Option Strategies

Follow these steps to implement the short 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(-10, 10, 0, 30);
}

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(-10, 10, 0, 30);

2. In the OnDataon_data method, select 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;

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

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

    // Select the OTM contracts
    var otmCallContract = calls.OrderBy(x => x.Strike).Last();
    var otmPutContract = puts.OrderBy(x => x.Strike).First();

    // Select the ATM contracts
    var atmCallContract = calls.Where(x => x.Strike == atmStrike).First();
    var atmPutsContract = puts.Where(x => x.Strike == atmStrike).First();

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

    # Separate the call and put contracts
    call = [i for i in chain if i.right == 0]
    put = [i for i in chain if i.right == 1]
    if len(call) == 0 or len(put) == 0 : return

    # Select the OTM contracts
    call_contracts = sorted(call, key = lambda x: x.strike)
    put_contracts = sorted(put, key = lambda x: x.strike)
    otm_call = call_contracts[-1]
    otm_put = put_contracts[0]

    # Select the ATM contracts
    atm_put = sorted(put_contracts, key = lambda x: abs(chain.underlying.price - x.strike))[0]
    atm_call = sorted(call_contracts, key = lambda x: abs(chain.underlying.price - x.strike))[0]

3. In the OnDataon_data method, submit the orders.

Sell(atmPutsContract.Symbol, 1);
Sell(atmCallContract.Symbol, 1);
Buy(otmCallContract.Symbol, 1);
Buy(otmPutContract.Symbol, 1);

self.sell(atm_put.symbol, 1)
self.sell(atm_call.symbol, 1)
self.buy(otm_call.symbol, 1)
self.buy(otm_put.symbol, 1)

The iron butterfly can be long or short.

Long Iron Butterfly

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

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

The following chart shows the payoff at expiration:

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

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

If the Option is 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

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

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 sold contracts.

The following table shows the price details of the assets in the algorithm:

Asset	Price ($)	Strike ($)
OTM call	1.85	857.50
OTM put	2.75	810.00
ATM call	8.10	832.00
ATM put	7.40	832.00
Underlying Equity at expiration	851.20	-

Therefore, the payoff is

$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^C_{OTM})^{+}\\ & = & (851.20-857.50)^{+}\\ & = & 0\\ C^{ATM}_T & = & (S_T - K^C_{ATM})^{+}\\ & = & (851.20-832.00)^{+}\\ & = & 19.20\\ P^{OTM}_T & = & (K^P_{OTM} - S_T)^{+}\\ & = & (832.00-851.20)^{+}\\ & = & 0\\ P^{ATM}_T & = & (K^P_{ATM} - S_T)^{+}\\ & = & (810.00-851.20)^{+}\\ & = & 0\\ P_T & = & (C^{OTM}_T + P^{OTM}_T - C^{ATM}_T - P^{ATM}_T - C^{OTM}_0 - P^{OTM}_0 + C^{ATM}_0 + P^{ATM}_0)\times m - fee\\ & = & (0+0-19.20-0+8.10+7.40-1.85-2.75)\times100-1\times4\\ & = & -834 \end{array} $$

So, the strategy losses $834.

The following algorithm implements a short iron butterfly Option strategy: