Option Strategies

Follow these steps to implement the call butterfly strategy:

1. In the Initialize 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);

    var option = AddOption("GOOG", Resolution.Minute);
    _symbol = option.Symbol;
    option.SetFilter(universe => universe.IncludeWeeklys()
                                         .Strikes(-15, 15)
                                         .Expiration(TimeSpan.FromDays(0), TimeSpan.FromDays(31)));
}

def Initialize(self) -> None:
    self.SetStartDate(2017, 2, 1)
    self.SetEndDate(2017, 3, 5)
    self.SetCash(500000)

    option = self.AddOption("GOOG", Resolution.Minute)
    self.symbol = option.Symbol
    option.SetFilter(self.UniverseFunc)

def UniverseFunc(self, universe: OptionFilterUniverse) -> OptionFilterUniverse:
    return universe.IncludeWeeklys().Strikes(-15, 15).Expiration(timedelta(0), timedelta(31))

2. In the OnData 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 OnData(self, slice: Slice) -> None:
    if self.Portfolio.Invested: return

    # Get the OptionChain
    chain = slice.OptionChains.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 OnData method, call the OptionStrategies.CallButterfly method and then submit the order.

var optionStrategy = OptionStrategies.CallButterfly(_symbol, otmStrike, atmStrike, itmStrike, expiry);
Buy(optionStrategy, 1);    // if long call butterfly
Sell(optionStrategy, 1);   // if short call butterfly

option_strategy = OptionStrategies.CallButterfly(self.symbol, otm_strike, atm_strike, itm_strike, expiry)
self.Buy(option_strategy, 1)    # if long call butterfly
self.Sell(option_strategy, 1)   # if short call butterfly

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 and Sell methods.

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

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

The call butterfly can be long or short.

Long Call Butterfly

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.

Short Call Butterfly

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 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 version of the algorithm:

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: