Option Strategies

Follow these steps to implement the naked call strategy:

1. In the Initialize method, set the start date, end date, starting cash, and Options universe.

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)

2. In the OnData method, select the Option contract.

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]

3. In the OnData method, call the OptionStrategies.NakedCall method and then submit the order.

var nakedCall = OptionStrategies.NakedCall(_symbol, atmCall.Strike, expiry);
Buy(nakedCall, 1);

_call = atmCall.Symbol;

naked_call = OptionStrategies.NakedCall(self.symbol, atm_call.Strike, expiry)
self.Buy(naked_call, 1)

self.call = atm_call.Symbol

Option strategies synchronously execute by default. To asynchronously execute Option strategies, set the asynchronous argument to Falsefalse. 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)

The payoff of the strategy is

$$ \begin{array}{rcll} C^{K}_T & = & (S_T - K)^{+}\\ P_T & = & (C^{K}_0 - C^{K}_T)\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C^{K}_T & = & \textrm{Call value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K & = & \textrm{Call strike price}\\ & P_T & = & \textrm{Payout total at time T}\\ & C^{K}_0 & = & \textrm{Call price when the trade opened (credit received)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$

The following chart shows the payoff at expiration:

The maximum profit is $C^{K}_0$, which occurs when the underlying price is at or below the strike price of the call at expiration.

The maximum loss is unlimited because there is no limit to how high the underlying asset's price can rise.

If the Option is American Option, there is risk of early assignment on the sold contract.

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

Asset	Price ($)	Strike ($)
Call	3.35	185.00
Underlying Equity at expiration	190.01	-

Therefore, the payoff is

$$ \begin{array}{rcll} C^{K}_T & = & (S_T - K)^{+}\\ & = & (190.01 - 185)^{+}\\ & = & 5.01\\ P_T & = & (C^{K}_0 - C^{K}_T)\times m - fee\\ & = & (3.35 - 5.01)\times m - fee\\ & = & -1.66 \times 100 - 2\\ & = & -167 \end{array} $$

So, the strategy loses $167.

The following algorithm implements a naked call strategy: