Option Strategies

Short Box Spread

Introduction

A Short Box Spread is the inverse of a box spread, as well as the combination of a bear call spread and a bull put spread. It consists of buying an OTM call at strike $A$, selling an ITM put at strike $A$, buying an OTM put and strike $B < A$, and selling an ITM call at strike $B$, where all of the contracts have the same expiry date. This strategy serves as an delta-neutral arbitration from Option mispricing. Note that it only attains a true profit when the risk-free return is greater than the risk-free interest rate.

Implementation

Follow these steps to implement the short box spread strategy:

  1. In the Initializeinitialize method, set the start date, set the end date, subscribe to the underlying Equity, and create an Option universe.
    2. private Symbol _symbol;

public override void Initialize()
{
    SetStartDate(2017, 4, 1);
    SetEndDate(2017, 4, 30);
    SetCash(100000);

    UniverseSettings.Asynchronous = true;
    var option = AddOption("GOOG", Resolution.Minute);
    _symbol = option.Symbol;
    option.SetFilter(universe => universe.IncludeWeeklys().BoxSpread(30, 5));
}
    def initialize(self) -> None:
    self.set_start_date(2017, 4, 1)
    self.set_end_date(2017, 4, 30)
    self.set_cash(100000)

    self.universe_settings.asynchronous = True
    option = self.add_option("GOOG", Resolution.MINUTE)
    self._symbol = option.symbol
    option.set_filter(lambda universe: universe.include_weeklys().box_spread(30, 5))

    The BoxSpreadbox_spread filter narrows the universe down to just the four contracts you need to form a short box spread.

  2. In the OnDataon_data method, select the strike and expiry of the contracts in the strategy legs.
    3. public override void OnData(Slice slice)
{
    if (Portfolio.Invested) return;

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

    // Select an expiry date and ITM & OTM strike prices
    var expiry = chain.Max(x => x.Expiry);
    var contracts = chain.Where(x => x.Expiry == expiry).ToList();
    var higherStrike = contracts.Max(x => x.Strike);
    var lowerStrike = contracts.Min(x => x.Strike);
    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
    expiry = max([x.expiry for x in chain])
    contracts = [x for x in chain if x.expiry == expiry]
    lower_strike = min([x.strike for x in contracts])
    higher_strike = max([x.strike for x in contracts])
  3. In the OnDataon_data method, select the contracts and place the orders.

    4. Approach A: Call the OptionStrategies.ShortBoxSpreadOptionStrategies.short_box_spread method with the details of each leg and then pass the result to the Buybuy method.

    var shortBoxSpread = OptionStrategies.ShortBoxSpread(_symbol, higherStrike, lowerStrike, expiry);
Buy(shortBoxSpread, 1);
    short_box_spread = OptionStrategies.short_box_spread(self._symbol, higher_strike, lower_strike, expiry)
self.buy(short_box_spread, 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 itmCall = chain.Single(x => x.Expiry == expiry && x.Strike == lowerStrike && x.Right == OptionRight.Call);
var otmCall = chain.Single(x => x.Expiry == expiry && x.Strike == higherStrike && x.Right == OptionRight.Call);
var itmPut = chain.Single(x => x.Expiry == expiry && x.Strike == higherStrike && x.Right == OptionRight.Put);
var otmPut = chain.Single(x => x.Expiry == expiry && x.Strike == lowerStrike && x.Right == OptionRight.Put);
    
var legs = new List<Leg>()
    {
        Leg.Create(itmCall.Symbol, -1),
        Leg.Create(itmPut.Symbol, -1),
        Leg.Create(otmCall.Symbol, 1),
        Leg.Create(otmPut.Symbol, 1),
    };
ComboMarketOrder(legs, 1);
    # Select the call and put contracts
itm_call = [x for x in chain if x.right == OptionRight.CALL and x.expiry == expiry and x.strike == lower_strike][0]
otm_call = [x for x in chain if x.right == OptionRight.CALL and x.expiry == expiry and x.strike == higher_strike][0]
itm_put = [x for x in chain if x.right == OptionRight.PUT and x.expiry == expiry and x.strike == higher_strike][0]
otm_put = [x for x in chain if x.right == OptionRight.PUT and x.expiry == expiry and x.strike == lower_strike][0]
    
legs = [
    Leg.create(itm_call.symbol, -1),
    Leg.create(itm_put.symbol, -1),
    Leg.create(otm_call.symbol, 1),
    Leg.create(otm_put.symbol, 1),
]
self.combo_market_order(legs, 1)

Strategy Payoff

This is a fixed payoff, delta-neutral strategy. The payoff is

$$ \begin{array}{rcll} C_T^{ITM} & = & (S_T - K_{-})^{+}\\ C_T^{OTM} & = & (S_T - K_{+})^{+}\\ P_T^{ITM} & = & (K_{+} - S_T)^{+}\\ P_T^{OTM} & = & (K_{-} - S_T)^{+}\\ Payoff_T & = & (C_{T_0}^{ITM} - C_T^{ITM} + P_{T_0}^{ITM} - P_T^{ITM} - C_{T_0}^{OTM} + C_T^{OTM} - P_{T_0}^{OTM} + P_T^{OTM})\times m - fee\\ & = & (K_{-} - K_{+} + C_{T_0}^{ITM} + P_{T_0}^{ITM} - C_{T_0}^{OTM} - P_{T_0}^{OTM})\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C_T^{ITM} & = & \textrm{ITM Call value at time T}\\ & C_T^{OTM} & = & \textrm{OTM Call value at time T}\\ & P_T^{ITM} & = & \textrm{ITM Put value at time T}\\ & P_T^{OTM} & = & \textrm{OTM Put value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K_{+} & = & \textrm{Higher strike price}\\ & K_{-} & = & \textrm{Lower strike price}\\ & Payoff_T & = & \textrm{Payout total at time T}\\ & C_{T_0}^{ITM} & = & \textrm{ITM Call price when the trade opened (debit paid)}\\ & C_{T_0}^{OTM} & = & \textrm{OTM Call price when the trade opened (credit received)}\\ & P_{T_0}^{ITM} & = & \textrm{ITM Put price when the trade opened (debit paid)}\\ & P_{T_0}^{OTM} & = & \textrm{OTM Put price when the trade opened (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$

The following chart shows the payoff at expiration:

short box spread strategy payoff

The payoff is only dependent on the strike price and the initial asset prices.

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

Example

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

AssetPrice ($)Strike ($)
ITM Call23.00810.00
ITM Put23.80857.50
OTM Call1.85857.50
OTM Put2.75810.00
Underlying Equity at expiration843.25-

Therefore, the payoff is

$$ \begin{array}{rcll} Payoff_T & = & (K_{-} - K_{+} + C_0^{ITM} + P_0^{ITM} - C_0^{OTM} - P_0^{OTM})\times m - fee\\ & = & (810.00 - 857.50 + 23.00 + 23.80 - 1.85 - 2.75)\times100 - 1.00\times4\\ & = & -534.00\\ \end{array} $$

So, the strategy loses $534.

The following algorithm implements a short box spread Option strategy:

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