--- title: "Long Call Butterfly" description: "The long call butterfly strategy is the combination of buying a bull call spread and a bear call spread." canonical: https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/long-call-butterfly markdown: https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/long-call-butterfly.md language: python source: https://github.com/QuantConnect/Documentation/tree/master/03%20Writing%20Algorithms/22%20Trading%20and%20Orders/08%20Option%20Strategies/05%20Long%20Call%20Butterfly modified: 2026-10-30 index: https://www.quantconnect.com/llms.txt --- # Long Call Butterfly [Documentation](https://www.quantconnect.com/docs/v2.md) > [Writing Algorithms](https://www.quantconnect.com/docs/v2/writing-algorithms.md) > Trading and Orders > [Option Strategies](https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies.md) > Long Call Butterfly > Code examples are shown in Python. Append `?lang=csharp` to this URL for the C# version of this page. ## Introduction The **long call butterfly** strategy is the combination of a [bull call spread](https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/bull-call-spread.md) and a [bear call spread](https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/bear-call-spread.md). In the call butterfly, all of the calls should have the same underlying Equity, the same expiration date, and the same strike price distance between the ITM-ATM and OTM-ATM call pairs. The long call butterfly consists of a long ITM call, a long OTM call, and 2 short ATM calls. This strategy profits from low volatility in the underlying Equity price. ## Implementation Follow these steps to implement the long call butterfly strategy: 1. In the `initialize` method, set the start date, end date, cash, and [Option universe](https://www.quantconnect.com/docs/v2/writing-algorithms/universes/equity-options.md). ```python def initialize(self) -> None: self.set_start_date(2024, 9, 1) self.set_end_date(2024, 12, 31) self.set_cash(500000) self.universe_settings.asynchronous = True option = self.add_option("GOOG", Resolution.MINUTE) self._symbol = option.symbol option.set_filter(lambda universe: universe.call_butterfly(30, 5)) ``` The `call_spread` filter narrows the universe down to just the three contracts you need to form a long call butterfly. 2. In the `on_data` method, select the contracts of the strategy legs. ```python def on_data(self, slice: Slice) -> None: if self.portfolio.invested: return # Get the OptionChain. chain = slice.option_chains.get(self._symbol, None) if not chain: return # Get the furthest expiry date of the contracts. expiry = max([x.expiry for x in chain]) # Select the call Option contracts with the furthest expiry. calls = [i for i in chain if i.expiry == expiry and i.right == OptionRight.CALL] if len(calls) == 0: return # Select the target contracts. atm_call = sorted(calls, key=lambda x: abs(x.strike - chain.underlying.price))[0] itm_call = sorted(calls, key=lambda x: x.strike)[-2] otm_call = [x for x in calls if x.strike == atm_call.strike * 2 - itm_call.strike][0] ``` 3. In the `on_data` method, place the orders. **Approach A:** Call the `OptionStrategies.butterfly_call` method with the details of each leg and then pass the result to the `buy` method. ```python option_strategy = OptionStrategies.butterfly_call(self._symbol, itm_call.strike, atm_call.strike, otm_call.strike, expiry) self.buy(option_strategy, 1) ``` **Approach B:** Create a list of `Leg` objects and then call the [combo_market_order](https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/order-types/combo-market-orders.md), [combo_limit_order](https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/order-types/combo-limit-orders.md), or [combo_leg_limit_order](https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/order-types/combo-leg-limit-orders.md) method. ```python legs = [ Leg.create(atm_call.symbol, -2), Leg.create(itm_call.symbol, 1), Leg.create(otm_call.symbol, 1) ] self.combo_market_order(legs, 1) ``` ## Strategy Payoff The long call butterfly is a limited-reward-limited-risk strategy. The payoff is $$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ P_T & = & (C^{OTM}_T + C^{ITM}_T - 2\times C^{ATM}_T + 2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0)\times m - fee\\ \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{OTM}_T & = & \textrm{OTM call value at time T}\\ & C^{ITM}_T & = & \textrm{ITM call value at time T}\\ & C^{ATM}_T & = & \textrm{ATM call value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K^{OTM} & = & \textrm{OTM call strike price}\\ & K^{ITM} & = & \textrm{ITM call strike price}\\ & K^{ATM} & = & \textrm{ATM call strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & C^{ITM}_0 & = & \textrm{ITM call value at position opening (debit paid)}\\ & C^{OTM}_0 & = & \textrm{OTM call value at position opening (debit paid)}\\ & C^{ATM}_0 & = & \textrm{OTM call value at position opening (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$ In this example, the underlying stock price at expiration is $829.08. You bought an OTM call at a strike of $767.50 for $4.90, sold 2 ATM calls at a strike of $800.00 for $15.00 each, and bought an ITM call at a strike of $832.50 for $41.00. The following chart shows the payoff at expiration: ![Long Call Butterfly strategy payoff at expiration](https://cdn.quantconnect.com/docs/i/writing-algorithms/trading-and-orders/option-strategies/long-call-butterfly.png) The maximum profit is $K^{ATM} - K^{ITM} + 2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0$. It occurs when the underlying price is the same price at expiration as it was when opening the position and the payouts of the bull and bear call spreads are at their maximum. The maximum loss is the net debit paid: $2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0$. It occurs when the underlying price is less than ITM strike or greater than OTM strike at expiration. If the Option is American Option, there is a risk of [early assignment](https://www.quantconnect.com/docs/v2/writing-algorithms/reality-modeling/options-models/assignment.md) on the contracts you sell. ## Example The following table shows the price details of the assets in the long call butterfly: | Asset | Price ($) | Strike ($) | | --- | --- | --- | | OTM call | 4.90 | 767.50 | | ATM call | 15.00 | 800.00 | | ITM call | 41.00 | 832.50 | | Underlying Equity at expiration | 829.08 | - | Therefore, the payoff is $$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ & = & (767.50-829.08)^{+}\\ & = & 0\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ & = & (832.50-829.08)^{+}\\ & = & 3.42\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ & = & (800.00-829.08)^{+}\\ & = & 0\\ P_T & = & (C^{OTM}_T + C^{ITM}_T - 2\times C^{ATM}_T + 2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0)\times m - fee\\ & = & (0+3.42-0\times2-4.90-41.00+15.00\times2)\times100-1.00\times4\\ & = & -1252 \end{array} $$ So, the strategy loses $1,252. The following algorithm implements a long call butterfly Option strategy: ```python class LongCallButterflyStrategy(QCAlgorithm): def initialize(self) -> None: self.set_start_date(2024, 9, 1) self.set_end_date(2024, 12, 31) self.set_cash(500000) option = self.add_option("GOOG", Resolution.MINUTE) self.symbol = option.symbol option.set_filter(self.universe_func) def universe_func(self, universe: OptionFilterUniverse) -> OptionFilterUniverse: return universe.strikes(-15, 15).expiration(timedelta(0), timedelta(31)) def on_data(self, data: Slice) -> None: # avoid extra orders if self.portfolio.invested: return # Get the OptionChain of the self.symbol chain = data.option_chains.get(self.symbol, None) if not chain: return # sorted the optionchain by expiration date and choose the furthest date expiry = sorted(chain, key = lambda x: x.expiry, reverse=True)[0].expiry # filter the call options from the contracts which expire on the furthest expiration date in the option chain. calls = [i for i in chain if i.expiry == expiry and i.right == OptionRight.CALL] if len(calls) == 0: return # sort the call options with the same expiration date according to their strike price. call_strikes = sorted([x.strike for x in calls]) # get at-the-money strike atm_strike = sorted(calls, key=lambda x: abs(x.strike - chain.underlying.price))[0].strike # Get the distance between lowest strike price and ATM strike, and highest strike price and ATM strike. # Get the lower value as the spread distance as equidistance is needed for both side. spread = min(abs(call_strikes[0] - atm_strike), abs(call_strikes[-1] - atm_strike)) # select the strike prices for forming the option legs itm_strike = atm_strike - spread otm_strike = atm_strike + spread option_strategy = OptionStrategies.call_butterfly(self.symbol, otm_strike, atm_strike, itm_strike, expiry) # We open a position with 1 unit of the option strategy self.buy(option_strategy, 1) # self.sell(option_strategy, 1) if short call butterfly ``` ### Other Examples For more examples, see the following algorithms: **Demonstration Algorithm** - [IndexOptionCallButterflyAlgorithm.py](https://github.com/QuantConnect/Lean/blob/master/Algorithm.Python/IndexOptionCallButterflyAlgorithm.py) (Python)