Option Strategies
Call Butterfly
Introduction
The call butterfly strategy is the combination of a bull call spread and a bear call spread. In the call butterfly, all of the calls should have the same underlying Equity, the same expiration date, and the same strike price distance between the ITM-ATM and OTM-ATM call pairs. The call butterfly can be long or short.
Long Call Butterfly
The long call butterfly consists of a long ITM call, a long OTM call, and 2 short ATM calls. This strategy profits from low volatility in the underlying Equity price.
Short Call Butterfly
The short call butterfly consists of a short ITM call, a short OTM call, and 2 long ATM calls. This strategy profits from high volatility in the underlying Equity price.
Implementation
Follow these steps to implement the call butterfly strategy:
- In the
Initialize
method, set the start date, end date, cash, and Option universe. - In the
OnData
method, select the expiration and strikes of the contracts in the strategy legs. - In the
OnData
method, call theOptionStrategies.CallButterfly
method and then submit the order.
private Symbol _symbol; public override void Initialize() { SetStartDate(2017, 2, 1); SetEndDate(2017, 3, 5); SetCash(500000); var option = AddOption("GOOG", Resolution.Minute); _symbol = option.Symbol; option.SetFilter(universe => universe.IncludeWeeklys() .Strikes(-15, 15) .Expiration(TimeSpan.FromDays(0), TimeSpan.FromDays(31))); }
def Initialize(self) -> None: self.SetStartDate(2017, 2, 1) self.SetEndDate(2017, 3, 5) 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.IncludeWeeklys().Strikes(-15, 15).Expiration(timedelta(0), timedelta(31))
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 furthest expiry date of the contracts var expiry = chain.OrderByDescending(x => x.Expiry).First().Expiry; // Select the call Option contracts with the furthest expiry var calls = chain.Where(x => x.Expiry == expiry && x.Right == OptionRight.Call); if (calls.Count() == 0) return; // Get the strike prices of the all the call Option contracts var callStrikes = calls.Select(x => x.Strike).OrderBy(x => x); // Get the ATM strike price var atmStrike = calls.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().Strike; // Get the strike prices for the contracts not ATM var spread = Math.Min(Math.Abs(callStrikes.First() - atmStrike), Math.Abs(callStrikes.Last() - atmStrike)); var itmStrike = atmStrike - spread; var otmStrike = atmStrike + spread;
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 furthest expiry date of the contracts expiry = sorted(chain, key = lambda x: x.Expiry, reverse=True)[0].Expiry # Select the call Option contracts with the furthest expiry calls = [i for i in chain if i.Expiry == expiry and i.Right == OptionRight.Call] if len(calls) == 0: return # Get the strike prices of the all the call Option contracts call_strikes = sorted([x.Strike for x in calls]) # Get the ATM strike price atm_strike = sorted(calls, key=lambda x: abs(x.Strike - chain.Underlying.Price))[0].Strike # Get the strike prices for the contracts not ATM spread = min(abs(call_strikes[0] - atm_strike), abs(call_strikes[-1] - atm_strike)) itm_strike = atm_strike - spread otm_strike = atm_strike + spread
var optionStrategy = OptionStrategies.CallButterfly(_symbol, otmStrike, atmStrike, itmStrike, expiry); Buy(optionStrategy, 1); // if long call butterfly Sell(optionStrategy, 1); // if short call butterfly
option_strategy = OptionStrategies.CallButterfly(self.symbol, otm_strike, atm_strike, itm_strike, expiry) self.Buy(option_strategy, 1) # if long call butterfly self.Sell(option_strategy, 1) # if short call butterfly
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 call butterfly can be long or short.
Long Call Butterfly
The long call butterfly is a limited-reward-limited-risk strategy. The payoff is
$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ P_T & = & (C^{OTM}_T + C^{ITM}_T - 2\times C^{ATM}_T + 2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0)\times m - fee\\ \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{OTM}_T & = & \textrm{OTM call value at time T}\\ & C^{ITM}_T & = & \textrm{ITM call value at time T}\\ & C^{ATM}_T & = & \textrm{ATM call value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K^{OTM} & = & \textrm{OTM call strike price}\\ & K^{ITM} & = & \textrm{ITM call strike price}\\ & K^{ATM} & = & \textrm{ATM call strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & C^{ITM}_0 & = & \textrm{ITM call value at position opening (debit paid)}\\ & C^{OTM}_0 & = & \textrm{OTM call value at position opening (debit paid)}\\ & C^{ATM}_0 & = & \textrm{OTM call value at position opening (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$The following chart shows the payoff at expiration:

The maximum profit is $K^{ATM} - K^{ITM} + 2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0$. It occurs when the underlying price is the same price at expiration as it was when opening the position and the payouts of the bull and bear call spreads are at their maximum.
The maximum loss is the net debit paid: $2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0$. It occurs when the underlying price is less than ITM strike or greater than OTM strike at expiration.
If the Option is an American Option, there is a risk of early assignment on the sold contracts.
Short Call Butterfly
The short call butterfly is a limited-reward-limited-risk strategy. The payoff is
$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ P_T & = & (2\times C^{ATM}_T - C^{OTM}_T - C^{ITM}_T - 2\times C^{ATM}_0 + C^{ITM}_0 + C^{OTM}_0)\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{OTM}_T & = & \textrm{OTM call value at time T}\\ & C^{ITM}_T & = & \textrm{ITM call value at time T}\\ & C^{ATM}_T & = & \textrm{ATM call value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K^{OTM} & = & \textrm{OTM call strike price}\\ & K^{ITM} & = & \textrm{ITM call strike price}\\ & K^{ATM} & = & \textrm{ATM call strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & C^{ITM}_0 & = & \textrm{ITM call value at position opening (credit received)}\\ & C^{OTM}_0 & = & \textrm{OTM call value at position opening (credit received)}\\ & C^{ATM}_0 & = & \textrm{ATM call value at position opening (debit paid)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$The following chart shows the payoff at expiration:

The maximum profit is the net credit received: $C^{ITM}_0 + C^{OTM}_0 - 2\times C^{ATM}_0$. It occurs when the underlying price is less than ITM strike or greater than OTM strike at expiration.
The maximum loss is $K^{ATM} - K^{ITM} + C^{ITM}_0 + C^{OTM}_0 - 2\times C^{ATM}_0$. It occurs when the underlying price is at the same level as when you opened the trade.
If the Option is an American Option, there is a risk of early assignment on the sold contracts.
Example
The following table shows the price details of the assets in the long version of the algorithm:
Asset | Price ($) | Strike ($) |
---|---|---|
OTM call | 4.90 | 767.50 |
ATM call | 15.00 | 800.00 |
ITM call | 41.00 | 832.50 |
Underlying Equity at expiration | 829.08 | - |
Therefore, the payoff is
$$ \begin{array}{rcll} C^{OTM}_T & = & (S_T - K^{OTM})^{+}\\ & = & (767.50-829.08)^{+}\\ & = & 0\\ C^{ITM}_T & = & (S_T - K^{ITM})^{+}\\ & = & (832.50-829.08)^{+}\\ & = & 3.42\\ C^{ATM}_T & = & (S_T - K^{ATM})^{+}\\ & = & (800.00-829.08)^{+}\\ & = & 0\\ P_T & = & (C^{OTM}_T + C^{ITM}_T - 2\times C^{ATM}_T + 2\times C^{ATM}_0 - C^{ITM}_0 - C^{OTM}_0)\times m - fee\\ & = & (0+3.42-0\times2-4.90-41.00+15.00\times2)\times100-1.00\times4\\ & = & -1252 \end{array} $$So, the strategy losses $1,252.
The following algorithm implements a long call butterfly Option strategy: