--- title: "Long Put Butterfly" description: "Long Put butterfly is the combination of buying a bull put spread and a bear put spread." canonical: https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/long-put-butterfly markdown: https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/long-put-butterfly.md language: python source: https://github.com/QuantConnect/Documentation/tree/master/03%20Writing%20Algorithms/22%20Trading%20and%20Orders/08%20Option%20Strategies/07%20Long%20Put%20Butterfly modified: 2026-11-01 index: https://www.quantconnect.com/llms.txt --- # Long Put 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 Put Butterfly > Code examples are shown in Python. Append `?lang=csharp` to this URL for the C# version of this page. ## Introduction **Long Put butterfly** is the combination of a [bull put spread](https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/bull-put-spread.md) and a [bear put spread](https://www.quantconnect.com/docs/v2/writing-algorithms/trading-and-orders/option-strategies/bear-put-spread.md). In this strategy, all the puts have the same underlying stock, the same expiration date, and the strike price distance of ITM-ATM and OTM-ATM put pairs are the same. The long put butterfly strategy consists of buying an ITM put, buying an OTM put, and selling 2 ATM puts. This strategy profits from low volatility. ## Implementation Follow these steps to implement the long put 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.put_butterfly(30, 5)) ``` The `put_butterfly` filter narrows the universe down to just the three contracts you need to form a long put 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 puts = [i for i in chain if i.expiry == expiry and i.right == OptionRight.PUT] if len(puts) == 0: return # Select the ATM, ITM and OTM contracts from the remaining contracts atm_put = sorted(puts, key=lambda x: abs(x.strike - chain.underlying.price))[0] itm_put = sorted(puts, key=lambda x: x.strike)[-2] otm_put = [x for x in puts if x.strike == atm_put.strike * 2 - itm_put.strike][0] ``` 3. In the `on_data` method, place the orders. **Approach A:** Call the `OptionStrategies.butterfly_put` method with the details of each leg and then pass the result to the `buy` method. ```python option_strategy = OptionStrategies.butterfly_put(self._symbol, itm_put.strike, atm_put.strike, otm_put.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_put.symbol, -2), Leg.create(itm_put.symbol, 1), Leg.create(otm_put.symbol, 1) ] self.combo_market_order(legs, 1) ``` ## Strategy Payoff The long put butterfly is a limited-reward-limited-risk strategy. The payoff is $$ \begin{array}{rcll} P^{OTM}_T & = & (K^{OTM} - S_T)^{+}\\ P^{ITM}_T & = & (K^{ITM} - S_T)^{+}\\ P^{ATM}_T & = & (K^{ATM} - S_T)^{+}\\ P_T & = & (P^{OTM}_T + P^{ITM}_T - 2\times P^{ATM}_T + 2\times P^{ATM}_0 - P^{ITM}_0 - P^{OTM}_0)\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & P^{OTM}_T & = & \textrm{OTM put value at time T}\\ & P^{ITM}_T & = & \textrm{ITM put value at time T}\\ & P^{ATM}_T & = & \textrm{ATM put value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K^{OTM} & = & \textrm{OTM put strike price}\\ & K^{ITM} & = & \textrm{ITM put strike price}\\ & K^{ATM} & = & \textrm{ATM put strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & P^{ITM}_0 & = & \textrm{ITM put value at position opening (debit paid)}\\ & P^{OTM}_0 & = & \textrm{OTM put value at position opening (debit paid)}\\ & P^{ATM}_0 & = & \textrm{ATM put value at position opening (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$ In this example, the underlying stock price at expiration is $829.08. You bought an ITM put at a strike of $832.50 for $37.80, sold 2 ATM puts at a strike of $800.00 for $14.70 each, and bought an OTM put at a strike of $767.50 for $5.70. The following chart shows the payoff at expiration: ![Long Put Butterfly strategy payoff at expiration](https://cdn.quantconnect.com/docs/i/writing-algorithms/trading-and-orders/option-strategies/long-put-butterfly.png) The maximum profit is $K^{ATM} - K^{OTM} + 2\times P^{ATM}_0 - P^{ITM}_0 - P^{OTM}_0$. It occurs when the underlying price is the same at expiration as it was when you open the trade. In this case, the payout of the combined bull put and bear put spreads are at their maximum. The maximum loss is the net debit paid, $2\times P^{ATM}_0 - P^{ITM}_0 - P^{OTM}_0$. It occurs when the underlying price is below the ITM strike price or above the OTM strike price 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 put butterfly algorithm: | Asset | Price ($) | Strike ($) | | --- | --- | --- | | ITM put | 37.80 | 832.50 | | ATM put | 14.70 | 800.00 | | OTM put | 5.70 | 767.50 | | Underlying Equity at expiration | 829.08 | - | Therefore, the payoff is $$ \begin{array}{rcll} P^{OTM}_T & = & (K^{OTM} - S_T)^{+}\\ & = & (829.08-832.50)^{+}\\ & = & 0\\ P^{ITM}_T & = & (K^{ITM} - S_T)^{+}\\ & = & (829.08-767.50)^{+}\\ & = & 61.58\\ P^{ATM}_T & = & (K^{ATM} - S_T)^{+}\\ & = & (829.08-800.00)^{+}\\ & = & 29.08\\ P_T & = & (P^{OTM}_T + P^{ITM}_T - 2\times P^{ATM}_T + 2\times P^{ATM}_0 - P^{ITM}_0 - P^{OTM}_0)\times m - fee\\ & = & (61.58+0-29.08\times2-5.70-37.80+14.70\times2)\times100-1.00\times4\\ & = & -1072 \end{array} $$ So, the strategy loses $1,072. The following algorithm implements a long put butterfly Option strategy: ```python class PutButterflyStrategy(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.put_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 put options from the contracts which expire on the furthest expiration date in the option chain. puts = [i for i in chain if i.expiry == expiry and i.right == OptionRight.PUT] if len(puts) == 0: return # sort the put options with the same expiration date according to their strike price. put_strikes = sorted([x.strike for x in puts]) # get at-the-money strike atm_strike = sorted(puts, 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(put_strikes[0] - atm_strike), abs(put_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.put_butterfly(self.symbol, itm_strike, atm_strike, otm_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 put butterfly ``` ### Other Examples For more examples, see the following algorithms: **Demonstration Algorithm** - [IndexOptionPutButterflyAlgorithm.py](https://github.com/QuantConnect/Lean/blob/master/Algorithm.Python/IndexOptionPutButterflyAlgorithm.py) (Python)