Option Strategies

Long Call Calendar Spread

Introduction

Long call calendar spread, also known as call horizontal spread, is a combination of a longer-term (far-leg/front-month) call and a shorter-term (near-leg/back-month) call, where all calls have the same underlying stock and the same strike price. The long call calendar spread consists of buying a longer-term call and selling a shorter-term call. This strategy profits from a decrease in the underlying price. It also profits from the time decay value because the theta $\theta$ (the Option price decay by 1 day closer to maturity) of the shorter-term call is larger than longer-term call.

Implementation

Follow these steps to implement the long call calendar 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(2024, 9, 1);
    SetEndDate(2024, 12, 31);
    SetCash(500000);

    UniverseSettings.Asynchronous = true;
    var option = AddOption("GOOG", Resolution.Minute);
    _symbol = option.Symbol;
    option.SetFilter(universe => universe.IncludeWeeklys().CallCalendarSpread(0, 30, 60));
}
    def initialize(self) -> None:
    self.set_start_date(2024, 9, 1)
    self.set_end_date(2024, 12, 31)
    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_calendar_spread(0, 30, 60))

    The CallCalendarSpreadcall_calendar_spread filter narrows the universe down to just the two contracts you need to form a long call calendar spread.

  2. In the OnDataon_data method, select the strike price and expiration dates of the contracts in the strategy legs.
    3. public override void OnData(Slice slice)
{
    if (Portfolio.Invested ||
        !slice.OptionChains.TryGetValue(_symbol, out var chain))
    {
        return;
    }

    // Get the ATM strike
    var atmStrike = chain.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().Strike;

    // Select the ATM call Option contracts
    var calls = chain.Where(x => x.Strike == atmStrike && x.Right == OptionRight.Call);
    if (calls.Count() == 0) return;

    // Select the near and far expiry contracts
    var expiries = calls.Select(x => x.Expiry).ToList();
    var nearExpiry = expiries.Min();
    var farExpiry = expiries.Max();
    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

    # Get the ATM strike
    atm_strike = sorted(chain, key=lambda x: abs(x.strike - chain.underlying.price))[0].strike

    # Select the ATM call Option contracts
    calls = [i for i in chain if i.strike == atm_strike and i.right == OptionRight.CALL]
    if len(calls) == 0:
        return

    # Select the near and far expiry dates
    expiries = sorted([x.expiry for x in calls])
    near_expiry = expiries[0]
    far_expiry = expiries[-1]
  3. In the OnDataon_data method, select the contracts and place the orders.

    4. Approach A: Call the OptionStrategies.CallCalendarSpreadOptionStrategies.call_calendar_spread method with the details of each leg and then pass the result to the Buybuy method.

    var optionStrategy = OptionStrategies.CallCalendarSpread(_symbol, atmStrike, nearExpiry, farExpiry);
Buy(optionStrategy, 1);
    option_strategy = OptionStrategies.call_calendar_spread(self._symbol, atm_strike, near_expiry, far_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 nearExpiryCall = calls.Single(x => x.Expiry == nearExpiry);
var farExpiryCall = calls.Single(x => x.Expiry == farExpiry);

var legs = new List<Leg>()
    {
        Leg.Create(nearExpiryCall.Symbol, -1),
        Leg.Create(farExpiryCall.Symbol, 1)
    };
ComboMarketOrder(legs, 1);
    near_expiry_call = [x for x in calls if x.expiry == near_expiry][0]
far_expiry_call = [x for x in calls if x.expiry == far_expiry][0]

legs = [
    Leg.create(near_expiry_call.symbol, -1),
    Leg.create(far_expiry_call.symbol, 1)
]
self.combo_market_order(legs, 1)

Strategy Payoff

The long call calendar spread is a limited-reward-limited-risk strategy. The payoff at the shorter-term expiration is

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

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of long call calendar spread

The maximum profit is undetermined because it depends on the underlying volatility. It occurs when $S_T = S_0$ and the spread of the calls are at their maximum.

The maximum loss is the net debit paid, $C^{\textrm{short-term}}_0 - C^{\textrm{long-term}}_0$. It occurs when the underlying price moves very deep ITM or OTM so the values of both calls are close to zero.

If the Option is American Option, there is a risk of early assignment on the contract you sell. If the buyer exercises the call you sell, you could lose all the debit you received if you don't close the long call and the underlying price drops below the long call strike price.

Example

The following table shows the price details of the assets in the long call calendar spread:

AssetPrice ($)Strike ($)
Longer-term call at the start of the trade4.40835.00
Shorter-term call at the start of the trade36.80767.50
Longer-term call at time $T$31.35835.00
Underlying Equity at time $T$829.08-

Therefore, the payoff at time $T$ (the expiration of the short-term call) is

$$ \begin{array}{rcll} C^{\textrm{short-term}}_T & = & (S_T - K)^{+}\\ & = & (828.07-800.00)^{+}\\ & = & 28.07\\ P_T & = & (C^{\textrm{long-term}}_T - C^{\textrm{short-term}}_T + C^{\textrm{short-term}}_0 - C^{\textrm{long-term}}_0)\times m - fee\\ & = & (31.35-28.07+11.30-20.00)\times100-1.00\times2\\ & = & -544 \end{array} $$

So, the strategy loses $544.

The following algorithm implements a long call calendar spread Option strategy:

public class BearPutSpreadStrategy : QCAlgorithm
{
    private Symbol _symbol;

    public override void Initialize()
    {
        SetStartDate(2024, 9, 1);
        SetEndDate(2024, 12, 31);
        SetCash(500000);

        var option = AddOption("GOOG", Resolution.Minute);
        _symbol = option.Symbol;
        option.SetFilter(universe => universe.IncludeWeeklys().CallCalendarSpread(0, 30, 60));
    }

    public override void OnData(Slice slice)
    {
        if (Portfolio.Invested) return;

        // Get the OptionChain of the symbol
        var chain = slice.OptionChains.get(_symbol, null);
        if (chain == null || chain.Count() == 0) return;

        // get at-the-money strike
        var atmStrike = chain.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().Strike;

        // filter the call options from the contracts which is ATM in the option chain.
        var calls = chain.Where(x => x.Strike == atmStrike && x.Right == OptionRight.Call);
        if (calls.Count() == 0) return;

        // sorted the optionchain by expiration date
        var expiries = calls.Select(x => x.Expiry).OrderBy(x => x);

        // select the farest expiry as far-leg expiry, and the nearest expiry as near-leg expiry
        var nearExpiry = expiries.First();
        var farExpiry = expiries.Last();

        var optionStrategy = OptionStrategies.CallCalendarSpread(_symbol, atmStrike, nearExpiry, farExpiry);
        // We open a position with 1 unit of the option strategy
        Buy(optionStrategy, 1);        // if long call calendar spread
        //Sell(optionStrategy, 1);     // if short call calendar spread
    }
}
class LongCallCalendarSpreadStrategy(QCAlgorithm): 
    def initialize(self) -> None:
        self.set_start_date(2024, 9, 1)
        self.set_end_date(2024, 12, 31)
        self.set_cash(500000)

        option = self.add_option("GOOG", Resolution.MINUTE)
        self.symbol = option.symbol
        option.set_filter(self.universe_func)

    def universe_func(self, universe: OptionFilterUniverse) -> OptionFilterUniverse:
        return universe.include_weeklys().call_calendar_spread(0, 30, 60)

    def on_data(self, data: Slice) -> None:
        # avoid extra orders
        if self.portfolio.invested: return

        # Get the OptionChain of the self.symbol
        chain = data.option_chains.get(self.symbol, None)
        if not chain: return

        # get at-the-money strike
        atm_strike = sorted(chain, key=lambda x: abs(x.strike - chain.underlying.price))[0].strike

        # filter the call options from the contracts which is ATM in the option chain.
        calls = [i for i in chain if i.strike == atm_strike and i.right == OptionRight.CALL]
        if len(calls) == 0: return

        # sorted the optionchain by expiration date
        expiries = sorted([x.expiry for x in calls], key = lambda x: x)
        
        # select the farest expiry as far-leg expiry, and the nearest expiry as near-leg expiry
        near_expiry = expiries[0]
        far_expiry = expiries[-1]

        option_strategy = OptionStrategies.call_calendar_spread(self.symbol, atm_strike, near_expiry, far_expiry)
        # We open a position with 1 unit of the option strategy
        self.buy(option_strategy, 1)
        # self.sell(option_strategy, 1) if short call calendar spread

Other Examples

For more examples, see the following algorithms:

Demonstration Algorithm
IndexOptionCallCalendarSpreadAlgorithm.py Python LongAndShortCallCalendarSpreadStrategiesAlgorithm.py Python IndexOptionCallCalendarSpreadAlgorithm.cs C# LongAndShortCallCalendarSpreadStrategiesAlgorithm.cs C#

You can also see our Videos. You can also get in touch with us via Discord.

Did you find this page helpful?

Contribute to the documentation: