# Option Strategies

### Introduction

A Short Straddle consists of selling a call and a put, where both contracts have the same underlying asset, strike price (normally at-the-money), and expiration date. If you enter a short straddle, you bet that the underlying asset will remain relatively stable and not experience significant price movements before the Option expires.

### Implementation

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, 6, 30);
SetCash(100000);

_symbol = option.Symbol;
option.SetFilter(-1, 1, 30, 60);
}
def Initialize(self) -> None:
self.SetStartDate(2017, 4, 1)
self.SetEndDate(2017, 6, 30)
self.SetCash(100000)

self.symbol = option.Symbol
option.SetFilter(-1, 1, 30, 60)
3. In the OnData method, select the expiration date and strike price of the contracts in the strategy legs.
4. public override void OnData(Slice slice)
{
if (Portfolio.Invested ||
!slice.OptionChains.TryGetValue(_symbol, out var chain))
{
return;
}

// Find ATM options with the nearest expiry
var expiry = chain.Min(contract => contract.Expiry);
var contracts = chain.Where(contract => contract.Expiry == expiry)
.OrderBy(contract => Math.Abs(contract.Strike - chain.Underlying.Price))
.ToArray();

if (contracts.Length < 2) return;
def OnData(self, slice: Slice) -> None:
if self.Portfolio.Invested:
return

chain = slice.OptionChains.get(self.symbol, None)
if not chain:
return

# Find ATM options with the nearest expiry
expiry = min([x.Expiry for x in chain])
contracts = sorted([x for x in chain if x.Expiry == expiry],
key=lambda x: abs(chain.Underlying.Price - x.Strike))

if len(contracts) < 2:
return
5. In the OnData method, call the OptionStrategies.Straddle method and then submit the order.
6. var shortStraddle = OptionStrategies.ShortStraddle(_symbol, contracts.Strike, expiry);
Buy(shortStraddle, 1);
short_straddle = OptionStrategies.ShortStraddle(self.symbol, contracts.Strike, expiry)
self.Buy(short_straddle, 1)

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)


### Strategy Payoff

The payoff of the strategy is

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

The following chart shows the payoff at expiration: The maximum profit is $C^{ATM}_0 + P^{ATM}_0$. It occurs when the price of the underlying asset remains exactly at the strike price upon expiration.

The maximum loss is unlimited if the underlying price rises to infinity or drops to zero at expiration.

### Example

The following table shows the price details of the assets in the algorithm at Option expiration (2017-05-20):

AssetPrice ($)Strike ($)
Call19.6835.00
Put21.4835.00
Underlying Equity at early (2017-05-15) call assignment932.22-
Underlying Equity at expiration934.01-

Therefore, the payoff is

$$\begin{array}{rcll} C^{ATM}_T & = & (S_T - K^{C})^{+}\\ & = & (934.01-835.00)^{+}\\ & = & 99.01\\ P^{ATM}_T & = & (K^{P} - S_T)^{+}\\ & = & (835.00-934.01)^{+}\\ & = & 0\\ P_T & = & (-C^{ATM}_T - P^{ATM}_T + C^{ATM}_0 + P^{ATM}_0)\times m - fee\\ & = & (-99.01-0+19.6+21.4)\times 100 - 2.00\\ & = & -5803 \end{array}$$

So, the strategy loses \$5,277. The early assigment doesn't influence the payoff.

The following algorithm implements a short straddle strategy:

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