Option Strategies

Reverse Conversion

Introduction

A Reverse Conversion, or Reversal, is the inverse of a conversion and also a special case of a protective collar. It consist of shorting one lot of the underlying security, buying a call, and selling a put with lower strike price. However, the strategy now serves as an delta-neutral arbitration from Option mispricing instead of a hedge strategy. Note that it only attains a true profit when the risk-free return is greater than the risk-free interest rate.

Implementation

Follow these steps to implement the reverse conversion strategy:

  1. In the Initializeinitialize method, set the start date, set the end date, subscribe to the underlying Equity, and create an Option universe.
    2. private Symbol _symbol;

public override void Initialize()
{
    SetStartDate(2017, 4, 1);
    SetEndDate(2017, 4, 30);
    SetCash(100000);

    UniverseSettings.Asynchronous = true;
    var option = AddOption("GOOG", Resolution.Minute);
    _symbol = option.Symbol;
    option.SetFilter(universe => universe.IncludeWeeklys().Conversion(30, -5));
}
    def initialize(self) -> None:
    self.set_start_date(2017, 4, 1)
    self.set_end_date(2017, 4, 30)
    self.set_cash(100000)

    self.universe_settings.asynchronous = True
    option = self.add_option("GOOG", Resolution.MINUTE)
    self._symbol = option.symbol
    option.set_filter(lambda universe: universe.include_weeklys().conversion(30, -5))

    The Conversionconversion filter narrows the universe down to just the two contracts you need to form a reverse conversion.

  2. In the OnDataon_data method, select the strike and expiry of the contracts in the strategy legs.
    3. public override void OnData(Slice slice)
{
    if (Portfolio.Invested) return;

    // Get the OptionChain
    if (!slice.OptionChains.TryGetValue(_symbol, out var chain)) return;

    // Select an expiry date and ATM strike price
    var expiry = chain.Max(x => x.Expiry);
    var strike = chain.OrderBy(x => Math.Abs(x.Strike - chain.Underlying.Price)).First().Strike;
    def on_data(self, slice: Slice) -> None:
    if self.portfolio.invested:
        return

    # Get the OptionChain
    chain = slice.option_chains.get(self._symbol, None)
    if not chain:
        return

    # Select an expiry date and ATM strike price
    expiry = max([x.expiry for x in chain])
    strike = sorted(chain, key = lambda x: abs(x.strike - chain.underlying.price))[0].strike
  3. In the OnDataon_data method, select the contracts and place the orders.

    4. Approach A: Call the OptionStrategies.ReverseConversionOptionStrategies.reverse_conversion method with the details of each leg and then pass the result to the Buybuy method.

    var reverseConversion = OptionStrategies.ReverseConversion(_symbol, strike, expiry);
Buy(reverseConversion, 1);
    reverse_conversion = OptionStrategies.reverse_conversion(self._symbol, strike, expiry)
self.buy(reverse_conversion, 1)

    Approach B: Create a list of Leg objects and then call the Combo Market Ordercombo_market_order, Combo Limit Ordercombo_limit_order, or Combo Leg Limit Ordercombo_leg_limit_order method.

    // Select the call and put contracts
var call = chain.Single(x => x.Expiry == expiry && x.Strike == strike && x.Right == OptionRight.Call);
var put = chain.Single(x => x.Expiry == expiry && x.Strike == strike && x.Right == OptionRight.Put);

var legs = new List<Leg>()
    {
        Leg.Create(call.Symbol, 1),
        Leg.Create(put.Symbol, -1),
        Leg.Create(chain.Underlying.Symbol, -chain.Underlying.SymbolProperties.ContractMultiplier)
    };
ComboMarketOrder(legs, 1);
    # Select the call and put contracts
call = [x for x in chain if x.right == OptionRight.CALL and x.expiry == expiry and x.strike == strike][0]
put = [x for x in chain if x.right == OptionRight.PUT and x.expiry == expiry and x.strike == strike][0]

legs = [
    Leg.create(call.symbol, 1),
    Leg.create(put.symbol, -1),
    Leg.create(chain.underlying.symbol, -chain.underlying.symbol_properties.contract_multiplier)
]
self.combo_market_order(legs, 1)

Strategy Payoff

This is a fixed payoff, delta-neutral strategy. The payoff is

$$ \begin{array}{rcll} C_T & = & (S_T - K)^{+}\\ P_T & = & (K - S_T)^{+}\\ Payoff_T & = & (S_0 - S_T + C_T - P_T - C_0 + P_0)\times m - fee\\ & = & (S_0 - K - C_0 + P_0)\times m - fee \end{array} $$ $$ \begin{array}{rcll} \textrm{where} & C_T & = & \textrm{Call value at time T}\\ & P_T & = & \textrm{Put value at time T}\\ & S_T & = & \textrm{Underlying asset price at time T}\\ & K & = & \textrm{Strike price}\\ & Payoff_T & = & \textrm{Payout total at time T}\\ & S_0 & = & \textrm{Underlying asset price when the trade opened}\\ & C_0 & = & \textrm{Call price when the trade opened (credit received)}\\ & P_0 & = & \textrm{Put price when the trade opened (debit paid)}\\ & m & = & \textrm{Contract multiplier}\\ & T & = & \textrm{Time of expiration} \end{array} $$

The following chart shows the payoff at expiration:

reverse conversion strategy payoff

The payoff is only dependent on the strike price and the initial asset prices.

If the Option is American Option, there is a risk of early assignment on the contract you sell.

Example

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

AssetPrice ($)Strike ($)
Call10.30832.50
Put7.40832.50
Underlying Equity at position opens832.26-

Therefore, the payoff is

$$ \begin{array}{rcll} Payoff_T & = & (S_0 - K - C_0 + P_0)\times m - fee\\ & = & (832.26 - 832.50 - 10.30 + 7.40)\times100-1.00\times3\\ & = & -317.00\\ \end{array} $$

So, the strategy loses $317.

The following algorithm implements a reverse conversion Option strategy:

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