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Option Strategies

Long Put Calendar Spread

Introduction

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

Implementation

Follow these steps to implement the long put calendar spread strategy:

  1. In the initialize method, set the start date, end date, cash, and Option universe.
  2. Select Language:
    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 put_calendar_spread filter narrows the universe down to just the two contracts you need to form a long put calendar spread.

  3. In the on_data method, select the strike price and expiration dates of the contracts in the strategy legs.
  4. Select Language:
    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]
  5. In the on_data method, select the contracts and place the orders.
  6. Approach A: Call the OptionStrategies.put_calendar_spread method with the details of each leg and then pass the result to the buy method.

    Select Language:
    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_order, combo_limit_order, or combo_leg_limit_order method.

    Select Language:
    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)

Strategy Payoff

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

Pshort-termT=(KST)+PT=(Plong-termTPshort-termT+Pshort-term0Plong-term0)×mfee wherePshort-termT=Shorter term put value at time TPlong-termT=Longer term put value at time TST=Underlying asset price at time TK=Strike pricePT=Payout total at time TPshort-term0=Shorter term put value at position opening (credit received)Plong-term0=Longer term put value at position opening (debit paid)m=Contract multiplierT=Time of shorter term put expiration

The following chart shows the payoff at expiration:

Strategy payoff decomposition and analysis of long put calendar spread

The maximum profit is undetermined because it depends on the underlying volatility.  It occurs when ST=S0 and the spread of the puts are at their maximum.

The maximum loss is the net debit paid, Pshort-term0Plong-term0. 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.

Example

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

AssetPrice ($)Strike ($)
Shorter-term put at position opening11.30800.00
Longer-term put at position opening19.30800.00
Longer-term put at shorter-term expiration
3.50800.00
Underlying Equity at shorter-term expiration828.07-

Therefore, the payoff is

Pshort-termT=(KST)+=(800.00828.07)+=0PT=(Plong-termTPshort-termT+Pshort-term0Plong-term0)×mfee=(3.500+11.3019.30)×1001.00×2=452

So, the strategy loses $452.

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

Select Language:
class PutCalendarSpreadStrategy(QCAlgorithm): 
    def initialize(self) -> None:
        self.set_start_date(2017, 2, 1)
        self.set_end_date(2017, 2, 20)
        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().put_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 put options from the contracts which is ATM in the option chain.
        puts = [i for i in chain if i.strike == atm_strike and i.right == OptionRight.PUT]
        if len(puts) == 0: return

        # sorted the optionchain by expiration date
        expiries = sorted([x.expiry for x in puts], 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.put_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 put calendar spread
        
    def on_end_of_algorithm(self):
        for symbol, sec in self.securities.items():
            self.log(f"{symbol} :: {sec.price}")

Other Examples

For more examples, see the following algorithms:

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