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:
- In the
Initialize
initialize
method, set the start date, end date, cash, and Option universe. - In the
OnData
on_data
method, select the expiration and strikes of the contracts in the strategy legs. - In the
OnData
on_data
method, select the contracts and place the orders.
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().PutLadder(30, 5, 0, -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().put_ladder(30, 5, 0, -5))
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]
Approach A: Put the OptionStrategies.BullPutLadder
OptionStrategies.bull_put_ladder
method with the details of each leg and then pass the result to the Buy
buy
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](https://cdn.quantconnect.com/i/tu/bull-put-ladder-payoff.png)
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:
Asset | Price ($) | Strike ($) |
---|---|---|
Lower-Strike put | 6.00 | 822.50 |
Middle-strike put | 4.70 | 825.00 |
Higher-strike put | 5.60 | 827.50 |
Underlying Equity at expiration | 843.25 | - |
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: