Option Strategies

Follow these steps to implement the short 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 short 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.ShortButterflyPutOptionStrategies.short_butterfly_put method with the details of each leg and then pass the result to the Buybuy method.

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

option_strategy = OptionStrategies.short_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 short put butterfly is a limited-reward-limited-risk strategy. The payoff is

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

The following chart shows the payoff at expiration:

The maximum profit is the net credit received, $P^{ITM}_0 + P^{OTM}_0 - 2\times P^{ATM}_0$. It occurs when the underlying price is below the ITM strike or above the OTM strike at expiration.

The maximum loss is $K^{ATM} - K^{OTM} - 2\times P^{ATM}_0 + P^{ITM}_0 + P^{OTM}_0$. It occurs when the underlying price at expiration is at the same price 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 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

$$ \begin{array}{rcll} P^{OTM}_T & = & (K^{OTM} - S_T)^{+}\\ & = & (829.08-832.50)^{+}\\ & = & 0\\ P^{ITM}_T & = & (K^{ITM} - S_T)^{+}\\ & = & (829.08-767.50)^{+}\\ & = & 61.58\\ P^{ATM}_T & = & (K^{ATM} - S_T)^{+}\\ & = & (829.08-800.00)^{+}\\ & = & 29.08\\ P_T & = & (-P^{OTM}_T - P^{ITM}_T + 2\times P^{ATM}_T - 2\times P^{ATM}_0 + P^{ITM}_0 + P^{OTM}_0)\times m - fee\\ & = & (-61.58-0+29.08\times2+5.70+37.80-14.70\times2)\times100-1.00\times4\\ & = & 1064 \end{array} $$

So, the strategy gains $1,064.

The following algorithm implements a short put butterfly Option strategy: