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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 initialize method, set the start date, end date, cash, and Option universe.
    2. Select Language: 
    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_ladder(30, 5, 0, -5))
  2. In the on_data method, select the expiration and strikes of the contracts in the strategy legs.
    3. Select Language: 
    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]
  3. In the on_data method, select the contracts and place the orders.

    4. Approach A: Call the OptionStrategies.bull_call_ladder method with the details of each leg and then pass the result to the buy method.

    Select Language: 
    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_order, combo_limit_order, or combo_leg_limit_order method.

    Select Language: 
    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

ClowT=(ST−Klow)+CmidT=(ST−Kmid)+ChighT=(ST−Khigh)+PayoffT=(ClowT−Clow0+Cmid0−CmidT+Chigh0−ChighT)×m−fee whereClowT=Lower-strike call value at time TCmidT=Middle-strike call value at time TChighT=Higher-strike call value at time TST=Underlying asset price at time TKlow=Lower-strike call strike priceKmid=Middle-strike call strike priceKhigh=Higher-strike call strike priceClow0=Lower-strike call value at position opening (credit received)Cmid0=Middle-strikeTM call value at position opening (debit paid)Chigh0=Higher-strike call value at position opening (debit paid)m=Contract multiplierT=Time of expiration

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of bull call ladder

The maximum profit is Kmid−Klow−Clow0+Cmid0+Chigh0, 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

ClowT=(ST−Klow)+=(843.25−822.50)+=20.75CmidT=(ST−Kmid)+=(843.25−825.00)+=18.25ChighT=(ST−Khigh)+=(843.25−827.50)+=15.75PayoffT=(ClowT−Clow0+Cmid0−CmidT+Chigh0−ChighT)×m−fee=(20.75−17.10+12.00−18.25+10.90−15.75)×100−1.00×3=−748

So, the strategy loses $748.

The following algorithm implements a bull call ladder Option strategy:

Select Language: 
class BullCallLadderOptionStrategy(QCAlgorithm):
    def initialize(self) -> None:
        self.set_start_date(2017, 4, 1)
        self.set_end_date(2017, 4, 23)
        self.set_cash(100000)
        
        option = self.add_option("GOOG", Resolution.MINUTE)
        self._symbol = option.symbol

        # set our strike/expiry filter for this option chain
        option.set_filter(lambda x: x.include_weeklys().call_ladder(30, 5, 0, -5))

    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]
    
        option_strategy = OptionStrategies.bull_call_ladder(self._symbol, low_strike, middle_strike, high_strike, expiry)
        self.buy(option_strategy, 1)

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