Option Strategies

Strangle

Introduction

Long Strangle is an Options trading strategy that consists of simultaneously buying an OTM put and an OTM call, where both contracts have the same underlying asset and expiration date. This strategy aims to profit from volatile movements in the underlying stock, either positive or negative.

Compared to a long straddle, the net debit of a long strangle is lower since OTM Options are cheaper. Additionally, the losing range of a long straddle is wider and the strike spread is wider.

Implementation

Follow these steps to implement the long strangle 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, 4, 1);
        SetEndDate(2017, 4, 30);
        SetCash(100000);
    
        var option = AddOption("GOOG", Resolution.Minute);
        _symbol = option.Symbol;
        option.SetFilter(-5, 5, TimeSpan.FromDays(0), TimeSpan.FromDays(30));
    }
    def Initialize(self) -> None:
        self.SetStartDate(2017, 4, 1)
        self.SetEndDate(2017, 4, 30)
        self.SetCash(100000)
        
        option = self.AddOption("GOOG", Resolution.Minute)
        self.symbol = option.Symbol
        option.SetFilter(-5, 5, timedelta(0), timedelta(30))
  3. In the OnData method, select the expiration date and strike prices 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;
    
        // Select an expiration date
        var expiry = chain.OrderBy(contract => contract.Expiry).Last().Expiry;
    
        // Select the OTM call strike
        var callStrikes = chain.Where(contract => contract.Expiry == expiry 
                                                  && contract.Right == OptionRight.Call 
                                                  && contract.Strike > chain.Underlying.Price)
                               .Select(contract => contract.Strike);
        if (callStrikes.Count() == 0) return;
        var callStrike = callStrikes.Min();
    
        // Select the ITM put strike
        var putStrikes = chain.Where(contract => contract.Expiry == expiry 
                                                  && contract.Right == OptionRight.Put 
                                                  && contract.Strike < chain.Underlying.Price)
                              .Select(contract => contract.Strike);
        if (putStrikes.Count() == 0) return;
        var putStrike = putStrikes.Max();
    }
    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
    
        # Select an expiration date
        expiry = sorted(chain, key=lambda contract: contract.Expiry, reverse=True)[0].Expiry
    
        # Select the OTM call strike
        strikes = [contract.Strike for contract in chain if contract.Expiry == expiry]
        call_strikes = [contract.Strike for contract in chain 
            if contract.Expiry == expiry 
            and contract.Right == OptionRight.Call
            and contract.Strike > chain.Underlying.Price]
        if len(call_strikes) == 0: return
        call_strike = min(call_strikes)
    
        # Select the OTM put strike
        put_strikes = [contract.Strike for contract in chain 
            if contract.Expiry == expiry 
            and contract.Right == OptionRight.Put
            and contract.Strike < chain.Underlying.Price]
        if len(put_strikes) == 0: return
        put_strike = max(put_strikes)
  5. In the OnData method, call the OptionStrategies.Strangle method and then submit the order.
  6. var optionStrategy = OptionStrategies.Strangle(_symbol, callStrike, putStrike, expiry);
    Buy(optionStrategy, 1);
    option_strategy = OptionStrategies.Strangle(self.symbol, call_strike, put_strike, expiry)
    self.Buy(option_strategy, 1)

Strategy Payoff

The payoff of the strategy is

$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{C})^{+}\\ P^{OTM}_T & = & (K^{P} - S_T)^{+}\\ P_T & = & (C^{OTM}_T + P^{OTM}_T - C^{OTM}_0 - P^{OTM}_0)\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{OTM}_T & = & \textrm{OTM call value at time T}\\ & P^{OTM}_T & = & \textrm{OTM put value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K^{C} & = & \textrm{OTM call strike price}\\ & K^{P} & = & \textrm{OTM put strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & C^{OTM}_0 & = & \textrm{OTM call value at position opening (debit paid)}\\ & P^{OTM}_0 & = & \textrm{OTM put value at position opening (debit paid)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$

The following chart shows the payoff at expiration:

long strangle strategy payoff

The maximum profit is unlimited if the underlying price rises to infinity at expiration.

The maximum loss is the net debit paid, $C^{OTM}_0 + P^{OTM}_0$. It occurs when the underlying price at expiration is the same as when you opened the trade. In this case, both Options expire worthless.

Example

The following table shows the price details of the assets in the algorithm at Option expiration (2017-04-22):

AssetPrice ($)Strike ($)
Call8.80835.00
Put9.50832.50
Underlying Equity at expiration843.19-

Therefore, the payoff is

$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{C})^{+}\\ & = & (843.19-835.00)^{+}\\ & = & 8.19\\ P^{OTM}_T & = & (K^{P} - S_T)^{+}\\ & = & (832.50-843.19)^{+}\\ & = & 0\\ P_T & = & (C^{OTM}_T + P^{OTM}_T - C^{OTM}_0 - P^{OTM}_0)\times m - fee\\ & = & (8.19+0-8.80-9.50)\times100-1.00\times2\\ & = & -1013 \end{array} $$

So, the strategy losses $1,013.

The following algorithm implements a long strangle Option strategy:

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