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 $\theta$ (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. 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 strike price and expiration dates 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 price
        var atmStrike = chain.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().Strike;
    
        // Select the ATM put contracts
        var puts = chain.Where(x => x.Strike == atmStrike && x.Right == OptionRight.Put);
        if (puts.Count() == 0) return;
    
        // Select the near and far expiration dates
        var expiries = puts.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 price
        atm_strike = sorted(chain, key=lambda x: abs(x.strike - chain.underlying.price))[0].strike
    
        # Select the ATM put 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 expiration dates
        expiries = sorted([x.expiry for x in puts], key = lambda x: x)
        near_expiry = expiries[0]
        far_expiry = expiries[-1]
  5. In the OnData method, call the OptionStrategies.PutCalendarSpread method and then submit the order.
  6. 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)

    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 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:

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 $S_T = S_0$ 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 risk of early assignment on the sold contract. 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

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

So, the strategy losses $452.

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

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