Option Strategies

Follow these steps to implement the long box spread strategy:

1. In the Initializeinitialize method, set the start date, set the end date, subscribe to the underlying Equity, and create an Option universe.

private Symbol _symbol;

public override void Initialize()
{
    SetStartDate(2017, 4, 1);
    SetEndDate(2017, 4, 30);
    SetCash(100000);

    UniverseSettings.Asynchronous = true;
    var option = AddOption("GOOG", Resolution.Minute);
    _symbol = option.Symbol;
    option.SetFilter(universe => universe.IncludeWeeklys().BoxSpread(30, 5));
}

def initialize(self) -> None:
    self.set_start_date(2017, 4, 1)
    self.set_end_date(2017, 4, 30)
    self.set_cash(100000)

    self.universe_settings.asynchronous = True
    option = self.add_option("GOOG", Resolution.MINUTE)
    self._symbol = option.symbol
    option.set_filter(lambda universe: universe.include_weeklys().box_spread(30, 5))

The BoxSpreadbox_spread filter narrows the universe down to just the four contracts you need to form a box spread.

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

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

    // Get the OptionChain
    if (!slice.OptionChains.TryGetValue(_symbol, out var chain))
    {
        return;
    }

    // Select an expiry date and ITM & OTM strike prices
    var expiry = chain.Max(x => x.Expiry);
    var contracts = chain.Where(x => x.Expiry == expiry).ToList();
    var higherStrike = contracts.Max(x => x.Strike);
    var lowerStrike = contracts.Min(x => x.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

    # Select an expiry date and ITM & OTM strike prices
    expiry = max([x.expiry for x in chain])
    contracts = [x for x in chain if x.expiry == expiry]
    lower_strike = min([x.strike for x in contracts])
    higher_strike = max([x.strike for x in contracts])

3. In the OnDataon_data method, select the contracts and place the order.

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

var boxSpread = OptionStrategies.BoxSpread(_symbol, higherStrike, lowerStrike, expiry);
Buy(boxSpread, 1);

box_spread = OptionStrategies.box_spread(self._symbol, higher_strike, lower_strike, expiry)
self.buy(box_spread, 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.

// Select the call and put contracts
var itmCall = contracts.Single(x => x.Strike == lowerStrike && x.Right == OptionRight.Call);
var otmCall = contracts.Single(x => x.Strike == higherStrike && x.Right == OptionRight.Call);
var itmPut = contracts.Single(x => x.Strike == higherStrike && x.Right == OptionRight.Put);
var otmPut = contracts.Single(x => x.Strike == lowerStrike && x.Right == OptionRight.Put);

var legs = new List<Leg>()
{
    Leg.Create(itmCall.Symbol, 1),
    Leg.Create(itmPut.Symbol, 1),
    Leg.Create(otmCall.Symbol, -1),
    Leg.Create(otmPut.Symbol, -1),
};
ComboMarketOrder(legs, 1);

# Select the call and put contracts
itm_call = next(filter(lambda x: x.right == OptionRight.CALL and x.strike == lower_strike, contracts))
otm_call = next(filter(lambda x: x.right == OptionRight.CALL and x.strike == higher_strike, contracts))
itm_put = next(filter(lambda x: x.right == OptionRight.PUT and x.strike == higher_strike, contracts))
otm_put = next(filter(lambda x: x.right == OptionRight.PUT and x.strike == lower_strike, contracts))           

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

This is a fixed payoff, delta-neutral strategy. The payoff is

$$ \begin{array}{rcll} C_T^{ITM} & = & (S_T - K_{-})^{+}\\ C_T^{OTM} & = & (S_T - K_{+})^{+}\\ P_T^{ITM} & = & (K_{+} - S_T)^{+}\\ P_T^{OTM} & = & (K_{-} - S_T)^{+}\\ Payoff_T & = & (C_T^{ITM} - C_{T_0}^{ITM} + P_T^{ITM} - P_{T_0}^{ITM} - C_T^{OTM} + C_{T_0}^{OTM} - P_T^{OTM} + P_{T_0}^{OTM})\times m - fee\\ & = & (K_{+} - K_{-} + C_{T_0}^{OTM} + P_{T_0}^{OTM} - C_{T_0}^{ITM} - P_{T_0}^{ITM})\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C_T^{ITM} & = & \textrm{ITM Call value at time T}\\ & C_T^{OTM} & = & \textrm{OTM Call value at time T}\\ & P_T^{ITM} & = & \textrm{ITM Put value at time T}\\ & P_T^{OTM} & = & \textrm{OTM Put value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K_{+} & = & \textrm{Higher strike price}\\ & K_{-} & = & \textrm{Lower strike price}\\ & Payoff_{T_1} & = & \textrm{Payout total at time T1}\\ & C_{T_0}^{ITM} & = & \textrm{ITM Call price when the trade opened (debit paid)}\\ & C_{T_0}^{OTM} & = & \textrm{OTM Call price when the trade opened (credit received)}\\ & P_{T_0}^{ITM} & = & \textrm{ITM Put price when the trade opened (debit paid)}\\ & P_{T_0}^{OTM} & = & \textrm{OTM Put price when the trade opened (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$

The following chart shows the payoff at expiration:

The payoff is only dependent on the strike price and the initial asset prices.

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 algorithm:

Asset	Price ($)	Strike ($)
ITM Call	27.30	810.00
ITM Put	28.00	857.50
OTM Call	1.05	857.50
OTM Put	1.50	810.00
Underlying Equity at expiration	843.25	-

Therefore, the payoff is

$$ \begin{array}{rcll} Payoff_T & = & (K_{+} - K_{-} + C_0^{OTM} + P_0^{OTM} - C_0^{ITM} - P_0^{ITM})\times m - fee\\ & = & (857.50 - 810.00 + 1.05 + 1.50 - 27.30 - 28.00)\times100 - 1.00\times4\\ & = & -529.00\\ \end{array} $$

So, the strategy loses $529.

The following algorithm implements a long box spread Option strategy: