call butterfly: long 90 at 20, short two 100s at 10, long 110 at 5. Net debit 5. These points match the chart’s expiry line.
Spot pinned at 100
The body is worth 10 intrinsic on the long 90, the short 100s expire, the 110 expires. Net +5 — the maximum on a 10-point fly that cost 5.
- Expiry P&L
- 5
- Max gain (long)
- 5
Implied vols on the three legs
After Calculate, each premium is inverted on its own strike. A short butterfly would flip the P&L signs of the first two cards.
- 90 / 100 / 110 IV
- 37.04% / 23.97% / 21.03%
Related calculators on this site
A spread is two of these strikes. An iron condor uses puts on the left and calls on the right. A straddle is the uncapped cousin of a short fly.
Butterfly FAQ
When you think realized volatility will be lower than the wings imply and you want spot near the body. Risk is limited to the net debit. A short butterfly is a defined-risk long-volatility view.
A balanced fly is 1 / 2 / 1 so the strike gaps cancel outside the wings. The form defaults to that. If you change the sizes, residual directional risk remains.
Yes — choose Put. Live P&L reprices puts. The expiry chart still plots call-style intrinsic (spot minus each strike), which is the existing behaviour of this page.
Equal gaps (10 points on each side in the default) keep the payoff symmetric. Wider wings raise max gain and usually raise the debit. Compare with a two-strike spread if you only want one side.
A 20 price on a 90-strike call with spot at 100 is a rich ITM premium, so implied vol prints 37.04%. The 5-priced 110 call is closer to a 30% market at 21.03%.
European vanilla Black-Scholes on each of the three legs, the same engine as the option calculator. Each vol slider is independent.
Disclaimer: the contents of this website are for informational purposes only and do not constitute any investment recommendation. The visitor acts at his own risk.