Option Strategies

Bull Call Ladder

Introduction

Bull call ladder, also known as long call ladder, is a combination of a bull call spread and a short call with a higher strike price than the 2 legs of the call spread. All calls have the same underlying Equity and expiration date. This strategy profits from low volatility of the underlying asset. For instance, the underlying price stays similar to its current price.

Implementation

Follow these steps to implement the bull call ladder strategy:

  1. In the Initializeinitialize method, set the start date, end date, cash, and Option universe.
  2. 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.Strikes(-5, 5).Expiration(0, 30));
    }
    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.strikes(-5, 5).expiration(0, 30))
  3. In the OnDataon_data method, select the expiration and strikes of the contracts in the strategy legs.
  4. 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 < 3)
        {
            return;
        }
        
        var lowStrike = strikes[0];
        var middleStrike = strikes[1];
        var highStrike = strikes[2];
    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) < 3:
            return
        
        low_strike = strikes[0]
        middle_strike = strikes[1]
        high_strike = strikes[2]
  5. In the OnDataon_data method, select the contracts and place the orders.
  6. Approach A: Call the OptionStrategies.BullCallLadderOptionStrategies.bull_call_ladder method with the details of each leg and then pass the result to the Buybuy method.

    var optionStrategy = OptionStrategies.BullCallLadder(_symbol, lowStrike, middleStrike, highStrike, expiry);
    Buy(optionStrategy, 1);
    option_strategy = OptionStrategies.bull_call_ladder(self._symbol, low_strike, middle_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 middleStrikeCall = calls.Single(x => x.Strike == middleStrike);
    var highStrikeCall = calls.Single(x => x.Strike == highStrike);
    
    var legs = new List<Leg>()
    {
        Leg.Create(lowStrikeCall.Symbol, 1),
        Leg.Create(middleStrikeCall.Symbol, -1),
        Leg.Create(highStrikeCall.Symbol, -1)
    };
    ComboMarketOrder(legs, 1, true);
    low_strike_call = next(filter(lambda x: x.strike == low_strike, calls))
    middle_strike_call = next(filter(lambda x: x.strike == middle_strike, calls))
    high_strike_call = next(filter(lambda x: x.strike == high_strike, calls))
    
    legs = [
        Leg.create(low_strike_call.symbol, 1),
        Leg.create(middle_strike_call.symbol, -1),
        Leg.create(high_strike_call.symbol, -1)
    ]
    self.combo_market_order(legs, 1)

Strategy Payoff

The bull call spread is an limited-profit strategy. The payoff is

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

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of bull call ladder

The maximum profit is $K^{mid} - K^{low} - C^{low}_0 + C^{mid}_0 + C^{high}_0$, which occurs when the underlying price is between the two higher strike prices.

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

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

Example

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

AssetPrice ($)Strike ($)
Lower-Strike call17.10822.50
Middle-strike call12.00825.00
Higher-strike call10.90827.50
Underlying Equity at expiration843.25-

Therefore, the payoff is

$$ \begin{array}{rcll} C^{low}_T & = & (S_T - K^{low})^{+}\\ & = & (843.25-822.50)^{+}\\ & = & 20.75\\ C^{mid}_T & = & (S_T - K^{mid})^{+}\\ & = & (843.25-825.00)^{+}\\ & = & 18.25\\ C^{high}_T & = & (S_T - K^{high})^{+}\\ & = & (843.25-827.50)^{+}\\ & = & 15.75\\ Payoff_T & = & (C^{low}_T - C^{low}_0 + C^{mid}_0 - C^{mid}_T + C^{high}_0 - C^{high}_T)\times m - fee\\ & = & (20.75 - 17.10 + 12.00 - 18.25 + 10.90 - 15.75)\times100-1.00\times3\\ & = & -748\\ \end{array} $$

So, the strategy loses $748.

The following algorithm implements a bull call ladder Option strategy:

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