Option Strategies

Short Call Calendar Spread

Introduction

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 short call calendar spread consists of selling a longer-term call and buying a shorter-term call. The strategy profits from from an increase in the underlying price.

Implementation

Follow these steps to implement the short call calendar spread strategy:

  1. In the Initialize 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, 2, 19);
        SetCash(500000);
        UniverseSettings.Asynchronous = true;
        var option = AddOption("GOOG", Resolution.Minute);
        _symbol = option.Symbol;
        option.SetFilter(universe => universe.IncludeWeeklys().Strikes(-1, 1).Expiration(0, 62));
    }
    def initialize(self) -> None:
        self.set_start_date(2017, 2, 1)
        self.set_end_date(2017, 2, 19)
        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().strikes(-1, 1).expiration(0, 62))
  3. In the OnData method, select the expiration and strikes of the contracts in the strategy legs.
  4. public override void OnData(Slice slice)
    {
        if (Portfolio.Invested) return;
    
        // Get the OptionChain
        var chain = slice.OptionChains.get(_symbol, null);
        if (chain == null || chain.Count() == 0) 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 dates
        var expiries = calls.Select(x => x.Expiry).OrderBy(x => x);
        var nearExpiry = expiries.First();
        var farExpiry = expiries.Last();
    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]
  5. In the OnData method, call the OptionStrategies.ShortCallCalendarSpread method and then submit the order.
  6. var optionStrategy = OptionStrategies.ShortCallCalendarSpread(_symbol, atmStrike, nearExpiry, farExpiry);
    Buy(optionStrategy, 1);
    option_strategy = OptionStrategies.short_call_calendar_spread(self.symbol, atm_strike, near_expiry, far_expiry)
    self.buy(option_strategy, 1)

    Option strategies synchronously execute by default. To asynchronously execute Option strategies, set the asynchronous argument to Falsefalse. You can also provide a tag and order properties to the Buy method.

    Buy(optionStrategy, quantity, asynchronous, tag, orderProperties);
    
    self.Buy(option_strategy, quantity, asynchronous, tag, order_properties)
    

Strategy Payoff

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

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

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of short call calendar spread

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

The maximum loss is undetermined because it depends on the underlying volatility. It occurs when $S_T = S_0$ and the spread of the 2 calls are at their maximum.

If the Option is American Option, there is risk of early assignment on the sold contract. If you don't close the call positions together, the naked short call will have unlimited drawdown risk after the long call expires.

Example

The following table shows the price details of the assets in the short 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

$$ \begin{array}{rcll} C^{\textrm{short-term}}_T & = & (S_T - K)^{+}\\ & = & (828.07-800.00)^{+}\\ & = & 28.07\\ P_T & = & (-C^{\textrm{long-term}}_T + C^{\textrm{short-term}}_T - C^{\textrm{short-term}}_0 + C^{\textrm{long-term}}_0)\times m - fee\\ & = & (-31.35+28.07-11.30+20.00)\times100-1.00\times2\\ & = & 540 \end{array} $$

So, the strategy gains $540.

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

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