The strategy invests in U.S. equity options by forming ATM straddles, sorted by implied volatility slope. It buys options with upward sloping volatility and sells those with downward sloping, rebalancing monthly.
ASSET CLASS: options | REGION: United States | FREQUENCY:
Monthly | MARKET: equities | KEYWORD: Cross-Sectional, One-Month Equity ATM Straddle, Trading Strategy
I. STRATEGY IN A NUTSHELL
This strategy trades U.S. ATM equity options, focusing on straddles formed after monthly expiration. Only options with underlying prices above $10 and deltas between ±0.35 and ±0.65 are included. Straddles are sorted into deciles by the slope of the implied volatility term structure. The investor buys options in decile one (steepest upward slope) and sells options in decile ten (most inverted), holding until expiration. The portfolio is equally weighted, with a 20% allocation cap due to skewness risk.
II. ECONOMIC RATIONALE
The strategy exploits the relationship between risk prices and time horizons. Short-maturity options tend to overreact, creating predictable volatility risk premiums. An inverted term structure increases short-term premia while decreasing long-term premia, allowing the strategy to profit from differences in implied volatility across maturities.
III. SOURCE PAPER
Jump Risk and Option Returns [Click to Open PDF]
Jim Campasano, University of Massachusetts Amherst – Isenberg School of Managem
<Abstract>
We show that the term structure of equity volatility is a strong predictor of jumps in the underlying equity. Our analysis provides a risk-based explanation for some of the largest option-based anomalies from the literature. We show that returns of option strategies based upon different measures of term structure slope reflect the horizons over which each measure predicts jumps in the underlying. This further supports the theory that premiums associated with term structure are due to jump risk. In addition, we show that term structure outperforms existing jump predictors from the literature.
IV. BACKTEST PERFORMANCE
| Annualised Return | 34.58% |
| Volatility | 12.7% |
| Beta | 0.05 |
| Sharpe Ratio | 2.72 |
| Sortino Ratio | -1.453 |
| Maximum Drawdown | N/A |
| Win Rate | 36% |
V. FULL PYTHON CODE
from AlgorithmImports import *
from typing import List, Dict
from pandas.core.frame import dataframe
from pandas.core.series import Series
#endregion
class CrossSectionalOneMonthEquityATMStraddleTradingStrategy(QCAlgorithm):
def Initialize(self):
self.SetStartDate(2012, 1, 1)
self.SetCash(1000000)
self.tickers_to_ignore: List[str] = ['DFG']
self.min_expiry: int = 20
self.max_expiry: int = 45
self.period: int = 21 # need n of stock daily prices
self.percentage_traded: float = 0.2
self.min_share_price: int = 10
self.leverage: int = 5
self.quantile: int = 10
self.min_contracts: int = 2
self.day: int = -1
self.fundamental_count: int = 500
self.fundamental_sorting_key = lambda x: x.DollarVolume
self.selection_flag: bool = True
self.data: Dict[Symbol, RollingWindow] = {}
self.symbols_by_ticker: Dict[str, Symbol] = {}
self.subscribed_contracts: Dict[Symbol, Contracts] = {}
self.settings.daily_precise_end_time = False
self.Settings.MinimumOrderMarginPortfolioPercentage = 0.
self.UniverseSettings.Resolution = Resolution.Daily
self.AddUniverse(self.FundamentalSelectionFunction)
self.SetSecurityInitializer(lambda x: x.SetDataNormalizationMode(DataNormalizationMode.Raw))
self.UniverseSettings.DataNormalizationMode = DataNormalizationMode.Raw
def OnSecuritiesChanged(self, changes: SecurityChanges) -> None:
for security in changes.AddedSecurities:
security.SetFeeModel(CustomFeeModel())
security.SetLeverage(self.leverage)
def FundamentalSelectionFunction(self, fundamental: List[Fundamental]) -> List[Symbol]:
# update daily prices of stocks in self.data dictionary
for stock in fundamental:
symbol: Symbol = stock.Symbol
if symbol in self.data:
self.data[symbol].Add(stock.AdjustedPrice)
# rebalance, when contracts expiried
if not self.selection_flag:
return Universe.Unchanged
# select top n stocks by dollar volume
selected: List[Fundamental] = [
x for x in fundamental
if x.HasFundamentalData
and x.Market == 'usa'
and x.Price > self.min_share_price
and x.Symbol.Value not in self.tickers_to_ignore
]
if len(selected) > self.fundamental_count:
selected = [x for x in sorted(selected, key=self.fundamental_sorting_key, reverse=True)[:self.fundamental_count]]
for stock in selected:
symbol: Symbol = stock.Symbol
ticker: str = symbol.Value
self.symbols_by_ticker[ticker] = symbol
if symbol in self.data:
continue
self.data[symbol] = RollingWindow[float](self.period)
history: dataframe = self.History(symbol, self.period, Resolution.Daily)
if history.empty:
continue
closes: Series = history.loc[symbol].close
for time, close in closes.items():
self.data[symbol].Add(close)
# return newly selected symbols
return list(map(lambda x: x.Symbol, selected))
def OnData(self, data: Slice) -> None:
# execute once a day
if self.day == self.Time.day:
return
self.day = self.Time.day
# check if any of the subscribed contracts expired
for _, symbol in self.symbols_by_ticker.items():
if symbol in self.subscribed_contracts and self.subscribed_contracts[symbol].expiry_date <= self.Time.date():
# remove expired contracts
for contract in self.subscribed_contracts[symbol].contracts:
if self.Securities[contract].IsTradable:
# self.RemoveSecurity(contract)
self.Liquidate(contract)
# remove Contracts object for current symbol
del self.subscribed_contracts[symbol]
# perform next selection, when there are no active contracts
if len(self.subscribed_contracts) == 0 and not self.selection_flag:
# liquidate leftovers
if self.Portfolio.Invested:
self.Liquidate()
self.symbols_by_ticker.clear()
self.selection_flag = True
return
# subscribe to new contracts after selection
elif len(self.subscribed_contracts) == 0 and self.selection_flag:
for _, symbol in self.symbols_by_ticker.items():
if symbol in self.data and self.data[symbol].IsReady:
if self.Securities[symbol].IsDelisted:
continue
# get all contracts for current stock symbol
contracts: List[Symbol] = self.OptionChainProvider.GetOptionContractList(symbol, self.Time)
# get current price for etf
underlying_price: float = self.data[symbol][0]
# get strikes from commodity future contracts
strikes: List[float] = [i.ID.StrikePrice for i in contracts]
# can't filter contracts, if there isn't any strike price
if len(strikes) <= 0 or underlying_price == 0:
continue
# filter calls and puts contracts with one month expiry
calls, puts = self.FilterContracts(strikes, contracts, underlying_price)
# make sure, there is at least one call and put contract
if len(calls) > 0 and len(puts) > 0:
# sort by expiry
call: Symbol = sorted(calls, key = lambda x: x.ID.Date, reverse=True)[0]
put: Symbol = sorted(puts, key = lambda x: x.ID.Date, reverse=True)[0]
subscriptions = self.SubscriptionManager.SubscriptionDataConfigService.GetSubscriptionDataConfigs(call.Underlying)
if subscriptions:
# add call contract
self.AddContract(call)
# add put contract
self.AddContract(put)
# retrieve expiry date for contracts
expiry_date: datetime.date = call.ID.Date.date() if call.ID.Date.date() < put.ID.Date.date() else put.ID.Date.date()
# store contracts with expiry date under stock's symbol
self.subscribed_contracts[symbol] = Contracts(expiry_date, underlying_price, [call, put])
# calculate term structure and trade options
elif len(self.subscribed_contracts) != 0 and data.OptionChains.Count != 0 and self.selection_flag:
self.selection_flag = False # this makes sure, there will be no other trades until next selection
term_structure = {} # storing term structures keyed by stock's symbol
for kvp in data.OptionChains:
chain: OptionChain = kvp.Value
ticker: str = chain.Underlying.Symbol.Value
if ticker in self.symbols_by_ticker:
# get stock's symbol
symbol: Symbol = self.symbols_by_ticker[ticker]
# get contracts
contracts: List[Symbol] = [x for x in chain]
# check if there are enough contracts for option and daily prices are ready
if len(contracts) < self.min_contracts or not self.data[symbol].IsReady:
continue
# get call and put implied volatility
call_iv, put_iv = self.GetImpliedVolatilities(contracts)
if call_iv and put_iv:
# make mean from call implied volatility and put implied volatility
iv: float = (call_iv + put_iv) / 2
# get historical volatility
hv: float = self.GetHistoricalVolatility(self.data[symbol])
# store stock's term structure
term_structure[symbol] = (iv - hv) / hv
# can't perform selection
if len(term_structure) < self.quantile:
return
# perform quantile selection
quantile: int = int(len(term_structure) / self.quantile)
sorted_by_term_structure: List[Symbol] = [x[0] for x in sorted(term_structure.items(), key=lambda item: item[1])]
# long top
long: List[Symbol] = sorted_by_term_structure[-quantile:]
# short bottom
short: List[Symbol] = sorted_by_term_structure[:quantile]
# trade execution
self.Liquidate()
# trade long
self.TradeOptions(data, long, True)
# trade short
self.TradeOptions(data, short, False)
def FilterContracts(self,
strikes: List[float],
contracts: List[Symbol],
underlying_price: float) -> List[Symbol]:
''' filter call and put contracts from contracts parameter '''
''' return call and put contracts '''
# Straddle
call_strike: float = min(strikes, key=lambda x: abs(x-underlying_price))
put_strike: float = call_strike
calls: List[Symbol] = [] # storing call contracts
puts: List[Symbol] = [] # storing put contracts
for contract in contracts:
# check if contract has one month expiry
if self.min_expiry < (contract.ID.Date - self.Time).days < self.max_expiry:
# check if contract is call
if contract.ID.OptionRight == OptionRight.Call and contract.ID.StrikePrice == call_strike:
calls.append(contract)
# check if contract is put
elif contract.ID.OptionRight == OptionRight.Put and contract.ID.StrikePrice == put_strike:
puts.append(contract)
# return filtered calls and puts with one month expiry
return calls, puts
def AddContract(self, contract: Symbol) -> None:
''' subscribe option contract, set price mondel and normalization mode '''
option = self.AddOptionContract(contract, Resolution.Daily)
option.PriceModel = OptionPriceModels.CrankNicolsonFD()
def GetImpliedVolatilities(self, contracts: List[Symbol]) -> float:
''' retrieve implied volatility of contracts from contracts parameteres '''
''' returns call and put implied volatility '''
call_iv: Union[None, float] = None
put_iv: Union[None, float] = None
# go through option contracts
for c in contracts:
if c.Right == OptionRight.Call:
# found call option
call_iv = c.ImpliedVolatility
else:
# found put option
put_iv = c.ImpliedVolatility
return call_iv, put_iv
def GetHistoricalVolatility(self, rolling_window_prices: RollingWindow) -> np.ndarray:
''' calculate historical volatility based on daily prices in rolling_window_prices parameter '''
prices: np.ndarray = np.array([x for x in rolling_window_prices])
returns: np.ndarray = (prices[:-1] - prices[1:]) / prices[1:]
return np.std(returns)
def TradeOptions(self,
data: Slice,
symbols: List[Symbol],
long_flag: bool) -> None:
''' on long signal buy call and put option contract '''
''' on short signal sell call and put option contract '''
length: int = len(symbols)
# trade etf's call and put contracts
for symbol in symbols:
# get call and put contract
call, put = self.subscribed_contracts[symbol].contracts
# get underlying price
underlying_price: float = self.subscribed_contracts[symbol].underlying_price
options_q: int = int(((self.Portfolio.TotalPortfolioValue * self.percentage_traded) / length) / (underlying_price * 100))
if call in data and data[call] and put in data and data[put]:
if long_flag:
self.Buy(call, options_q)
self.Buy(put, options_q)
else:
self.Sell(call, options_q)
self.Sell(put, options_q)
class Contracts():
def __init__(self, expiry_date: datetime.date, underlying_price: float, contracts: List[Symbol]) -> None:
self.expiry_date: datetime.date = expiry_date
self.underlying_price: float = underlying_price
self.contracts: List[Symbol] = contracts
# Custom fee model
class CustomFeeModel(FeeModel):
def GetOrderFee(self, parameters: OrderFeeParameters) -> OrderFee:
fee: float = parameters.Security.Price * parameters.Order.AbsoluteQuantity * 0.00005
return OrderFee(CashAmount(fee, "USD"))VI. Backtest Performance
