Option Strategies
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 put calendar spread strategy can be long or short.
Long Put Calendar Spread
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.
Short Put Calendar Spread
The short put calendar spread consists of selling a longer-term put and buying a shorter-term put. This strategy profits from an increase in price movement.
Implementation
Follow these steps to implement the put calendar spread strategy:
- In the
Initialize
method, set the start date, end date, cash, and Option universe. - In the
OnData
method, select the strike price and expiration dates of the contracts in the strategy legs. - In the
OnData
method, call theOptionStrategies.PutCalendarSpread
method and then submit the order.
private Symbol _symbol; public override void Initialize() { SetStartDate(2017, 2, 1); SetEndDate(2017, 2, 19); SetCash(500000); var option = AddOption("GOOG", Resolution.Minute); _symbol = option.Symbol; option.SetFilter(universe => universe.IncludeWeeklys() .Strikes(-1, 1) .Expiration(TimeSpan.FromDays(0), TimeSpan.FromDays(62))); }
def Initialize(self) -> None: self.SetStartDate(2017, 2, 1) self.SetEndDate(2017, 2, 19) self.SetCash(500000) option = self.AddOption("GOOG", Resolution.Minute) self.symbol = option.Symbol option.SetFilter(self.UniverseFunc) def UniverseFunc(self, universe: OptionFilterUniverse) -> OptionFilterUniverse: return universe.Strikes(-1, 1).Expiration(timedelta(0), timedelta(62))
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 OnData(self, slice: Slice) -> None: if self.Portfolio.Invested: return # Get the OptionChain chain = slice.OptionChains.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]
var optionStrategy = OptionStrategies.PutCalendarSpread(_symbol, atmStrike, nearExpiry, farExpiry); Buy(optionStrategy, 1); // if long put calendar spread Sell(optionStrategy, 1); // if short put calendar spread
option_strategy = OptionStrategies.PutCalendarSpread(self.symbol, atm_strike, near_expiry, far_expiry) self.Buy(option_strategy, 1) # if long put calendar spread self.Sell(option_strategy, 1) # if short put calendar spread
Option strategies synchronously execute by default. To asynchronously execute Option strategies, set the asynchronous
argument to False
false
. You can also provide a tag and order properties to the
Buy
and Sell
methods.
Buy(optionStrategy, quantity, asynchronous, tag, orderProperties); Sell(optionStrategy, quantity, asynchronous, tag, orderProperties);
self.Buy(option_strategy, quantity, asynchronous, tag, order_properties) self.Sell(option_strategy, quantity, asynchronous, tag, order_properties)
Strategy Payoff
The put calendar spread can be long or short.
Long Put Calendar Spread
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 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.
Short Put Calendar Spread
The short put calendar spread is a limited-reward-limited-risk strategy. The payoff is taken at the shorter-term expiration. The payoff is
$$ \begin{array}{rcll} P^{\textrm{short-term}}_T & = & (K - S_T)^{+}\\ P_T & = & (P^{\textrm{short-term}}_T - P^{\textrm{long-term}}_T + P^{\textrm{long-term}}_0 - P^{\textrm{short-term}}_0)\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & P^{\textrm{short-term}}_T & = & \textrm{Shorter term put value at time T}\\ & P^{\textrm{long-term}}_T & = & \textrm{Longer term put value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K & = & \textrm{Strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & P^{\textrm{short-term}}_0 & = & \textrm{Shorter term put value at position opening (debit paid)}\\ & P^{\textrm{long-term}}_0 & = & \textrm{Longer term put value at position opening (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of shorter term put expiration} \end{array} $$The following chart shows the payoff at expiration:

The maximum profit is the net credit received, $P^{\textrm{long-term}}_0 - P^{\textrm{short-term}}_0$. It occurs when the underlying price moves very deep ITM or OTM so the values of both puts 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 puts are at their maximum.
If the Option is American Option, there is risk of early assignment on the sold contract. Additionally, if you don't close the put positions together, the naked short put will have unlimited drawdown risk after the long put expires.
Example
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 losses $452.
The following algorithm implements a long put calendar spread Option strategy: