Option Strategies

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.

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().CallCalendarSpread(0, 30, 60));
}

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().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.

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.

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)

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:

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.

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

Asset	Price ($)	Strike ($)
Longer-term call at the start of the trade	4.40	835.00
Shorter-term call at the start of the trade	36.80	767.50
Longer-term call at time $T$	31.35	835.00
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: