Butterfly Spread

Derivatives & Options · intermediate · CC-BY-4.0

A butterfly spread is a multi-leg options strategy that combines a bull spread and a bear spread to create a position that profits maximally when the underlying asset settles near a central strike price at expiration, with defined maximum loss limited to the net premium paid (for long butterfly) or maximum profit limited to the net premium received (for short butterfly).

Key takeaways

• A long call butterfly uses three strikes: buy 1 call at K1, sell 2 calls at K2 (the body), buy 1 call at K3, where K1 < K2 < K3 and K2 − K1 = K3 − K2 (equidistant strikes).
• Maximum profit equals (K2 − K1) − Net Premium Paid and is achieved when the underlying price equals K2 at expiration; maximum loss equals the Net Premium Paid.
• The butterfly is a 'low-volatility' trade: it profits from the underlying remaining near the body (K2), while a short butterfly profits from large moves in either direction — making it a vehicle for expressing directional and volatility views simultaneously.
• Butterflies are also used as proxies for implied probability distributions: the price of a butterfly centered on a strike reflects the market's risk-neutral probability of the underlying settling near that strike.
• Iron butterflies — constructed with puts and calls — create the same payoff profile using net credit collection: sell an ATM straddle, buy an OTM strangle, collecting premium while capping risk.

Explanation

The butterfly spread earns its name from the shape of its payoff diagram, which resembles a butterfly with two wings (the outer strikes) and a peaked body at the central strike. It is constructed as a combination of a bull spread (long K1 call, short K2 call) and a bear spread (long K3 call, short K2 call — note the K2 call is short in both spreads, hence the trader sells two K2 calls). The net debit is: C(K1) − 2×C(K2) + C(K3), which is always positive when strikes are equidistant (by put-call parity and convexity).

The payoff at expiration as a function of the underlying price S(T) is: Net debit if S(T) ≤ K1 (all calls expire worthless, full loss of premium); [S(T) − K1 − net debit] if K1 < S(T) ≤ K2; [K3 − S(T) − net debit] if K2 < S(T) < K3; zero gain above the debit if S(T) ≥ K3. The maximum payoff occurs at S(T) = K2, equaling (K2 − K1) − net debit. With equidistant strikes (K2 − K1 = K3 − K2 = w), maximum profit = w − net debit and the two breakeven points are K1 + net debit and K3 − net debit.

Beyond its basic directional use, the butterfly has important applications in volatility trading. A butterfly spread is the discrete-time analogue of a second-order volatility instrument: its value is sensitive to the implied probability density at K2, making it a tool for expressing views on the 'peak' of the implied volatility distribution. If the market overprices the probability of the underlying settling near K2 (high implied probability at K2 relative to the model), buying the butterfly is a vol-selling trade; if the market underprices this probability, selling the butterfly is a vol-buying trade. Professional volatility traders use butterfly spreads extensively for trading the kurtosis of the implied distribution.

In fixed income, 'butterfly trades' refer to positioning along three points of the yield curve (short-term, mid-term, and long-term yields), analogous to the three-strike option butterfly — this represents a different but structurally related concept. An investor might position for the 'belly' (10-year yield) to outperform both wings (2-year and 30-year yields), effectively constructing a yield-curve butterfly.

Formula

Long Call Butterfly Net Debit = C(K1) − 2×C(K2) + C(K3)
Max Profit = (K2 − K1) − Net Debit  [at S(T) = K2]
Max Loss = Net Debit  [at S(T) ≤ K1 or S(T) ≥ K3]
Breakevens: K1 + Net Debit and K3 − Net Debit

Example

With the S&P 500 ETF (SPY) trading at $475, a trader expects the market to close near this level in 30 days. She buys a butterfly: buy 1 SPY $465 call at $12.00, sell 2 SPY $475 calls at $7.00 each, buy 1 SPY $485 call at $3.50. Net debit = $12.00 − $14.00 + $3.50 = $1.50 per share ($150 per contract set). Maximum profit = ($475 − $465) − $1.50 = $8.50 per share ($850 per 4-leg set). Maximum loss = $1.50 per share ($150). Breakeven at expiration: lower = $465 + $1.50 = $466.50; upper = $485 − $1.50 = $483.50. If SPY closes exactly at $475, all four positions are in or at the money and the payoff is maximized. The $150 maximum risk for $850 maximum gain represents a risk-reward ratio of nearly 5.7:1, but the trade requires the market to remain very close to $475.

Related terms

Accumulator Bear Spread Bull Spread Class Of Options Convexity Implied Volatility Kurtosis Option Premium Put Call Parity Strike Price Time Spread