Option Strategies
Protective Call
Introduction
A Protective Call consists of a short position in a stock and a long position in a call Option for the same amount of stock. Protective calls aim to hedge the short position of a stock with a long ATM or slightly OTM call Option. At any time for American Options or at expiration for European Options, if the stock moves below the strike price, the Option contract becomes worthless but the short position acquires an unrealized gain. If the underlying price moves above the strike, you can exercise the Options contract and receive the underlying Equity, which closes your short position.
Implementation
Follow these steps to implement the protective call strategy:
- In the
Initialize
method, set the start date, end date, cash, and Options universe. - In the
OnData
method, select the Option contract. - In the
OnData
method, call theOptionStrategies.ProtectiveCall
method and then submit the order.
private Symbol _call, _symbol; public override void Initialize() { SetStartDate(2014, 1, 1); SetEndDate(2014, 3, 1); SetCash(100000); var option = AddOption("IBM"); _symbol = option.Symbol; option.SetFilter(-3, 3, 0, 31); }
def Initialize(self) -> None: self.SetStartDate(2014, 1, 1) self.SetEndDate(2014, 3, 1) self.SetCash(100000) option = self.AddOption("IBM") self.symbol = option.Symbol self.call = None option.SetFilter(-3, 3, 0, 31)
public override void OnData(Slice slice) { if (_call != null && Portfolio[_call].Invested) return; if (!slice.OptionChains.TryGetValue(_symbol, out var chain)) return; // Find ATM call with the farthest expiry var expiry = chain.Max(x => x.Expiry); var atmCall = chain .Where(x => x.Right == OptionRight.Call && x.Expiry == expiry) .OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)) .FirstOrDefault();
def OnData(self, slice: Slice) -> None: if self.call and self.Portfolio[self.call].Invested: return chain = slice.OptionChains.get(self.symbol) if not chain: return # Find ATM call with the farthest expiry expiry = max([x.Expiry for x in chain]) call_contracts = sorted([x for x in chain if x.Right == OptionRight.Call and x.Expiry == expiry], key=lambda x: abs(chain.Underlying.Price - x.Strike)) if not call_contracts: return atm_call = call_contracts[0]
var protectiveCall = OptionStrategies.ProtectiveCall(_symbol, atmCall.Strike, expiry); Buy(protectiveCall, 1); _call = atmCall.Symbol;
protective_call = OptionStrategies.ProtectiveCall(self.symbol, atm_call.Strike, expiry) self.Buy(protective_call, 1) self.call = atm_call.Symbol
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
method.
Buy(optionStrategy, quantity, asynchronous, tag, orderProperties);
self.Buy(option_strategy, quantity, asynchronous, tag, order_properties)
Strategy Payoff
The payoff of the strategy is
$$ \begin{array}{rcll} C^{K}_T & = & (S_T - K)^{+}\\ P_T & = & (S_0 - S_T + C^{K}_T - C^{K}_0)\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{K}_T & = & \textrm{Call value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K & = & \textrm{Call strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & S_0 & = & \textrm{Underlying asset price when the trade opened}\\ & C^{K}_0 & = & \textrm{Call price when the trade opened (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$The following chart shows the payoff at expiration:

The maximum profit is $S_0 - C^{K}_0$, which occurs when the underlying price is $0$.
The maximum loss is $S_0 - K - C^{K}_0$, which occurs when the underlying price is above the strike price.
Example
The following table shows the price details of the assets in the algorithm:
Asset | Price ($) | Strike ($) |
---|---|---|
Call | 3.50 | 185.00 |
Underlying Equity at start of the trade | 186.94 | - |
Underlying Equity at expiration | 190.01 | - |
Therefore, the payoff is
$$ \begin{array}{rcll} C^{K}_T & = & (S_T - K)^{+}\\ & = & (190.01 - 185)^{+}\\ & = & 5.01\\ P_T & = & (S_0 - S_T + C^{K}_T - C^{K}_0)\times m - fee\\ & = & (186.94 - 190.01 + 5.01 - 3.50)\times m - fee\\ & = & -1.56 \times 100 - 2\\ & = & -158 \end{array} $$So, the strategy losses $158.
The following algorithm implements a protective call Option strategy: