Option Strategies

Follow these steps to implement the long put 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().PutButterfly(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().put_butterfly(30, 5))

The PutButterflyput_butterfly filter narrows the universe down to just the three contracts you need to form a long put 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 puts = chain.Where(x => x.Expiry == expiry && x.Right == OptionRight.Put);
    if (puts.Count() == 0) return;

    // Select the ATM, ITM and OTM contracts from the remaining contracts
    var atmPut = puts.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First();
    var itmPut = puts.OrderBy(x => x.Strike).SkipLast(1).Last();
    var otmPut = puts.Single(x => x.Strike == atmPut.Strike * 2 - itmPut.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
    puts = [i for i in chain if i.expiry == expiry and i.right == OptionRight.PUT]
    if len(puts) == 0:
        return

    # Select the ATM, ITM and OTM contracts from the remaining contracts
    atm_put = sorted(puts, key=lambda x: abs(x.strike - chain.underlying.price))[0]
    itm_put = sorted(puts, key=lambda x: x.strike)[-2]
    otm_put = [x for x in puts if x.strike == atm_put.strike * 2 - itm_put.strike][0]

3. In the OnDataon_data method, place the orders.

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

var optionStrategy = OptionStrategies.ButterflyPut(_symbol, itmPut.Strike, atmPut.Strike, otmPut.Strike, expiry);
Buy(optionStrategy, 1);

option_strategy = OptionStrategies.butterfly_put(self._symbol, itm_put.strike, atm_put.strike, otm_put.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(atmPut.Symbol, -2),
        Leg.Create(itmPut.Symbol, 1),
        Leg.Create(otmPut.Symbol, 1)
    };
ComboMarketOrder(legs, 1);

legs = [
    Leg.create(atm_put.symbol, -2),
    Leg.create(itm_put.symbol, 1),
    Leg.create(otm_put.symbol, 1)
]
self.combo_market_order(legs, 1)

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

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

The following chart shows the payoff at expiration:

The maximum profit is $K^{ATM} - K^{OTM} + 2\times P^{ATM}_0 - P^{ITM}_0 - P^{OTM}_0$. It occurs when the underlying price is the same at expiration as it was when you open the trade. In this case, the payout of the combined bull put and bear put spreads are at their maximum.

The maximum loss is the net debit paid, $2\times P^{ATM}_0 - P^{ITM}_0 - P^{OTM}_0$. It occurs when the underlying price is below the ITM strike price or above the OTM 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 long put butterfly algorithm:

Asset	Price ($)	Strike ($)
ITM put	37.80	832.50
ATM put	14.70	800.00
OTM put	5.70	767.50
Underlying Equity at expiration	829.08	-

Therefore, the payoff is

$$ \begin{array}{rcll} P^{OTM}_T & = & (K^{OTM} - S_T)^{+}\\ & = & (829.08-832.50)^{+}\\ & = & 0\\ P^{ITM}_T & = & (K^{ITM} - S_T)^{+}\\ & = & (829.08-767.50)^{+}\\ & = & 61.58\\ P^{ATM}_T & = & (K^{ATM} - S_T)^{+}\\ & = & (829.08-800.00)^{+}\\ & = & 29.08\\ P_T & = & (P^{OTM}_T + P^{ITM}_T - 2\times P^{ATM}_T + 2\times P^{ATM}_0 - P^{ITM}_0 - P^{OTM}_0)\times m - fee\\ & = & (61.58+0-29.08\times2-5.70-37.80+14.70\times2)\times100-1.00\times4\\ & = & -1072 \end{array} $$

So, the strategy loses $1,072.

The following algorithm implements a long put butterfly Option strategy: