Option Strategies
Long Put Butterfly
Introduction
Long Put butterfly is the combination of a bull put spread and a bear put spread. 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:
- In the
initialize
method, set the start date, end date, cash, and Option universe. - In the
on_data
method, select the contracts of the strategy legs. - In the
on_data
method, place the orders.
def initialize(self) -> None: self.set_start_date(2017, 2, 1) self.set_end_date(2017, 3, 5) 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.include_weeklys().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.
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]
Approach A: Call the OptionStrategies.butterfly_put
method with the details of each leg and then pass the result to the buy
method.
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, combo_limit_order, or combo_leg_limit_order method.
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
POTMT=(KOTM−ST)+PITMT=(KITM−ST)+PATMT=(KATM−ST)+PT=(POTMT+PITMT−2×PATMT+2×PATM0−PITM0−POTM0)×m−fee wherePOTMT=OTM put value at time TPITMT=ITM put value at time TPATMT=ATM put value at time TST=Underlying asset price at time TKOTM=OTM put strike priceKITM=ITM put strike priceKATM=ATM put strike pricePT=Payout total at time TPITM0=ITM put value at position opening (debit paid)POTM0=OTM put value at position opening (debit paid)PATM0=ATM put value at position opening (credit received)m=Contract multiplierT=Time of expirationThe following chart shows the payoff at expiration:

The maximum profit is KATM−KOTM+2×PATM0−PITM0−POTM0. 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×PATM0−PITM0−POTM0. 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 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
POTMT=(KOTM−ST)+=(829.08−832.50)+=0PITMT=(KITM−ST)+=(829.08−767.50)+=61.58PATMT=(KATM−ST)+=(829.08−800.00)+=29.08PT=(POTMT+PITMT−2×PATMT+2×PATM0−PITM0−POTM0)×m−fee=(61.58+0−29.08×2−5.70−37.80+14.70×2)×100−1.00×4=−1072So, the strategy loses $1,072.
The following algorithm implements a long put butterfly Option strategy:
class PutButterflyStrategy(QCAlgorithm): def initialize(self) -> None: self.set_start_date(2017, 2, 1) self.set_end_date(2017, 3, 6) 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.include_weeklys().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: