Option Strategies

Follow these steps to implement the long iron 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, 4, 1);
    SetEndDate(2017, 5, 10);
    SetCash(100000);

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

def initialize(self) -> None:
    self.set_start_date(2017, 4, 1)
    self.set_end_date(2017, 5, 10)
    self.set_cash(100000)

    self.universe_settings.asynchronous = True
    option = self.add_option("GOOG", Resolution.MINUTE)
    self._symbol = option.symbol
    option.set_filter(lambda universe: universe.include_weeklys().iron_butterfly(30, 5));

The IronButterflyiron_butterfly filter narrows the universe down to just the four contracts you need to form a long iron butterfly.

2. In the OnDataon_data method, select the contracts in the strategy legs.

public override void OnData(Slice slice)
{
    if (Portfolio.Invested ||
        !slice.OptionChains.TryGetValue(_symbol, out var chain))
    {
        return;
    }

    // Select expiry
    var expiry = chain.Max(x => x.Expiry);

    // Separate the call and put contracts
    var calls = chain.Where(x => x.Right == OptionRight.Call  && x.Expiry == expiry);
    var puts = chain.Where(x => x.Right == OptionRight.Put && x.Expiry == expiry);
    if (calls.Count() == 0 || puts.Count() == 0) return;

    // Get the ATM and OTM strike prices
    var atmStrike = calls.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().Strike;
    var otmPutStrike = puts.Min(x => x.Strike);
    var otmCallStrike = 2 * atmStrike - otmPutStrike;

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

    # Select expiry
    expiry = max([x.expiry for x in chain])

    # Separate the call and put contracts
    calls = [i for i in chain if i.right == OptionRight.CALL and i.expiry == expiry]
    puts = [i for i in chain if i.right == OptionRight.PUT and i.expiry == expiry]
    if not calls or not puts:
        return

    # Get the ATM and OTM strike prices
    atm_strike = sorted(calls, key = lambda x: abs(chain.underlying.price - x.strike))[0].strike
    otm_put_strike = min([x.strike for x in puts])
    otm_call_strike = 2 * atm_strike - otm_put_strike

3. In the OnDataon_data method, select the contracts and place the orders.

Approach A: Call the OptionStrategies.IronButterflyOptionStrategies.iron_butterfly method with the details of each leg and then pass the result to the Buybuy method.

var ironButterfly = OptionStrategies.IronButterfly(_symbol, otmPutStrike, atmStrike, otmCallStrike, expiry);
Buy(ironButterfly, 2);

iron_butterfly = OptionStrategies.iron_butterfly(self._symbol, otm_put_strike, atm_strike, otm_call_strike, expiry)
self.buy(iron_butterfly, 2)

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.

// Select the contracts
var atmCall = calls.Single(x => x.Strike == atmStrike);
var atmPut = puts.Single(x => x.Strike == atmStrike);
var otmCall = calls.Single(x => x.Strike == otmCallStrike);
var otmPut = puts.Single(x => x.Strike == otmPutStrike);

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

# Select the contracts
atm_call = [x for x in calls if x.strike == atm_strike][0]
atm_put = [x for x in puts if x.strike == atm_strike][0]
otm_call = [x for x in calls if x.strike == otm_call_strike][0]
otm_put = [x for x in puts if x.strike == otm_put_strike][0]

legs = [
    Leg.create(atm_call.symbol, -1),
    Leg.create(atm_put.symbol, -1),
    Leg.create(otm_call.symbol, 1),
    Leg.create(otm_put.symbol, 1)
]
self.combo_market_order(legs, 1)

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

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

The following chart shows the payoff at expiration:

The maximum profit is the net credit received, $C^{ATM}_0 + P^{ATM}_0 - C^{OTM}_0 - P^{OTM}_0$. It occurs when the underlying price stays the same as when you opened the trade.

The maximum loss is $K^C_{OTM} - K^C_{ATM} - C^{ATM}_0 - P^{ATM}_0 + C^{OTM}_0 + P^{OTM}_0$. It occurs when the underlying price is below the OTM put strike price or above the OTM call strike price 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 algorithm:

Asset	Price ($)	Strike ($)
OTM call	1.35	855.00
OTM put	1.50	810.00
ATM call	10.30	832.50
ATM put	9.50	832.50
Underlying Equity at expiration	843.25	-

Therefore, the payoff is

$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^C_{OTM})^{+}\\ & = & (843.25-855.00)^{+}\\ & = & 0\\ C^{ATM}_T & = & (S_T - K^C_{ATM})^{+}\\ & = & (843.25-832.50)^{+}\\ & = & 10.75\\ P^{OTM}_T & = & (K^P_{OTM} - S_T)^{+}\\ & = & (810.00-843.25)^{+}\\ & = & 0\\ P^{ATM}_T & = & (K^P_{ATM} - S_T)^{+}\\ & = & (832.50.00-843.25)^{+}\\ & = & 0\\ P_T & = & (C^{ATM}_T + P^{ATM}_T - C^{OTM}_T - P^{OTM}_T - C^{ATM}_0 - P^{ATM}_0 + C^{OTM}_0 + P^{OTM}_0)\times m - fee\\ & = & (10.75+0-0-0-10.30-9.50+1.35+1.50)\times100-1\times4\\ & = & -624 \end{array} $$

So, the strategy losses $624.

The following algorithm implements a long iron butterfly Option strategy: