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Option Strategies

Long Call Butterfly

Introduction

The long call butterfly strategy is the combination of a bull call spread and a bear call spread. 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.
  2. Select Language:
    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().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.

  3. In the on_data method, select the contracts of the strategy legs.
  4. Select Language:
    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]
  5. In the on_data method, place the orders.
  6. Approach A: Call the OptionStrategies.butterfly_call method with the details of each leg and then pass the result to the buy method.

    Select Language:
    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, combo_limit_order, or combo_leg_limit_order method.

    Select Language:
    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

COTMT=(STKOTM)+CITMT=(STKITM)+CATMT=(STKATM)+PT=(COTMT+CITMT2×CATMT+2×CATM0CITM0COTM0)×mfee
whereCOTMT=OTM call value at time TCITMT=ITM call value at time TCATMT=ATM call value at time TST=Underlying asset price at time TKOTM=OTM call strike priceKITM=ITM call strike priceKATM=ATM call strike pricePT=Payout total at time TCITM0=ITM call value at position opening (debit paid)COTM0=OTM call value at position opening (debit paid)CATM0=OTM call value at position opening (credit received)m=Contract multiplierT=Time of expiration

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of long call butterfly

The maximum profit is KATMKITM+2×CATM0CITM0COTM0. 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×CATM0CITM0COTM0. 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 on the contracts you sell.

Example

The following table shows the price details of the assets in the long call butterfly:

AssetPrice ($)Strike ($)
OTM call4.90767.50
ATM call15.00800.00
ITM call41.00832.50
Underlying Equity at expiration829.08-

Therefore, the payoff is

COTMT=(STKOTM)+=(767.50829.08)+=0CITMT=(STKITM)+=(832.50829.08)+=3.42CATMT=(STKATM)+=(800.00829.08)+=0PT=(COTMT+CITMT2×CATMT+2×CATM0CITM0COTM0)×mfee=(0+3.420×24.9041.00+15.00×2)×1001.00×4=1252

So, the strategy loses $1,252.

The following algorithm implements a long call butterfly Option strategy:

Select Language:
class LongCallButterflyStrategy(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().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:

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