Iron Butterfly
An iron butterfly writes a put and a call at the same strike, at the money, and buys a lower put and a higher call as wings. The worked example writes the FTSE 100 October 10,750 put and call and buys the 10,500 put and 11,000 call for 203.0 points, £2,030.00 at £10 a point. Its worst case is one wing, 250 points, less the credit: £470.00, or £476.80 with opening commissions. In exchange, almost any move costs money: the full credit needs the index to settle exactly on 10,750, and the profit is gone 203 points either side. It is built for a market expected to stay very close to where it is, or for falling implied volatility.
This page assumes the reader has met the iron condor, which it is compared with throughout. Every figure is modelled, not quoted: inputs and method.
Selling the at-the-money straddle and buying both wings
The straddle alone would bring in £4,200.00; the wings cost £2,170.00 of it, and in exchange the loss stops at £470.00 in either direction. Credit : maximum loss is £2,030.00 : £470.00, or 1 : 0.23, the reverse of the condor's £910.00 : £1,590.00. The two body options are one strike, so the position is a short straddle with a floor; move either wing and the result is a broken-wing butterfly, which leans to one side and needs Level 3 on this library's ladder.
These are ICE FTSE 100 options (ESX): £10 a point, European and cash-settled on the exchange delivery settlement price, so neither short option can be assigned early and no shares change hands (FTSE 100 contracts; contract sizes). The four legs are two credit spreads, which IBKR places at its Options Level 3, and spreads need a margin account at IBKR; on the Cboe method the requirement is one wing's width, £2,500.00, of which the £2,030.00 credit covers all but the £470.00 maximum loss (account types and permissions; spread margin).
Open this worked example in the strategy builder. The builder solves each leg's volatility from the fills above.
A 406-point tent: the result at each settlement price
The tent is 406 points wide, 3.8% of the index, between 10,547 and 10,953 (10,547.68 and 10,952.32 after the opening commission). Every point the EDSP lands away from 10,750 costs £10 until a wing is reached. Before expiry the shape is much flatter: with seven days left and the index still at 10,750 the model marks the position at £603.45, less than a third of the credit, because the short straddle still carries a week of time value.
Where the EDSP lands, and why the body is almost never hit
The full £2,023.20 is paid only if the settlement price is exactly 10,750. The model gives each small interval of settlement prices a probability (risk-neutral, from the FTSE skew surface), and the chart multiplies each interval's probability by what the butterfly pays there. The green area is where the expected profit comes from; the red areas are where the expected loss comes from.
The green area adds up to £306.39 and the red areas, with the tails beyond the chart (−£68.24), to −£314.01. They cancel apart from −£7.62, a little less than the £9.41 the credit would earn at Bank Rate over the 45 days. On the model that prices it, the butterfly is a fair bet whose profit is concentrated in a narrow band and whose loss is spread thinly across everything else. The table puts numbers on how narrow the band is.
The model probability of any profit is 29.9%; of the maximum loss, beyond a wing, 63.6%. That is the trade in one line: a large payment in a minority of outcomes and a small, capped loss in most of them. Because an ESX option settles in cash on a Friday-morning auction, the body has no pull of its own; there is no delivery to arrange at 10,750, and nothing in the contract makes the auction more likely to land there. On a physically settled single-stock butterfly the same point becomes pin risk, which the long butterfly page works on GSK and the assignment page explains.
Butterfly or condor: two ways to sell the same 45 days
The gamma row is the real difference. The condor's short strikes are 350 points away, so with the index unchanged its gamma grows only 1.9 times into the last week; the butterfly's short strikes are where the index is, and its gamma grows 12.8 times. The butterfly is paid more per pound at risk and exposed sooner. It is also the smaller position: on the library's 2% sizing convention it fits an account of £23,840 where the condor needs £79,840. The condor page's strike menu shows the same trade-off in six steps; the butterfly is the end of that menu where the short strikes meet.
What skew does to the wings
The two body options sit at the money, where the surface gives 14.00% whichever way it is read, so skew acts on the wings. At a flat 14% the 10,500 put would be worth 103.46 points and the 11,000 call 113.70. On the surface the put wing costs 12.42 points more and the call wing 12.51 points less, and the two almost cancel: the butterfly's credit is 202.82 points on the surface and 202.73 flat. What skew changes is where the loss is likely to come from. On a flat chain the model gives the index about the same chance of settling below 10,500 (31.9%) as above 11,000 (31.8%). On the surface the chances are 28.0% below and 35.6% above: a skewed chain expects moderate rises more often than moderate falls, and balances that with a fatter tail of large falls further out (skew). A butterfly priced off a flat volatility would describe its two wings as equally likely to be reached, and they are not.
The October butterfly from 1 September to 16 October 2026
Branch A: 21 days left, and a half-credit mark that arrives two days before expiry
On Friday 25 September the index is still at 10,750. The butterfly marks 183.13 points: only 10% of the credit has been earned in 24 of the 45 days, because the short straddle's time value decays slowly at first. The library's 21-day convention closes here, at 183.0 points, for +£186.40 after eight commissions. The half-credit convention it uses for credit positions would need a mark of 101.50 points, and with the index unchanged that arrives only on Wednesday 14 October, when the mark falls from 105.15 to 87.86, two days before expiry. On an iron butterfly the two conventions are more than two weeks apart.
What changes the picture is volatility. Had every strike's implied volatility fallen three points by 25 September, the same position would have marked 166.87 and closed at 167.0 for +£346.40. An iron butterfly is paid by the index staying on the body or by implied volatility falling; the calendar alone pays little until the last fortnight, when the gamma is at its largest (see the Greeks below).
Branch B: the lower breakeven tested, and the inverted roll
On Wednesday 16 September, with 30 days left, the index is at 10,550, just above the lower breakeven, and every strike's volatility is two points higher. The butterfly marks 199.96 points, a gain of £30.44 before costs because 15 days of decay offset the fall, and its delta is now £0.21 a point. The risk now sits on the put side. The call spread above the market, 10,750/11,000, can still be bought back for less than it was sold for, and the question is whether moving it down to collect more premium is worth it.
After the roll the short call is below the short put, so the butterfly is inverted: anywhere between 10,550 and 10,750 both short options finish in the money and together pay out exactly 200 points. The roll only makes sense if the total credit collected exceeds that 200 points, which here it does, £2,420.00 against £2,000.00; had it not, the rolled position could not show a profit at any settlement price. The check at seven settlement prices:
The roll turns a worst case of −£476.80 into −£93.60 and caps the best case at +£406.40; it trades the chance of a large profit near 10,750 for a small profit across the middle. A different "defence" on the same day would widen the wings instead, selling the 10,500 put and 11,000 call and buying the 10,250 put and 11,250 call: that collects £1,145.00 more and looks attractive on the screen, while raising the maximum loss to £1,825.00, 3.9 times the original. The mechanics and tax of rolls are on the rolling page; converting a tested condor into a butterfly is priced there too (condor adjustments).
Branch C: through the lower wing with 11 days left
On Monday 5 October the index opens at 10,300, 200 points below the lower wing, with every strike's volatility three points higher. The butterfly marks 215.88 points, a result of −£128.75 before costs, and closing at 216.0 fixes −£143.60. Holding cannot lose more than £476.80; the only way back to a profit is a 250-point recovery into the tent. Past the wing the delta has turned positive, £1.32 a point: the position gains if the index recovers, and its result now rests mostly on where the settlement price lands.
Branch D: held to an EDSP of 10,860
On Friday 16 October the EDSP is 10,860, 110 points above the body. Only the call spread is in the money, and it settles for 110 points, paid by the writer; the put spread expires with nothing to pay. The result is +£923.20: the £2,030.00 credit less £1,100.00 paid and the £6.80 opening commission, with no closing commission on a cash settlement. The tax consequences are worked below.
Across the four branches the conventions moved money between outcomes rather than creating it: +£186.40 at 21 days against £2,023.20 at best by holding; a roll that swapped a −£476.80 worst case for −£93.60; a close at −£143.60 against a £476.80 floor. On the library's 2% sizing convention one butterfly fits an account of £23,840 (sizing framework).
Gamma at the body: Greeks from entry to expiry week
The third column is the one this structure is built around. With a week left and the index on the body, theta is £60.76 a day, but gamma has grown to −£0.197 per 10 points. An instant 1% rise from 10,750 changes the mark by −£31.88 at entry, −£55.90 with 21 days left and −£139.39 with seven. That is why the time convention sits at 21 days, and why the last fortnight is where both the money and the risk arrive together. The stress columns show the delta turning against the move in either direction. Units are explained on the Greeks page.
UK tax: settlement, lapse, and a profitable butterfly that crosses 5 April
Both body options are written: each is a grant dated 1 September, adjusted by any buy-back (s148) or, when settled against the writer, redated to the settlement (s144A(2)). The wings are bought options, each a disposal when sold, when it lapses or when it settles in cash (the rules). Figures assume the £3,000 annual exempt amount is used by other gains; the rate is 18% or 24%.
For the 2026/27 SA108 the four results sit together under "Other property, assets and gains" (which boxes): box 14 counts 4 disposals, box 15 takes the £4,200.00 of premiums received, box 16 the £3,276.80 of costs (the wings, the settlement and the commissions), box 17 the £3,096.60 of gains and box 19 the £2,173.40 of losses. HMRC's own example of a written cash-settled option is in its manual at CG12321.
The trap particular to this structure is the size of its grants. The body options bring in £4,200.00 to earn £2,030.00, so when the trade crosses 5 April the year-by-year figures can be far larger than the result. Open the same butterfly on Tuesday 2 March 2027 for the 16 April 2027 expiry (45 days, the index and volatilities assumed the same, so the prices are the same) and let it settle at 10,860. The put expires, so its grant gain of £2,053.30 belongs to 2026/27, the year it was written. The call's settlement and the two lapsed wings are dated 16 April 2027 and belong to 2027/28, a net result of −£1,130.10. A trade that made £923.20 leaves a 2026/27 gain 2.2 times as large: £369.59 of tax at 18% or £492.79 at 24%, with the 2027/28 loss carried forward. That is relief deferred, not lost, unless it is never used. Closing both body options before the April expiry would have folded each buy-back into its March grant (s148) and kept both body options' results in 2026/27, the year they were written; the wings would still be 2027/28 disposals. The split across 5 April follows from s144A(2), and HMRC's manual does not work such a case through; the tax page sets out the rules: Example 5, written options, counting computations, across 5 April. Options cannot be held in an ISA (wrappers).
Costs, and the same shape on BP
Commission is £6.80 to open and £6.80 to close if the position is closed rather than settled: 0.67% of the credit round trip, the smallest share of any structure in this family because the credit is so large. The bid-ask matters more. If the four-leg package is quoted 3% wide (6.09 points around the mid), paying half of that on the way in and half on the way out costs £30.45 each way, £60.90 round trip: 4.5 times the commission.
On a single share the same shape carries physical settlement. On BP, priced at the 530p model level on Monday 17 August 2026 with 60 days to 16 October and 26% volatility (no ex-dividend date before then), the 500/530/560 iron butterfly fills at 9.00p, 20.75p, 24.00p and 12.00p for a credit of 23.75p, £237.50 on one 1,000-share contract, with a maximum loss of £68.10 including £5.60 of opening commission. Three things differ from the index version. If each BP leg is quoted 10% wide and half of that is paid on the way in and again on the way out, the spread costs £65.75, 27.7% of the credit. Both body options are American and can be assigned early. And if BP finishes near 530p the writer does not know until the next morning whether the put or the call has been exercised against it: an assigned put means buying 1,000 shares for £5,300.00 plus £26.50 of stamp duty (who pays SDRT). A cash-settled index butterfly has none of these; BP is a model underlying here, not a view on BP.
What Cboe's iron butterfly index has returned
Cboe's S&P 500 Iron Butterfly Index (BFLY) writes a one-month at-the-money SPX put and call every month, buys a put and a call 5% out of the money, holds to the monthly settlement and keeps a Treasury bill account of ten times the worst case. Its figures include that interest and assume trades at mid-prices with no costs. Cboe launched it on 3 August 2015; earlier values are Cboe's back-test.
Since launch the index has returned −2.78% a year even with its Treasury bill interest included; its largest fall from a peak, −42.38%, ran from August 2017 to July 2024, and the peak had not been regained by September 2026. It rose in fewer than half of its months. The back-test before launch shows a positive return, the gap that often separates a rule fitted to history from the same rule run forward. The index is a US benchmark with a monthly roll and no costs, so it is evidence about the strategy rather than about this page's example; the condor version is on the iron condor page.