Option Strategies

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.

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().CallButterfly(30, 5));
}

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 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.

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.

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)

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:

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.

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

Asset	Price ($)	Strike ($)
OTM call	4.90	767.50
ATM call	15.00	800.00
ITM call	41.00	832.50
Underlying Equity at expiration	829.08	-

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: