Option Strategies

Follow these steps to implement the long call backspread strategy:

1. In the Initializeinitialize method, set the start date, end date, cash, and Option universe. You can use the CallSpreadcall_spread helper method in option universe filtering, since a call backspread consists of the same contracts as a call spread.

private Symbol _symbol;

public override void Initialize()
{
    SetStartDate(2017, 4, 1);
    SetEndDate(2017, 4, 22);
    SetCash(1000000);

    UniverseSettings.Asynchronous = true;
    var option = AddOption("GOOG", Resolution.Minute);
    _symbol = option.Symbol;
    option.SetFilter(universe => universe.IncludeWeeklys().CallSpread(20, 5));
}

def initialize(self) -> None:
    self.set_start_date(2017, 4, 1)
    self.set_end_date(2017, 4, 22)
    self.set_cash(1000000)

    self.universe_settings.asynchronous = True
    option = self.add_option("GOOG", Resolution.MINUTE)
    self._symbol = option.symbol
    option.set_filter(lambda universe: universe.include_weeklys().call_spread(20, 5))

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 ||
        !slice.OptionChains.TryGetValue(_symbol, out var chain))
    {
        return;
    }

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

    // Select the strike prices from the remaining contracts
    var strikes = calls.Select(x => x.Strike).Distinct().OrderBy(x => x).ToList();
    if (strikes.Count < 2)
    {
        return;
    }
    
    var lowStrike = strikes[0];
    var highStrike = strikes[1];

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 the call Option contracts with the furthest expiry
    expiry = max([x.expiry for x in chain])
    calls = [i for i in chain if i.expiry == expiry and i.right == OptionRight.CALL]
    if not calls:
        return

    # Select the strike prices from the remaining contracts
    strikes = sorted(set(x.strike for x in calls))
    if len(strikes) < 2:
        return
    
    low_strike = strikes[0]
    high_strike = strikes[1]

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

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

var optionStrategy = OptionStrategies.CallBackspread(_symbol, lowStrike, highStrike, expiry);
Buy(optionStrategy, 1);

option_strategy = OptionStrategies.call_backspread(self._symbol, low_strike, high_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 lowStrikeCall = calls.Single(x => x.Strike == lowStrike);
var highStrikeCall = calls.Single(x => x.Strike == highStrike);

var legs = new List<Leg>()
{
    Leg.Create(lowStrikeCall.Symbol, -1),
    Leg.Create(highStrikeCall.Symbol, 2)
};
ComboMarketOrder(legs, 1, true);

low_strike_call = next(filter(lambda x: x.strike == low_strike, calls))
high_strike_call = next(filter(lambda x: x.strike == high_strike, calls))

legs = [
    Leg.create(low_strike_call.symbol, -1),
    Leg.create(high_strike_call.symbol, 2)
]
self.combo_market_order(legs, 1)

The long call backspread is an unlimited-profit-limited-risk strategy. The payoff is

$$ \begin{array}{rcll} C^{low}_T & = & (S_T - K^{low})^{+}\\ C^{high}_T & = & (S_T - K^{high})^{+}\\ Payoff_T & = & (C^{low}_0 - C^{low}_T + C^{high}_T \times 2 - C^{high}_0 \times 2)\times m - fee\\ \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{low}_T & = & \textrm{Lower-strike call value at time T}\\ & C^{high}_T & = & \textrm{Higher-strike call value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K^{low} & = & \textrm{Lower-strike call strike price}\\ & K^{high} & = & \textrm{Higher-strike call strike price}\\ & C^{low}_0 & = & \textrm{Lower-strike call value at position opening (credit received)}\\ & C^{high}_0 & = & \textrm{Higher-strike call value at position opening (debit paid)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$

The following chart shows the payoff at expiration:

The maximum profit is unlimited, which occurs when the underlying price increases indefinitely.

The maximum loss is $K^{low} - K^{high} + C^{low}_0 - C^{high}_0 \times 2$, which occurs when the underlying price is exactly at the higher strike at expiry.

If the Option is American Option, there is a risk of early assignment on the contract you sell.

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

Asset	Price ($)	Strike ($)
Lower-Strike call	12.00	825.00
Higher-strike call	8.80	835.00
Underlying Equity at expiration	843.19	-

Therefore, the payoff is

$$ \begin{array}{rcll} C^{low}_T & = & (S_T - K^{low})^{+}\\ & = & (843.19-825.00)^{+}\\ & = & 18.19\\ C^{high}_T & = & (S_T - K^{high})^{+}\\ & = & (843.19-835.00)^{+}\\ & = & 8.19\\ Payoff_T & = & (C^{low}_0 - C^{low}_T + C^{high}_T \times 2 - C^{high}_0 \times 2)\times m - fee\\ & = & (12.00 - 18.19 + 8.19\times2 - 8.80\times2)\times100-2.30\\ & = & -743.30\\ \end{array} $$

So, the strategy loses $743.30.

The following algorithm implements a long call backspread Option strategy: