# Option Strategies

### 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

1. In the Initializeinitialize 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;
_symbol = option.Symbol;
}
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
self._symbol = option.symbol

The PutCalendarSpreadput_calendar_spread filter narrows the universe down to just the two contracts you need to form a long put calendar spread.

3. In the OnDataon_data 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 ||
!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]
5. In the OnDataon_data method, select the contracts and place the orders.

var optionStrategy = OptionStrategies.PutCalendarSpread(_symbol, atmStrike, nearExpiry, farExpiry);
option_strategy = OptionStrategies.put_calendar_spread(self._symbol, atm_strike, near_expiry, far_expiry)

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)

### 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:

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.

### 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 loses \$452.

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

You can also see our Videos. You can also get in touch with us via Discord.