Option Strategies

Bull Put Ladder

Introduction

Bull put ladder, also known as short put ladder, is a combination of a bull put spread and short put with a lower strike price than the 2 legs of the put spread. All puts have the same underlying Equity and expiration date. This strategy profits from increasing volatility of the underlying asset. For instance, the underlying price moves away from its current price.

Implementation

Follow these steps to implement the bull put 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 put Option contracts with the furthest expiry
        var expiry = chain.Max(x => x.Expiry);    
        var puts = chain.Where(x => x.Expiry == expiry && x.Right == OptionRight.Put);
        if (puts.Count() == 0) return;
    
        // Select the strike prices from the remaining contracts
        var strikes = puts.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 put Option contracts with the furthest expiry
        expiry = max([x.expiry for x in chain])
        puts = [i for i in chain if i.expiry == expiry and i.right == OptionRight.PUT]
        if not puts:
            return
    
        # Select the strike prices from the remaining contracts
        strikes = sorted(set(x.strike for x in puts))
        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: Put the OptionStrategies.BullPutLadderOptionStrategies.bull_put_ladder method with the details of each leg and then pass the result to the Buybuy method.

    var optionStrategy = OptionStrategies.BullPutLadder(_symbol, highStrike, middleStrike, lowStrike, expiry);
    Buy(optionStrategy, 1);
    option_strategy = OptionStrategies.bull_put_ladder(self._symbol, high_strike, middle_strike, low_strike, expiry)
    self.buy(option_strategy, 1)

    Approach B: Create a list of Leg objects and then put the Combo Market Ordercombo_market_order, Combo Limit Ordercombo_limit_order, or Combo Leg Limit Ordercombo_leg_limit_order method.

    var lowStrikePut = puts.Single(x => x.Strike == lowStrike);
    var middleStrikePut = puts.Single(x => x.Strike == middleStrike);
    var highStrikePut = puts.Single(x => x.Strike == highStrike);
    
    var legs = new List<Leg>()
    {
        Leg.Create(lowStrikePut.Symbol, 1),
        Leg.Create(middleStrikePut.Symbol, 1),
        Leg.Create(highStrikePut.Symbol, -1)
    };
    ComboMarketOrder(legs, 1, true);
    low_strike_put = next(filter(lambda x: x.strike == low_strike, puts))
    middle_strike_put = next(filter(lambda x: x.strike == middle_strike, puts))
    high_strike_put = next(filter(lambda x: x.strike == high_strike, puts))
    
    legs = [
        Leg.create(low_strike_put.symbol, 1),
        Leg.create(middle_strike_put.symbol, 1),
        Leg.create(high_strike_put.symbol, -1)
    ]
    self.combo_market_order(legs, 1)

Strategy Payoff

The bull put spread is an limited-risk strategy. The payoff is

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

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of bull put ladder

The maximum profit is $K^{mid} + K^{low} - K^{high} - P^{low}_0 - P^{mid}_0 + P^{high}_0$, which occurs when the underlying price decreases to $0.

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

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 put6.00822.50
Middle-strike put4.70825.00
Higher-strike put5.60827.50
Underlying Equity at expiration843.25-

Therefore, the payoff is

$$ \begin{array}{rcll} P^{low}_T & = & (K^{low} - S_T)^{+}\\ & = & (822.50-843.25)^{+}\\ & = & 0\\ P^{mid}_T & = & (K^{mid} - S_T)^{+}\\ & = & (825.00-843.25)^{+}\\ & = & 0\\ P^{high}_T & = & (K^{high} - S_T)^{+}\\ & = & (827.50-843.25)^{+}\\ & = & 0\\ Payoff_T & = & (P^{low}_T - P^{low}_0 + P^{mid}_T - P^{mid}_0 + P^{high}_0 - P^{high}_T)\times m - fee\\ & = & (0 - 6.00 + 0 - 4.70 + 5.60 - 0)\times100-1.00\times3\\ & = & -513\\ \end{array} $$

So, the strategy loses $513.

The following algorithm implements a bull put ladder Option strategy:

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