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 Initializeinitialize method, set the start date, end date, cash, and Option universe.
    2. private Symbol _symbol;

public override void Initialize()
{
    SetStartDate(2024, 9, 1);
    SetEndDate(2024, 12, 31);
    SetCash(500000);

    UniverseSettings.Asynchronous = true;
    var option = AddOption("GOOG", Resolution.Minute);
    _symbol = option.Symbol;
    option.SetFilter(universe => universe.IncludeWeeklys().CallButterfly(30, 5));
}
    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.include_weeklys().call_butterfly(30, 5))

    The CallSpreadcall_spread filter narrows the universe down to just the three contracts you need to form a long call butterfly.

  2. In the OnDataon_data method, select the contracts of the strategy legs.
    3. public override void OnData(Slice slice)
{
    if (Portfolio.Invested ||
        !slice.OptionChains.TryGetValue(_symbol, out var chain))
    {
        return;
    }

    // Select the call Option contracts with the furthest expiry
    var expiry = chain.Max(x =x> x.Expiry);    
    var calls = chain.Where(x => x.Expiry == expiry && x.Right == OptionRight.Call);
    if (calls.Count() == 0) return;

    // Select the ATM, ITM and OTM contracts from the remaining contracts
    var atmCall = calls.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First();
    var itmCall = calls.OrderBy(x => x.Strike).SkipLast(1).Last();
    var otmCall = calls.Single(x => x.Strike == atmCall.Strike * 2 - itmCall.Strike);
    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 OnDataon_data method, place the orders.

    4. Approach A: Call the OptionStrategies.ButterflyCallOptionStrategies.butterfly_call method with the details of each leg and then pass the result to the Buybuy method.

    var optionStrategy = OptionStrategies.ButterflyCall(_symbol, itmCall.Strike, atmCall.Strike, otmCall.Strike, expiry);
Buy(optionStrategy, 1);
    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 Ordercombo_market_order, Combo Limit Ordercombo_limit_order, or Combo Leg Limit Ordercombo_leg_limit_order method.

    var legs = new List<Leg>()
    {
        Leg.Create(atmCall.Symbol, -2),
        Leg.Create(itmCall.Symbol, 1),
        Leg.Create(otmCall.Symbol, 1)
    };
ComboMarketOrder(legs, 1);
    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

$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ P_T & = & (C^{OTM}_T + C^{ITM}_T - 2\times C^{ATM}_T + 2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0)\times m - fee\\ \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{OTM}_T & = & \textrm{OTM call value at time T}\\ & C^{ITM}_T & = & \textrm{ITM call value at time T}\\ & C^{ATM}_T & = & \textrm{ATM call value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K^{OTM} & = & \textrm{OTM call strike price}\\ & K^{ITM} & = & \textrm{ITM call strike price}\\ & K^{ATM} & = & \textrm{ATM call strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & C^{ITM}_0 & = & \textrm{ITM call value at position opening (debit paid)}\\ & C^{OTM}_0 & = & \textrm{OTM call value at position opening (debit paid)}\\ & C^{ATM}_0 & = & \textrm{OTM call value at position opening (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of long call butterfly

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 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

$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ & = & (767.50-829.08)^{+}\\ & = & 0\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ & = & (832.50-829.08)^{+}\\ & = & 3.42\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ & = & (800.00-829.08)^{+}\\ & = & 0\\ P_T & = & (C^{OTM}_T + C^{ITM}_T - 2\times C^{ATM}_T + 2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0)\times m - fee\\ & = & (0+3.42-0\times2-4.90-41.00+15.00\times2)\times100-1.00\times4\\ & = & -1252 \end{array} $$

So, the strategy loses $1,252.

The following algorithm implements a long call butterfly Option strategy:

public class BearPutSpreadStrategy : QCAlgorithm
{
    private Symbol _symbol;

    public override void Initialize()
    {
        SetStartDate(2024, 9, 1);
        SetEndDate(2024, 12, 31);
        SetCash(500000);

        var option = AddOption("GOOG", Resolution.Minute);
        _symbol = option.Symbol;
        option.SetFilter(universe => universe.IncludeWeeklys().CallButterfly(30, 5));
    }

    public override void OnData(Slice slice)
    {
        if (Portfolio.Invested) return;

        // Get the OptionChain of the symbol
        var chain = slice.OptionChains.get(_symbol, null);
        if (chain == null || chain.Count() == 0) return;

        // sorted the optionchain by expiration date and choose the furthest date
        var expiry = chain.OrderByDescending(x => x.Expiry).First().Expiry;
        
        // filter the call options from the contracts which expire on the furthest expiration date in the option chain.
        var calls = chain.Where(x => x.Expiry == expiry && x.Right == OptionRight.Call);
        if (calls.Count() == 0) return;

        // sort the call options with the same expiration date according to their strike price.
        var callStrikes = calls.Select(x => x.Strike).OrderBy(x => x);

        // get at-the-money strike
        var atmStrike = calls.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().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.
        var spread = Math.Min(Math.Abs(callStrikes.First() - atmStrike), Math.Abs(callStrikes.Last() - atmStrike));

        // select the strike prices for forming the option legs
        var itmStrike = atmStrike - spread;
        var otmStrike = atmStrike + spread;

        var optionStrategy = OptionStrategies.CallButterfly(_symbol, otmStrike, atmStrike, itmStrike, expiry);
        // We open a position with 1 unit of the option strategy
        Buy(optionStrategy, 1);    // if long call butterfly
        //Sell(optionStrategy, 1);   // if short call butterfly
    }
}
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.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:

Demonstration Algorithm
IndexOptionCallButterflyAlgorithm.py Python IndexOptionCallButterflyAlgorithm.cs C#

You can also see our Videos. You can also get in touch with us via Discord.

Did you find this page helpful?

Contribute to the documentation: