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().Strikes(-15, 15).Expiration(0, 31));
}

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().strikes(-15, 15).expiration(0, 31))

2. In the OnDataon_data method, select the expiration and strikes of the contracts in the strategy legs.

public override void OnData(Slice slice)
{
    if (Portfolio.Invested) return;

    // Get the OptionChain
    var chain = slice.OptionChains.get(_symbol, null);
    if (chain == null || chain.Count() == 0) return;

    // Get the furthest expiry date of the contracts
    var expiry = chain.OrderByDescending(x => x.Expiry).First().Expiry;
    
    // Select the call Option contracts with the furthest expiry
    var calls = chain.Where(x => x.Expiry == expiry && x.Right == OptionRight.Call);
    if (calls.Count() == 0) return;

    // Get the strike prices of the all the call Option contracts
    var callStrikes = calls.Select(x => x.Strike).OrderBy(x => x);

    // Get the ATM strike price
    var atmStrike = calls.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().Strike;

    // Get the strike prices for the contracts not ATM
    var spread = Math.Min(Math.Abs(callStrikes.First() - atmStrike), Math.Abs(callStrikes.Last() - atmStrike));
    var itmStrike = atmStrike - spread;
    var otmStrike = atmStrike + spread;

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 = sorted(chain, key = lambda x: x.expiry, reverse=True)[0].expiry
    
    # 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

    # Get the strike prices of the all the call Option contracts
    call_strikes = sorted([x.strike for x in calls])

    # Get the ATM strike price
    atm_strike = sorted(calls, key=lambda x: abs(x.strike - chain.underlying.price))[0].strike

    # Get the strike prices for the contracts not ATM
    spread = min(abs(call_strikes[0] - atm_strike), abs(call_strikes[-1] - atm_strike))
    itm_strike = atm_strike - spread
    otm_strike = atm_strike + spread

3. In the OnDataon_data method, call the OptionStrategies.ButterflyCall method and then submit the order.

var optionStrategy = OptionStrategies.ButterflyCall(_symbol, otmStrike, atmStrike, itmStrike, expiry);
Buy(optionStrategy, 1);

option_strategy = OptionStrategies.butterfly_call(self.symbol, otm_strike, atm_strike, itm_strike, expiry)
self.buy(option_strategy, 1)

Option strategies synchronously execute by default. To asynchronously execute Option strategies, set the asynchronous argument to Falsefalse. You can also provide a tag and order properties to the Buy method.

Buy(optionStrategy, quantity, asynchronous, tag, orderProperties);

self.Buy(option_strategy, quantity, asynchronous, tag, order_properties)

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 an American Option, there is a risk of early assignment on the sold contracts.

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 losses $1,252.

The following algorithm implements a long call butterfly Option strategy: