Option Strategies

Follow these steps to implement the short 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 CallButterflycall_butterfly filter narrows the universe down to just the three contracts you need to form a short 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).Skip(1).First();
    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 ATM, ITM and OTM contracts from the remaining contracts
    atm_call = sorted(calls, key=lambda x: abs(x.strike - chain.underlying.price))[0]
    itm_call = sorted(calls, key=lambda x: x.strike)[1]
    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.ShortButterflyCallOptionStrategies.short_butterfly_call method with the details of each leg and then pass the result to the Buybuy method.

var optionStrategy = OptionStrategies.ShortButterflyCall(_symbol, otmCall.Strike, atmCall.Strike, itmCall.Strike, expiry);
Buy(optionStrategy, 1);

option_strategy = OptionStrategies.short_butterfly_call(self._symbol, otm_call.strike, atm_call.strike, itm_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)

If the Option is American Option, there is a risk of early assignment on the contracts you sell.

The short call butterfly is a limited-reward-limited-risk strategy. The payoff is

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

The following chart shows the payoff at expiration:

The maximum profit is the net credit received: $C^{ITM}_0 + C^{OTM}_0 - 2\times C^{ATM}_0$. It occurs when the underlying price is less than ITM strike or greater than OTM strike at expiration.

The maximum loss is $K^{ATM} - K^{ITM} + C^{ITM}_0 + C^{OTM}_0 - 2\times C^{ATM}_0$. It occurs when the underlying price is at the same level as when you opened the trade.

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 short 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 gains $1,244.

The following algorithm implements a short call butterfly Option strategy: