--- title: "Short Call Butterfly" description: "The short call butterfly strategy is the combination of selling a bull call spread and a bear call spread." canonical: https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/short-call-butterfly markdown: https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/short-call-butterfly.md language: python source: https://github.com/QuantConnect/Documentation/tree/master/03%20Writing%20Algorithms/22%20Trading%20and%20Orders/08%20Option%20Strategies/06%20Short%20Call%20Butterfly modified: 2026-10-30 index: https://www.quantconnect.com/llms.txt --- # Short 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) > Short Call Butterfly > Code examples are shown in Python. Append `?lang=csharp` to this URL for the C# version of this page. ## Introduction The **short 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 short call butterfly consists of a short ITM call, a short OTM call, and 2 long ATM calls. This strategy profits from high volatility in the underlying Equity price. ## Implementation Follow these steps to implement the short 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_butterfly` filter narrows the universe down to just the three contracts you need to form a short 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 ATM, ITM and OTM contracts from the remaining contracts atm_call = sorted(calls, key=lambda x: abs(x.strike - chain.underlying.price))[0] itm_call = sorted(calls, key=lambda x: x.strike)[1] 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.short_butterfly_call` method with the details of each leg and then pass the result to the `buy` method. ```python option_strategy = OptionStrategies.short_butterfly_call(self._symbol, otm_call.strike, atm_call.strike, itm_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) ``` 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. ## Strategy Payoff The short call butterfly is a limited-reward-limited-risk strategy. The payoff is $$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ P_T & = & (2\times C^{ATM}_T - C^{OTM}_T - C^{ITM}_T - 2\times C^{ATM}_0 + C^{ITM}_0 + C^{OTM}_0)\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{OTM}_T & = & \textrm{OTM call value at time T}\\ & C^{ITM}_T & = & \textrm{ITM call value at time T}\\ & C^{ATM}_T & = & \textrm{ATM call value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K^{OTM} & = & \textrm{OTM call strike price}\\ & K^{ITM} & = & \textrm{ITM call strike price}\\ & K^{ATM} & = & \textrm{ATM call strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & C^{ITM}_0 & = & \textrm{ITM call value at position opening (credit received)}\\ & C^{OTM}_0 & = & \textrm{OTM call value at position opening (credit received)}\\ & C^{ATM}_0 & = & \textrm{ATM call value at position opening (debit paid)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$ 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: ![Short Call Butterfly strategy payoff at expiration](https://cdn.quantconnect.com/docs/i/writing-algorithms/trading-and-orders/option-strategies/short-call-butterfly.png) The maximum profit is the net credit received: $C^{ITM}_0 + C^{OTM}_0 - 2\times C^{ATM}_0$. It occurs when the underlying price is less than ITM strike or greater than OTM strike at expiration. The maximum loss is $K^{ATM} - K^{ITM} + C^{ITM}_0 + C^{OTM}_0 - 2\times C^{ATM}_0$. It occurs when the underlying price is at the same level as when you opened the trade. 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 short 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 $$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ & = & (767.50-829.08)^{+}\\ & = & 0\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ & = & (832.50-829.08)^{+}\\ & = & 3.42\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ & = & (800.00-829.08)^{+}\\ & = & 0\\ P_T & = & (-C^{OTM}_T - C^{ITM}_T + 2\times C^{ATM}_T - 2\times C^{ATM}_0 + C^{ITM}_0 + C^{OTM}_0)\times m - fee\\ & = & (-0-3.42+0\times2+4.90+41.00-15.00\times2)\times100-1.00\times4\\ & = & 1244 \end{array} $$ So, the strategy gains $1,244. The following algorithm implements a short 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.call_butterfly(30, 5) 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.short_butterfly_call(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) ``` ### Other Examples For more examples, see the following algorithms: **Demonstration Algorithm** - [LongAndShortButterflyCallStrategiesAlgorithm.py](https://github.com/QuantConnect/Lean/blob/master/Algorithm.Python/LongAndShortButterflyCallStrategiesAlgorithm.py) (Python)