Broken-wing put butterfly: credit, vega, and assignment

Unequal put wings and a kept credit

A butterfly-spread is a three-strike structure that joins a nearer vertical with a farther vertical. Equal widths define a regular fly, and unequal widths define a broken wing. A broken-wing put butterfly joins a nearer, narrower bear put vertical to a farther, wider bull put vertical.

The unequal wings can open for a net credit. That credit is kept in full if the underlying finishes above the higher long strike at expiration.

The structure is an option-spread: a multi-leg procedure whose entry, hold, close, or assignment path can be checked as one position rather than as separate options.

How implied volatility moves the open mark

Implied volatility is the options-market volatility input that, through vega, moves the open mark of a short-vega fly before expiration even when the expiration graph is already known. Short-vega loses mark-to-market value when implied volatility rises and can gain when implied volatility falls while the trade is still open.

Before expiration, the broken wing can mark gains faster and larger than an equal-width butterfly if the underlying stabilizes and implied volatility declines, because the structure typically carries more negative vega. A rise in implied volatility while the trade is open can produce larger unrealized losses than a regular butterfly, even though expiration risk remains a remaining limited-loss vertical.

Closing the fly before expiration, instead of holding for assignment, can cost more when volatility is elevated than when volatility is flat or falling.

Assignment and the leftover short put

Assignment is exercise against a remaining short put that can convert the fly into long stock at the short strike, after credits and vertical results already earned. Cost basis is the net share price after applying the opening credit and the embedded vertical results to that assigned short strike.

Below the short strike, tighter-bear-put gains are reduced point for point as the wider bull-put wing dominates. Assigned stock can start with a cost basis above the contemporaneous market price.

Supplied payoff arithmetic

In the supplied payoff arithmetic, a 550/540/510 put butterfly opened for a 1.15 credit. The below-510 outcome was a 30 loss on the wide bull put, a 10 gain on the tight bear put, and the 1.15 credit, for a net of -18.85.

At an expiration print of 530.70, flattening at theoretical value combined a 10 gain, the 1.15 credit, and a 9.30 shortfall versus the extra short 540 strike for a 1.85 net. Taking the 540 assignment and applying the same 11.15 of spread proceeds produced a 528.85 share basis, 1.85 below that print, as unprotected long stock.