Option Strategies

Follow these steps to implement the long put 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().PutCalendarSpread(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().put_calendar_spread(0, 30, 60))

The PutCalendarSpreadput_calendar_spread filter narrows the universe down to just the two contracts you need to form a long put 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 put Option contracts
    var puts = chain.Where(x => x.Strike == atmStrike && x.Right == OptionRight.Put);
    if (puts.Count() == 0) return;

    // Select the near and far expiry contracts
    var expiries = puts.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 put Option contracts
    puts = [i for i in chain if i.strike == atm_strike and i.right == OptionRight.PUT]
    if len(puts) == 0:
        return

    # Select the near and far expiry dates
    expiries = sorted([x.expiry for x in puts])
    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.PutCalendarSpreadOptionStrategies.put_calendar_spread method with the details of each leg and then pass the result to the Buybuy method.

var optionStrategy = OptionStrategies.PutCalendarSpread(_symbol, atmStrike, nearExpiry, farExpiry);
Buy(optionStrategy, 1);

option_strategy = OptionStrategies.put_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 nearExpiryPut = puts.Single(x => x.Expiry == nearExpiry);
var farExpiryPut = puts.Single(x => x.Expiry == farExpiry);

var legs = new List<Leg>()
    {
        Leg.Create(nearExpiryPut.Symbol, -1),
        Leg.Create(farExpiryPut.Symbol, 1)
    };
ComboMarketOrder(legs, 1);

near_expiry_put = [x for x in puts if x.expiry == near_expiry][0]
far_expiry_put = [x for x in puts if x.expiry == far_expiry][0]

legs = [
    Leg.create(near_expiry_put.symbol, -1),
    Leg.create(far_expiry_put.symbol, 1)
]
self.combo_market_order(legs, 1)

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

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

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 puts are at their maximum.

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

If the Option is American Option, there is a risk of early assignment on the contract you sell. Naked long puts pose risk of losing all the debit paid if you don't close the position with short put together and the price drops below its strike.

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

Asset	Price ($)	Strike ($)
Shorter-term put at position opening	11.30	800.00
Longer-term put at position opening	19.30	800.00
Longer-term put at shorter-term expiration	3.50	800.00
Underlying Equity at shorter-term expiration	828.07	-

Therefore, the payoff is

$$ \begin{array}{rcll} P^{\textrm{short-term}}_T & = & (K - S_T)^{+}\\ & = & (800.00-828.07)^{+}\\ & = & 0\\ P_T & = & (P^{\textrm{long-term}}_T - P^{\textrm{short-term}}_T + P^{\textrm{short-term}}_0 - P^{\textrm{long-term}}_0)\times m - fee\\ & = & (3.50-0+11.30-19.30)\times100-1.00\times2\\ & = & -452\\ \end{array} $$

So, the strategy loses $452.

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