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. private Symbol _symbol;
    
    public override void Initialize()
    {
        SetStartDate(2017, 2, 1);
        SetEndDate(2017, 3, 5);
        SetCash(500000);
        UniverseSettings.Asynchronous = true;
        var option = AddOption("GOOG", Resolution.Minute);
        _symbol = option.Symbol;
        option.SetFilter(universe => universe.IncludeWeeklys().Strikes(-15, 15).Expiration(0, 31));
    }
    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().strikes(-15, 15).expiration(0, 31))
  3. In the OnData method, select the expiration and strikes of the contracts in the strategy legs.
  4. public override void OnData(Slice slice)
    {
        if (Portfolio.Invested) return;
    
        // Get the OptionChain
        var chain = slice.OptionChains.get(_symbol, null);
        if (chain == null || chain.Count() == 0) return;
    
        // Get the furthest expiry date of the contracts
        var expiry = chain.OrderByDescending(x => x.Expiry).First().Expiry;
        
        // Select the call Option contracts with the furthest expiry
        var calls = chain.Where(x => x.Expiry == expiry && x.Right == OptionRight.Call);
        if (calls.Count() == 0) return;
    
        // Get the strike prices of the all the call Option contracts
        var callStrikes = calls.Select(x => x.Strike).OrderBy(x => x);
    
        // Get the ATM strike price
        var atmStrike = calls.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().Strike;
    
        // Get the strike prices for the contracts not ATM
        var spread = Math.Min(Math.Abs(callStrikes.First() - atmStrike), Math.Abs(callStrikes.Last() - atmStrike));
        var itmStrike = atmStrike - spread;
        var otmStrike = atmStrike + spread;
    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 = sorted(chain, key = lambda x: x.expiry, reverse=True)[0].expiry
        
        # 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
    
        # Get the strike prices of the all the call Option contracts
        call_strikes = sorted([x.strike for x in calls])
    
        # Get the ATM strike price
        atm_strike = sorted(calls, key=lambda x: abs(x.strike - chain.underlying.price))[0].strike
    
        # Get the strike prices for the contracts not ATM
        spread = min(abs(call_strikes[0] - atm_strike), abs(call_strikes[-1] - atm_strike))
        itm_strike = atm_strike - spread
        otm_strike = atm_strike + spread
  5. In the OnData method, call the OptionStrategies.ButterflyCall method and then submit the order.
  6. var optionStrategy = OptionStrategies.ButterflyCall(_symbol, otmStrike, atmStrike, itmStrike, expiry);
    Buy(optionStrategy, 1);
    option_strategy = OptionStrategies.butterfly_call(self.symbol, otm_strike, atm_strike, itm_strike, expiry)
    self.buy(option_strategy, 1)

    Option strategies synchronously execute by default. To asynchronously execute Option strategies, set the asynchronous argument to Falsefalse. You can also provide a tag and order properties to the Buy method.

    Buy(optionStrategy, quantity, asynchronous, tag, orderProperties);
    
    self.Buy(option_strategy, quantity, asynchronous, tag, order_properties)
    

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 an American Option, there is a risk of early assignment on the sold contracts.

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 losses $1,252.

The following algorithm implements a long call butterfly Option strategy:


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