Option Strategies

Bull Call Spread

Introduction

Bull call spread, also known as long call spread, consists of buying an ITM call and selling an OTM call. Both calls have the same underlying Equity and the same expiration date. The OTM call serves as a hedge for the ITM call. The bull call spread profits from a rise in underlying asset price.

Implementation

Follow these steps to implement the bull call spread 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, 2, 1);
        SetEndDate(2017, 3, 5);
        SetCash(500000);
    
        UniverseSettings.Asynchronous = true;
        var option = AddOption("GOOG", Resolution.Minute);
        _symbol = option.Symbol;
        option.SetFilter(universe => universe.IncludeWeeklys().CallSpread(30, 5));
    }
    def initialize(self) -> None:
        self.set_start_date(2017, 2, 1)
        self.set_end_date(2017, 3, 5)
        self.set_cash(500000)
    
        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(30, 5))

    The CallSpreadcall_spread filter narrows the universe down to just the two contracts you need to form a bull call spread.

  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 ITM and OTM contract strike prices from the remaining contracts
        var strikes = calls.Select(x => x.Strike).ToList();
        var otmStrike = strikes.Max();
        var itmStrike = strikes.Min();
    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 == 0:
            return
    
        # Select the ITM and OTM contract strike prices from the remaining contracts
        strikes = [x.strike for x in calls]
        otm_strike = max(strikes)
        itm_strike = min(strikes)
  5. In the OnDataon_data method, select the contracts and place the orders.
  6. Approach A: Call the OptionStrategies.BullCallSpreadOptionStrategies.bull_call_spread method with the details of each leg and then pass the result to the Buybuy method.

    var optionStrategy = OptionStrategies.BullCallSpread(_symbol, itmStrike, otmStrike, expiry);
    Buy(optionStrategy, 1);
    option_strategy = OptionStrategies.bull_call_spread(self._symbol, itm_strike, otm_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 itmCall = calls.Single(x => x.Strike == itmStrike);
    var otmCall = calls.Single(x => x.Strike == otmStrike);
    
    var legs = new List<Leg>()
        {
            Leg.Create(itmCall.Symbol, 1),
            Leg.Create(otmCall.Symbol, -1)
        };
    ComboMarketOrder(legs, 1);
    itm_call = [x for x in calls if x.strike == itm_strike][0]
    otm_call = [x for x in calls if x.strike == otm_strike][0]
    
    legs = [
        Leg.create(itm_call.symbol, 1),
        Leg.create(otm_call.symbol, -1)
    ]
    self.combo_market_order(legs, 1)

Strategy Payoff

The bull call spread is a limited-reward-limited-risk strategy. The payoff is

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

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of bull call spread

The maximum profit is $K^{OTM} - K^{ITM} + C^{OTM}_0 - C^{ITM}_0$. If the underlying price increases to exceed both strikes at expiration, both calls are worth $(S_T - K)$ at expiration.

The maximum loss is the net debit you paid to open the position, $C^{OTM}_0 - C^{ITM}_0$.

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 ($)Strike ($)
OTM call3.00835.00
ITM call41.00767.50
Underlying Equity at expiration829.08-

Therefore, the payoff is

$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ & = & (829.08-835.00)^{+}\\ & = & 0\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ & = & (829.08-767.50)^{+}\\ & = & 61.58\\ P_T & = & (C^{ITM}_T - C^{OTM}_T + C^{OTM}_0 - C^{ITM}_0)\times m - fee\\ & = & (61.58-0+3.00-41.00)\times100-1.00\times2\\ & = & 2356\\ \end{array} $$

So, the strategy profits $2,356.

The following algorithm implements a bull call spread strategy:


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