public void BlackScholesPortfolioTest()
{
const decimal price = 20.00m;
const decimal underlyingPrice = 200m;
const decimal underlyingVol = 0.15m;
const decimal riskFreeRate = 0.01m;
var tz = TimeZones.NewYork;
var evaluationDate = new DateTime(2015, 2, 19);
var spy = Symbols.SPY;
var SPY_C_192_Feb19_2016E = GetOptionSymbol(spy, OptionStyle.European, OptionRight.Call);
// setting up underlying
var equity = GetEquity(spy, underlyingPrice, underlyingVol, tz);
// setting up European style call option
var contract = GetOptionContract(SPY_C_192_Feb19_2016E, spy, evaluationDate);
var optionCall = GetOption(SPY_C_192_Feb19_2016E, equity, tz);
optionCall.SetMarketPrice(new Tick {
Value = price
});
// running evaluation
var priceModel = OptionPriceModels.BlackScholes();
var results = priceModel.Evaluate(optionCall, null, contract);
var callPrice = results.TheoreticalPrice;
var greeks = results.Greeks;
// BS equation
var rightPart = greeks.Theta + riskFreeRate * underlyingPrice * greeks.Delta + 0.5m * underlyingVol * underlyingVol * underlyingPrice * underlyingPrice * greeks.Gamma;
var leftPart = riskFreeRate * callPrice;
Assert.AreEqual((double)leftPart, (double)rightPart, 0.0001);
}
public override void Initialize()
{
SetStartDate(2021, 1, 4);
SetEndDate(2021, 1, 31);
var spx = AddIndex("SPX", Resolution.Minute);
spx.VolatilityModel = new StandardDeviationOfReturnsVolatilityModel(60, Resolution.Minute, TimeSpan.FromMinutes(1));
_spx = spx.Symbol;
// Select an index option expiring ITM, and adds it to the algorithm.
_spxOption = AddIndexOptionContract(OptionChainProvider.GetOptionContractList(_spx, Time)
.Where(x => x.ID.StrikePrice <= 3200m && x.ID.OptionRight == OptionRight.Call && x.ID.Date.Year == 2021 && x.ID.Date.Month == 1)
.OrderByDescending(x => x.ID.StrikePrice)
.Take(1)
.Single(), Resolution.Minute);
_spxOption.PriceModel = OptionPriceModels.BlackScholes();
_expectedOptionContract = QuantConnect.Symbol.CreateOption(_spx, Market.USA, OptionStyle.European, OptionRight.Call, 3200m, new DateTime(2021, 1, 15));
if (_spxOption.Symbol != _expectedOptionContract)
{
throw new Exception($"Contract {_expectedOptionContract} was not found in the chain");
}
}
public void PutCallParityTest()
{
const decimal underlyingPrice = 200m;
const decimal underlyingVol = 0.15m;
const decimal riskFreeRate = 0.01m;
var tz = TimeZones.NewYork;
var evaluationDate = new DateTime(2015, 2, 19);
var spy = Symbols.SPY;
var SPY_C_192_Feb19_2016E = GetOptionSymbol(spy, OptionStyle.European, OptionRight.Call);
var SPY_P_192_Feb19_2016E = GetOptionSymbol(spy, OptionStyle.European, OptionRight.Put);
// setting up underlying
var equity = GetEquity(spy, underlyingPrice, underlyingVol, tz);
// setting up European style call option
var contractCall = GetOptionContract(SPY_C_192_Feb19_2016E, spy, evaluationDate);
var optionCall = GetOption(SPY_C_192_Feb19_2016E, equity, tz);
// setting up European style put option
var contractPut = GetOptionContract(SPY_P_192_Feb19_2016E, spy, evaluationDate);
var optionPut = GetOption(SPY_P_192_Feb19_2016E, equity, tz);
// running evaluation
var priceModel = OptionPriceModels.BlackScholes();
var resultsCall = priceModel.Evaluate(optionCall, null, contractCall);
var resultsPut = priceModel.Evaluate(optionPut, null, contractPut);
var callPrice = resultsCall.TheoreticalPrice;
var putPrice = resultsPut.TheoreticalPrice;
// Put-call parity equation
var rightPart = putPrice + underlyingPrice; // no yield
var leftPart = callPrice + contractCall.Strike * (decimal)Math.Exp((double)-riskFreeRate);
Assert.AreEqual((double)leftPart, (double)rightPart, 0.0001);
}
public void BlackScholesPortfolioTest()
{
const decimal price = 20.00m;
const decimal underlyingPrice = 200m;
const decimal underlyingVol = 0.15m;
const decimal riskFreeRate = 0.01m;
var tz = TimeZones.NewYork;
var evaluationDate = new DateTime(2015, 2, 19);
var SPY_C_192_Feb19_2016E = Symbol.CreateOption("SPY", Market.USA, OptionStyle.European, OptionRight.Call, 192m, new DateTime(2016, 02, 19));
// setting up underlying
var equity = new Equity(
SecurityExchangeHours.AlwaysOpen(tz),
new SubscriptionDataConfig(typeof(TradeBar), Symbols.SPY, Resolution.Minute, tz, tz, true, false, false),
new Cash(Currencies.USD, 0, 1m),
SymbolProperties.GetDefault(Currencies.USD),
ErrorCurrencyConverter.Instance,
RegisteredSecurityDataTypesProvider.Null
);
equity.SetMarketPrice(new Tick {
Value = underlyingPrice
});
equity.VolatilityModel = new DummyVolatilityModel(underlyingVol);
// setting up European style option
var contract = new OptionContract(SPY_C_192_Feb19_2016E, Symbols.SPY)
{
Time = evaluationDate
};
var optionCall = new Option(
SecurityExchangeHours.AlwaysOpen(tz),
new SubscriptionDataConfig(typeof(TradeBar), SPY_C_192_Feb19_2016E, Resolution.Minute, tz, tz, true, false, false),
new Cash(Currencies.USD, 0, 1m),
new OptionSymbolProperties(SymbolProperties.GetDefault(Currencies.USD)),
ErrorCurrencyConverter.Instance,
RegisteredSecurityDataTypesProvider.Null
);
optionCall.SetMarketPrice(new Tick {
Value = price
});
optionCall.Underlying = equity;
// running evaluation
var priceModel = OptionPriceModels.BlackScholes();
var results = priceModel.Evaluate(optionCall, null, contract);
var callPrice = results.TheoreticalPrice;
var greeks = results.Greeks;
// BS equation
var rightPart = greeks.Theta + riskFreeRate * underlyingPrice * greeks.Delta + 0.5m * underlyingVol * underlyingVol * underlyingPrice * underlyingPrice * greeks.Gamma;
var leftPart = riskFreeRate * callPrice;
Assert.AreEqual((double)leftPart, (double)rightPart, 0.0001);
}
public override void Initialize()
{
SetStartDate(2014, 6, 9);
SetEndDate(2014, 6, 9);
var option = AddOption("AAPL", Resolution.Minute);
// BlackSholes model does not support American style options
option.PriceModel = OptionPriceModels.BlackScholes();
SetWarmup(2, Resolution.Daily);
Init(option, optionStyleIsSupported: false);
}
public override void Initialize()
{
SetStartDate(2021, 1, 14);
SetEndDate(2021, 1, 14);
var option = AddIndexOption("SPX", Resolution.Hour);
// BlackScholes model supports European style options
option.PriceModel = OptionPriceModels.BlackScholes();
SetWarmup(7, Resolution.Daily);
Init(option, optionStyleIsSupported: true);
}
public void PutCallParityTest()
{
const decimal underlyingPrice = 200m;
const decimal underlyingVol = 0.15m;
const decimal riskFreeRate = 0.01m;
var tz = TimeZones.NewYork;
var evaluationDate = new DateTime(2015, 2, 19);
var SPY_C_192_Feb19_2016E = Symbol.CreateOption("SPY", Market.USA, OptionStyle.European, OptionRight.Call, 192m, new DateTime(2016, 02, 19));
var SPY_P_192_Feb19_2016E = Symbol.CreateOption("SPY", Market.USA, OptionStyle.European, OptionRight.Put, 192m, new DateTime(2016, 02, 19));
// setting up underlying
var equity = new Equity(SecurityExchangeHours.AlwaysOpen(tz), new SubscriptionDataConfig(typeof(TradeBar), Symbols.SPY, Resolution.Minute, tz, tz, true, false, false), new Cash(CashBook.AccountCurrency, 0, 1m), SymbolProperties.GetDefault(CashBook.AccountCurrency));
equity.SetMarketPrice(new Tick {
Value = underlyingPrice
});
equity.VolatilityModel = new DummyVolatilityModel(underlyingVol);
// setting up European style call option
var contractCall = new OptionContract(SPY_C_192_Feb19_2016E, Symbols.SPY)
{
Time = evaluationDate
};
var optionCall = new Option(SecurityExchangeHours.AlwaysOpen(tz), new SubscriptionDataConfig(typeof(TradeBar), SPY_C_192_Feb19_2016E, Resolution.Minute, tz, tz, true, false, false), new Cash(CashBook.AccountCurrency, 0, 1m), new OptionSymbolProperties(SymbolProperties.GetDefault(CashBook.AccountCurrency)));
optionCall.Underlying = equity;
// setting up European style put option
var contractPut = new OptionContract(SPY_P_192_Feb19_2016E, Symbols.SPY)
{
Time = evaluationDate
};
var optionPut = new Option(SecurityExchangeHours.AlwaysOpen(tz), new SubscriptionDataConfig(typeof(TradeBar), SPY_P_192_Feb19_2016E, Resolution.Minute, tz, tz, true, false, false), new Cash(CashBook.AccountCurrency, 0, 1m), new OptionSymbolProperties(SymbolProperties.GetDefault(CashBook.AccountCurrency)));
optionPut.Underlying = equity;
// running evaluation
var priceModel = OptionPriceModels.BlackScholes();
var resultsCall = priceModel.Evaluate(optionCall, null, contractCall);
var resultsPut = priceModel.Evaluate(optionPut, null, contractPut);
var callPrice = resultsCall.TheoreticalPrice;
var putPrice = resultsPut.TheoreticalPrice;
// Put-call parity equation
var rightPart = putPrice + underlyingPrice; // no yield
var leftPart = callPrice + contractCall.Strike * (decimal)Math.Exp((double)-riskFreeRate);
Assert.AreEqual((double)leftPart, (double)rightPart, 0.0001);
}
/// <summary>
/// Initialize your algorithm and add desired assets.
/// </summary>
public override void Initialize()
{
//SetStartDate(2013, 11, 1);
//SetEndDate(2018, 9, 30);
SetStartDate(2015, 5, 1);
SetEndDate(2015, 7, 30);
SetCash(1000000000);
foreach (string symbol in S_AND_P_500_SYMOLS)
{
var option = AddOption(symbol, Resolution.Daily, null, false);
option.PriceModel = OptionPriceModels.BlackScholes();
// set our strike/expiry filter for this option chain
//option.SetFilter((universe) => universe.WeeklysOnly().Expiration(TimeSpan.FromDays(0), TimeSpan.FromDays(7)));
//option.SetFilter(TimeSpan.FromDays(0), TimeSpan.FromDays(7));
if (!this.registerForEOD)
{
this.registerForEOD = true;
// Schedule an event to fire every trading day for a security
// The time rule here tells it to fire 10 minutes before market close
Schedule.On(DateRules.EveryDay(option.Symbol), TimeRules.BeforeMarketClose(option.Symbol, 15), () =>
{
Log("EveryDay 15 min before markets close: Fired at: " + Time);
this.LiquidateExpiredOptions();
});
}
}
// set the warm-up period for the pricing model
SetWarmup(TimeSpan.FromDays(15));
// set the benchmark to be the initial cash
SetBenchmark((d) => 1000000000);
}