Option Strategies

Follow these steps to implement the long jelly roll strategy:

1. In the Initializeinitialize method, set the start date, set the end date, and create an Option universe.

private Symbol _symbol;

public override void Initialize()
{
    SetStartDate(2017, 4, 1);
    SetEndDate(2017, 4, 22);
    SetCash(100000);

    UniverseSettings.Asynchronous = true;
    var option = AddOption("GOOG", Resolution.Minute);
    _symbol = option.Symbol;
    option.SetFilter(x => x.IncludeWeeklys().JellyRoll(5m, 30, 60));
}

def initialize(self) -> None:
    self.set_start_date(2017, 4, 1)
    self.set_end_date(2017, 4, 22)
    self.set_cash(100000)

    self.universe_settings.asynchronous = True
    option = self.add_option("GOOG", Resolution.MINUTE)
    self._symbol = option.symbol
    option.set_filter(lambda x: x.include_weeklys().jelly_roll(5.0, 30, 60))

2. In the OnDataon_data method, select the expiry and strikes of the contracts in the strategy legs.

public override void OnData(Slice slice)
{
    if (Portfolio.Invested) return;

    // Get the OptionChain
    if (!slice.OptionChains.TryGetValue(_symbol, out var chain))
    {
        return;
    }

    // Select expiry dates and strike price
    var strike = chain.OrderBy(x => Math.Abs(chain.Underlying.Price - x.Strike)).First().Strike;
    var contracts = chain.Where(x => x.Strike == strike).ToList();
    var farExpiry = contracts.Max(x => x.Expiry);
    var nearExpiry = contracts.Min(x => x.Expiry);

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

    # Select an expiry date and ITM & OTM strike prices
    strike = sorted([x.strike for x in chain], key=lambda x: abs(x - chain.underlying.price))[0]
    contracts = [x for x in chain if x.strike == strike]
    far_expiry = max([x.expiry for x in contracts])
    near_expiry = min([x.expiry for x in contracts])

3. In the OnDataon_data method, select the contracts and place the order.

Approach A: Call the OptionStrategies.JellyRollOptionStrategies.jelly_roll method with the details of each leg and then pass the result to the Buybuy method.

var jellyRoll = OptionStrategies.JellyRoll(_symbol, strike, nearExpiry, farExpiry);
Buy(jellyRoll, 1);

jelly_roll = OptionStrategies.jelly_roll(self._symbol, strike, near_expiry, far_expiry)
self.buy(jelly_roll, 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.

// Select the call and put contracts
var nearCall = contracts.Single(x => x.Expiry == nearExpiry && x.Right == OptionRight.Call);
var farCall = contracts.Single(x => x.Expiry == farExpiry && x.Right == OptionRight.Call);
var nearPut = contracts.Single(x => x.Expiry == nearExpiry && x.Right == OptionRight.Put);
var farPut = contracts.Single(x => x.Expiry == farExpiry && x.Right == OptionRight.Put);

var legs = new List<Leg>()
{
    Leg.Create(nearCall.Symbol, -1),
    Leg.Create(farCall.Symbol, 1),
    Leg.Create(nearPut.Symbol, 1),
    Leg.Create(farPut.Symbol, -1),
};
ComboMarketOrder(legs, 1);

# Select the call and put contracts
near_call = next(filter(lambda x: x.right == OptionRight.CALL and x.expiry == near_expiry, contracts))
far_call = next(filter(lambda x: x.right == OptionRight.CALL and x.expiry == far_expiry, contracts))
near_put = next(filter(lambda x: x.right == OptionRight.PUT and x.expiry == near_expiry, contracts))
call_put = next(filter(lambda x: x.right == OptionRight.PUT and x.expiry == far_expiry, contracts))           

legs = [
    Leg.create(near_call.symbol, -1),
    Leg.create(far_call.symbol, 1),
    Leg.create(near_put.symbol, 1),
    Leg.create(call_put.symbol, -1),
]
self.combo_market_order(legs, 1)

This is a delta-, gamma-, vega-, and theta-neutral strategy. The payoff is

$$ \begin{array}{rcll} C_{T_1}^{T_1} & = & (S_{T_1} - K)^{+}\\ P_{T_1}^{T_1} & = & (K - S_{T_1})^{+}\\ Payoff_{T_1} & = & (P_{T_1}^{T_1} - P_{T_0}^{T_1} - C_{T_1}^{T_1} + C_{T_0}^{T_1} + C_{T_1}^{T_2} - C_{T_0}^{T_2} - P_{T_1}^{T_2} + P_{T_0}^{T_2})\times m - fee\\ \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C_{T_1}^{T_1} & = & \textrm{Market value of Call with expiry at T1 at time T1}\\ & C_{T_1}^{T_2} & = & \textrm{Market value of Call with expiry at T2 at time T1}\\ & P_{T_1}^{T_1} & = & \textrm{Market value of Put with expiry at T1 at time T1}\\ & P_{T_1}^{T_2} & = & \textrm{Market value of Put with expiry at T2 at time T1}\\ & S_{T_1} & = & \textrm{Underlying asset price at time T1}\\ & K & = & \textrm{Strike price}\\ & Payoff_T & = & \textrm{Payout total at time T}\\ & C_{T_0}^{T_1} & = & \textrm{Market value of Call with expiry at T1 when the trade opened}\\ & C_{T_0}^{T_2} & = & \textrm{Market value of Call with expiry at T2 when the trade opened}\\ & P_{T_0}^{T_1} & = & \textrm{Market value of Put with expiry at T2 when the trade opened}\\ & P_{T_0}^{T_2} & = & \textrm{Market value of Put with expiry at T2 when the trade opened}\\ & m & = & \textrm{Contract multiplier}\\ & T_1 & = & \textrm{Time T1 as the near expiration}\\ & T_2 & = & \textrm{Time T2 as the far expiration} \end{array} $$

The following chart shows the payoff at expiration:

The payoff is dependent on the market prices of the Options, but in theory, if assuming call-put parity exists, the expected payoff would be

$$ \begin{array}{rcll} Payoff_{T_1} & = & Payoff_{\textrm{call calendar spread}} - Payoff_{\textrm{put calendar spread}}\\ & = & K \times (T_2 - T_1) \times r - D \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & r & = & \textrm{Continuous compounding interest rate}\\ & D & = & \textrm{Dividend payment during the life of the option} \end{array} $$

If the Option is American Option, there is a risk of early assignment on the contracts you sell.

The following table shows the price details of the assets in the algorithm:

Asset	Price at position open ($)	Price at the first expiry ($)	Strike ($)
Near-expiry Call	18.50	23.75	832.50
Near-expiry Put	22.50	12.85	832.50
Far-expiry Call	23.90	24.45	832.50
Far-expiry Put	19.00	13.70	832.50
Underlying Equity	-	843.2500	-

Therefore, the payoff is

$$ \begin{array}{rcll} Payoff_{T_1} & = & (P_{T_1}^{T_1} - P_0^{T_1} - C_{T_1}^{T_1} + C_0^{T_1} + C_{T_1}^{T_2} - C_0^{T_2} - P_{T_1}^{T_2} + P_0^{T_2})\times m - fee\\ & = & (12.85 - 22.50 - 23.75 + 18.50 + 24.45 - 23.90 - 13.70 + 19.00)\times100 - 1.00\times4\\ & = & -909.00\\ \end{array} $$

So, the strategy loses $909.

The following algorithm implements a long jelly roll Option strategy: