public void LVMC_PathsGenerated()
{
var origin = DateTime.Now.Date;
using var engine = new PathEngine(2.IntPow(IsCoverageOnly ? 6 : 12))
{
Parallelize = false
};
engine.AddPathProcess(new Random.MersenneTwister.MersenneTwister64()
{
UseNormalInverse = true,
UseAnthithetic = true
});
var tenorsStr = new[] { "1m", "2m", "3m", "6m" };
var tenors = tenorsStr.Select(x => new Frequency(x));
var expiries = tenors.Select(t => origin.AddPeriod(RollType.F, new Calendar(), t)).ToArray();
var deltaKs = new[] { 0.1, 0.25, 0.5, 0.75, 0.9 };
var smileVols = new[] { 0.32, 0.3, 0.29, 0.3, 0.32 };
var vols = Enumerable.Repeat(smileVols, expiries.Length).ToArray();
var tExp = (origin.AddMonths(6) - origin).TotalDays / 365.0;
var volSurface = new GridVolSurface(origin, deltaKs, expiries, vols,
StrikeType.ForwardDelta, Interpolator1DType.GaussianKernel,
Interpolator1DType.LinearInVariance, DayCountBasis.Act365F);
var fwdCurve = new Func <double, double>(t => { return(900 + 100 * t / tExp); });
var asset = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddMonths(6),
volSurface: volSurface,
forwardCurve: fwdCurve,
nTimeSteps: IsCoverageOnly ? 3 : 100,
name: "TestAsset"
);
engine.AddPathProcess(asset);
var payoff = new EuropeanPut("TestAsset", 900, origin.AddMonths(6));
var payoff2 = new EuropeanCall("TestAsset", 0, origin.AddMonths(6));
engine.AddPathProcess(payoff);
engine.AddPathProcess(payoff2);
engine.SetupFeatures();
engine.RunProcess();
var pv = payoff.AverageResult;
var blackVol = volSurface.GetVolForAbsoluteStrike(900, origin.AddMonths(6), fwdCurve(tExp));
var blackPv = BlackFunctions.BlackPV(fwdCurve(tExp), 900, 0, tExp, blackVol, OptionType.P);
if (!IsCoverageOnly)
{
Assert.True(System.Math.Abs(blackPv / pv - 1.0) < 0.02);
var fwd = payoff2.AverageResult;
Assert.True(System.Math.Abs(fwdCurve(tExp) / fwd - 1.0) < 0.005);
}
}
public void LVMC_PathsGenerated()
{
var origin = DateTime.Now.Date;
var engine = new PathEngine(2.IntPow(17));
//engine.AddPathProcess(new Random.MersenneTwister.MersenneTwister64()
//{
// UseNormalInverse = true,
// UseAnthithetic = false
//});
engine.AddPathProcess(new Random.Sobol.SobolShiftedPathGenerator(new Random.Sobol.SobolDirectionNumbers(s_directionNumbers), 0)
{
UseNormalInverse = true
});
var tenorsStr = new[] { "1m", "2m", "3m", "6m", "9m", "1y" };
var tenors = tenorsStr.Select(x => new Frequency(x));
var expiries = tenors.Select(t => origin.AddPeriod(RollType.F, new Calendar(), t)).ToArray();
var deltaKs = new[] { -0.1, -0.25, -0.5, -0.75, -0.9 };
var smileVols = new[] { 0.32, 0.3, 0.29, 0.3, 0.32 };
var vols = Enumerable.Repeat(smileVols, expiries.Length).ToArray();
var volSurface = new GridVolSurface(origin, deltaKs, expiries, vols,
Core.Basic.StrikeType.ForwardDelta, Interpolator1DType.LinearFlatExtrap,
Interpolator1DType.LinearInVariance, DayCountBasis.Act365F);
var fwdCurve = new Func <double, double>(t => { return(900 + 100 * t); });
var asset = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddYears(1),
volSurface: volSurface,
forwardCurve: fwdCurve,
nTimeSteps: 365,
name: "TestAsset"
);
engine.AddPathProcess(asset);
var payoff = new EuropeanPut("TestAsset", 900, origin.AddYears(1));
var payoff2 = new EuropeanCall("TestAsset", 0, origin.AddYears(1));
engine.AddPathProcess(payoff);
engine.AddPathProcess(payoff2);
engine.SetupFeatures();
engine.RunProcess();
var pv = payoff.AverageResult;
var blackVol = volSurface.GetVolForAbsoluteStrike(900, origin.AddYears(1), fwdCurve(1.0));
var blackPv = BlackFunctions.BlackPV(1000, 900, 0, 1, blackVol, OptionType.P);
Assert.Equal(blackPv, pv, 0);
var fwd = payoff2.AverageResult;
Assert.True(System.Math.Abs(fwdCurve(1) / fwd - 1.0) < 0.001);
//var output = new OutputPathsToImage(engine,2000,1000);
}
public static object CreateGridVolSurface(
[ExcelArgument(Description = "Object name")] string ObjectName,
[ExcelArgument(Description = "Origin date")] DateTime OriginDate,
[ExcelArgument(Description = "Strikes")] double[] Strikes,
[ExcelArgument(Description = "Expiries")] double[] Expiries,
[ExcelArgument(Description = "Volatilities")] double[,] Volatilities,
[ExcelArgument(Description = "Stike Type - default Absolute")] object StrikeType,
[ExcelArgument(Description = "Stike Interpolation - default Linear")] object StrikeInterpolation,
[ExcelArgument(Description = "Time Interpolation - default Linear")] object TimeInterpolation
)
{
return(ExcelHelper.Execute(_logger, () =>
{
var stikeType = StrikeType.OptionalExcel <string>("Absolute");
var expiries = ExcelHelper.ToDateTimeArray(Expiries);
var surface = new GridVolSurface(OriginDate, Strikes, expiries, Volatilities.SquareToJagged());
var cache = ContainerStores.GetObjectCache <GridVolSurface>();
cache.PutObject(ObjectName, new SessionItem <GridVolSurface> {
Name = ObjectName, Value = surface
});
return ObjectName + '¬' + cache.GetObject(ObjectName).Version;
}));
}
public void LVMCDualPathsGenerated(double correlation)
{
var origin = DateTime.Now.Date;
using var engine = new PathEngine(2.IntPow(IsCoverageOnly ? 6 : 8))
{
Parallelize = false
};
engine.AddPathProcess(new Random.MersenneTwister.MersenneTwister64()
{
UseNormalInverse = true,
UseAnthithetic = false,
});
engine.IncrementDepth();
var correlMatrix = new double[][]
{
new double[] { 1.0, correlation },
new double[] { correlation, 1.0 },
};
engine.AddPathProcess(new Cholesky(correlMatrix));
engine.IncrementDepth();
var tenorsStr = new[] { "1m", "2m", "3m", "6m" };
var tenors = tenorsStr.Select(x => new Frequency(x));
var expiries = tenors.Select(t => origin.AddPeriod(RollType.F, new Calendar(), t)).ToArray();
var deltaKs = new[] { -0.1, -0.25, -0.5, -0.75, -0.9 };
var smileVols = new[] { 0.32, 0.3, 0.29, 0.3, 0.32 };
var vols = Enumerable.Repeat(smileVols, expiries.Length).ToArray();
var volSurface = new GridVolSurface(origin, deltaKs, expiries, vols,
StrikeType.ForwardDelta, Interpolator1DType.GaussianKernel,
Interpolator1DType.LinearInVariance, DayCountBasis.Act365F);
var fwdCurve1 = new Func <double, double>(t => { return(1000); });
var asset1 = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddMonths(6),
volSurface: volSurface,
forwardCurve: fwdCurve1,
nTimeSteps: IsCoverageOnly ? 3 : 100,
name: "TestAsset1"
);
var fwdCurve2 = new Func <double, double>(t => { return(1000); });
var asset2 = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddMonths(6),
volSurface: volSurface,
forwardCurve: fwdCurve2,
nTimeSteps: IsCoverageOnly ? 3 : 100,
name: "TestAsset2"
);
engine.AddPathProcess(asset1);
engine.AddPathProcess(asset2);
engine.IncrementDepth();
var correl = new Correlation("TestAsset1", "TestAsset2");
engine.AddPathProcess(correl);
engine.SetupFeatures();
engine.RunProcess();
var corr = correl.AverageResult;
var errCorr = correl.ResultStdError;
if (!IsCoverageOnly)
{
Assert.Equal(correlation, corr, 1);
}
}
private AssetFxMCModel GetSut()
{
var buildDate = DateTime.Parse("2018-10-04");
var usd = TestProviderHelper.CurrencyProvider["USD"];
var zar = TestProviderHelper.CurrencyProvider["ZAR"];
TestProviderHelper.CalendarProvider.Collection.TryGetCalendar("NYC", out var usdCal);
var pair = new FxPair()
{
Domestic = zar, Foreign = usd, PrimaryCalendar = usdCal, SpotLag = 2.Bd()
};
var dfCurve = new IrCurve(new[] { buildDate, buildDate.AddDays(1000) }, new[] { 0.0, 0.0 }, buildDate, "disco", Interpolator1DType.Linear, usd, "DISCO");
var dates = new[] { buildDate, buildDate.AddDays(32), buildDate.AddDays(60), buildDate.AddDays(90) };
var times = dates.Select(d => buildDate.CalculateYearFraction(d, DayCountBasis.Act365F)).ToArray();
var vols = new[] { 0.32, 0.30, 0.29, 0.28 };
var comCurve = new PriceCurve(buildDate, dates, new[] { 100.0, 100.0, 100.0, 100.0 }, PriceCurveType.NYMEX, TestProviderHelper.CurrencyProvider)
{
Name = "CL",
AssetId = "CL"
};
var comSurface = new GridVolSurface(buildDate, new[] { 0.5 }, dates, vols.Select(x => new double[] { x }).ToArray(), StrikeType.ForwardDelta, Interpolator1DType.Linear, Interpolator1DType.LinearInVariance, DayCountBasis.Act365F)
{
AssetId = "CL"
};
var fxSurface = new ConstantVolSurface(buildDate, 0.16)
{
AssetId = "USD/ZAR"
};
var correlVector = new CorrelationTimeVector("CL", "USD/ZAR", _correls, times);
var fModel = new FundingModel(buildDate, new Dictionary <string, IrCurve> {
{ "DISCO", dfCurve }
}, TestProviderHelper.CurrencyProvider, TestProviderHelper.CalendarProvider);
var fxM = new FxMatrix(TestProviderHelper.CurrencyProvider);
fxM.Init(usd, buildDate, new Dictionary <Currency, double>()
{
{ zar, 14.0 }
}, new List <FxPair>()
{
pair
}, new Dictionary <Currency, string> {
{ usd, "DISCO" }, { zar, "DISCO" }
});
fModel.SetupFx(fxM);
fModel.VolSurfaces.Add("ZAR/USD", fxSurface);
fModel.VolSurfaces.Add("USD/ZAR", fxSurface);
var aModel = new AssetFxModel(buildDate, fModel);
aModel.AddVolSurface("CL", comSurface);
aModel.AddPriceCurve("CL", comCurve);
aModel.CorrelationMatrix = correlVector;
var product1 = AssetProductFactory.CreateAsianOption(dates[1], dates[1], 1400, "CL", OptionType.Call, usdCal, dates[1], zar);
product1.TradeId = "P1";
product1.DiscountCurve = "DISCO";
product1.FxConversionType = FxConversionType.AverageThenConvert;
var product2 = AssetProductFactory.CreateAsianOption(dates[2], dates[2], 1400, "CL", OptionType.Call, usdCal, dates[2], zar);
product2.TradeId = "P2";
product2.DiscountCurve = "DISCO";
product2.FxConversionType = FxConversionType.AverageThenConvert;
var product3 = AssetProductFactory.CreateAsianOption(dates[3], dates[3], 1400, "CL", OptionType.Call, usdCal, dates[3], zar);
product3.TradeId = "P3";
product3.DiscountCurve = "DISCO";
product3.FxConversionType = FxConversionType.AverageThenConvert;
var pfolio = new Portfolio {
Instruments = new List <IInstrument> {
product1, product2, product3
}
};
var settings = new McSettings
{
Generator = RandomGeneratorType.MersenneTwister,
NumberOfPaths = (int)2.0.IntPow(15),
NumberOfTimesteps = 1,
ReportingCurrency = zar,
Parallelize = false,
LocalCorrelation = true,
};
var sut = new AssetFxMCModel(buildDate, pfolio, aModel, settings, TestProviderHelper.CurrencyProvider, TestProviderHelper.FutureSettingsProvider, TestProviderHelper.CalendarProvider);
return(sut);
}
public void SolveSmileMarket()
{
var valDate = new DateTime(2018, 07, 28);
var expDate = valDate.AddDays(365);
var tExp = (expDate - valDate).TotalDays / 365.0;
var fwd = 1000;
double[] strikes = { 0.25, 0.5, 0.75 };
var atmConstraint = new ATMStraddleConstraint
{
ATMVolType = AtmVolType.ZeroDeltaStraddle,
MarketVol = 0.32
};
var smile25d = new RRBFConstraint
{
Delta = 0.25,
FlyVol = 0.01,
RisykVol = 0.02,
WingQuoteType = WingQuoteType.Market
};
var s = new AssetSmileSolver();
if (IsCoverageOnly)
{
s.Tollerance = 1;
}
var smile = s.Solve(atmConstraint, new[] { smile25d }, valDate, expDate, fwd, strikes, Interpolator1DType.Linear);
if (!IsCoverageOnly)
{
Assert.Equal(atmConstraint.MarketVol, smile[1], 8);
}
var surface = new GridVolSurface(valDate, strikes, new[] { expDate }, new[] { smile }, StrikeType.ForwardDelta, Interpolator1DType.Linear, Interpolator1DType.Linear, DayCountBasis.Act365F);
//reprice market RR structrure off smile, premium must match
var marketVolC = atmConstraint.MarketVol + smile25d.FlyVol + 0.5 * smile25d.RisykVol;
var marketVolP = atmConstraint.MarketVol + smile25d.FlyVol - 0.5 * smile25d.RisykVol;
var marketKC25 = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, 0.25, 0, tExp, marketVolC);
var marketKP25 = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.25, 0, tExp, marketVolP);
var marketC25FV = BlackFunctions.BlackPV(fwd, marketKC25, 0, tExp, marketVolC, OptionType.C);
var marketP25FV = BlackFunctions.BlackPV(fwd, marketKP25, 0, tExp, marketVolP, OptionType.P);
var marketRR = marketC25FV - marketP25FV;
var volC25d = surface.GetVolForAbsoluteStrike(marketKC25, expDate, fwd);
var volP25d = surface.GetVolForAbsoluteStrike(marketKP25, expDate, fwd);
var call25FV = BlackFunctions.BlackPV(fwd, marketKC25, 0, tExp, volC25d, OptionType.C);
var put25FV = BlackFunctions.BlackPV(fwd, marketKP25, 0, tExp, volP25d, OptionType.P);
var smileRR = call25FV - put25FV;
if (!IsCoverageOnly)
{
Assert.Equal(marketRR, smileRR, 8);
}
//reprice market BF structrure off smile, premium must match
var marketVolBF = atmConstraint.MarketVol + smile25d.FlyVol;
var marketKBFC25 = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, 0.25, 0, tExp, marketVolBF);
var marketKBFP25 = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, -0.25, 0, tExp, marketVolBF);
var marketBFC25FV = BlackFunctions.BlackPV(fwd, marketKBFC25, 0, tExp, marketVolBF, OptionType.C);
var marketBFP25FV = BlackFunctions.BlackPV(fwd, marketKBFP25, 0, tExp, marketVolBF, OptionType.P);
var marketBF = marketBFC25FV + marketBFP25FV;
var volCBF25d = surface.GetVolForAbsoluteStrike(marketKBFC25, expDate, fwd);
var volPBF25d = surface.GetVolForAbsoluteStrike(marketKBFP25, expDate, fwd);
var callBF25FV = BlackFunctions.BlackPV(fwd, marketKBFC25, 0, tExp, volCBF25d, OptionType.C);
var putBF25FV = BlackFunctions.BlackPV(fwd, marketKBFP25, 0, tExp, volPBF25d, OptionType.P);
var smileBF = callBF25FV + putBF25FV;
if (!IsCoverageOnly)
{
Assert.Equal(marketBF, smileBF, 8);
}
}
public static object CreateGridVolSurface(
[ExcelArgument(Description = "Object name")] string ObjectName,
[ExcelArgument(Description = "Asset Id")] string AssetId,
[ExcelArgument(Description = "Origin date")] DateTime OriginDate,
[ExcelArgument(Description = "Strikes")] double[] Strikes,
[ExcelArgument(Description = "Expiries")] double[] Expiries,
[ExcelArgument(Description = "Volatilities")] double[,] Volatilities,
[ExcelArgument(Description = "Stike Type - default Absolute")] object StrikeType,
[ExcelArgument(Description = "Stike Interpolation - default Linear")] object StrikeInterpolation,
[ExcelArgument(Description = "Time Interpolation - default Linear")] object TimeInterpolation,
[ExcelArgument(Description = "Time basis - default ACT365F")] object TimeBasis,
[ExcelArgument(Description = "Pillar labels (optional)")] object PillarLabels,
[ExcelArgument(Description = "Currency - default USD")] object Currency,
[ExcelArgument(Description = "Override spot lag - default none")] object SpotLag)
{
return(ExcelHelper.Execute(_logger, () =>
{
var labels = (PillarLabels is ExcelMissing) ? null : ((object[, ])PillarLabels).ObjectRangeToVector <string>();
var ccyStr = Currency.OptionalExcel("USD");
ContainerStores.SessionContainer.GetService <ICalendarProvider>().Collection.TryGetCalendar(ccyStr, out var ccyCal);
var stikeType = StrikeType.OptionalExcel <string>("Absolute");
var strikeInterpType = StrikeInterpolation.OptionalExcel <string>("Linear");
var timeInterpType = TimeInterpolation.OptionalExcel <string>("LinearInVariance");
var timeBasis = TimeBasis.OptionalExcel <string>("ACT365F");
var expiries = ExcelHelper.ToDateTimeArray(Expiries);
if (!Enum.TryParse(stikeType, out StrikeType sType))
{
return $"Could not parse strike type - {stikeType}";
}
if (!Enum.TryParse(strikeInterpType, out Interpolator1DType siType))
{
return $"Could not parse strike interpolator type - {strikeInterpType}";
}
if (!Enum.TryParse(timeInterpType, out Interpolator1DType tiType))
{
return $"Could not parse time interpolator type - {timeInterpType}";
}
if (!Enum.TryParse(timeBasis, out DayCountBasis basis))
{
return $"Could not parse time basis type - {timeBasis}";
}
var surface = new GridVolSurface(OriginDate, Strikes, expiries, Volatilities.SquareToJagged(), sType, siType, tiType, basis, labels)
{
Currency = ContainerStores.CurrencyProvider[ccyStr],
Name = AssetId ?? ObjectName,
AssetId = AssetId ?? ObjectName,
};
if (SpotLag != null && !(SpotLag is ExcelMissing))
{
surface.OverrideSpotLag = new Frequency((string)SpotLag);
}
return ExcelHelper.PushToCache <IVolSurface>(surface, ObjectName);
}));
}
public void LVMC_TriplePathsGenerated(double correlationAB, double correlationAC, double correlationBC)
{
var origin = DateTime.Now.Date;
var engine = new PathEngine(2.IntPow(15));
engine.AddPathProcess(new Random.MersenneTwister.MersenneTwister64()
{
UseNormalInverse = true,
UseAnthithetic = false
});
var correlMatrix = new double[][]
{
new double[] { 1.0, correlationAB, correlationAC },
new double[] { correlationAB, 1.0, correlationBC },
new double[] { correlationAC, correlationBC, 1.0 },
};
engine.AddPathProcess(new Cholesky(correlMatrix));
var tenorsStr = new[] { "1m", "2m", "3m", "6m", "9m", "1y" };
var tenors = tenorsStr.Select(x => new Frequency(x));
var expiries = tenors.Select(t => origin.AddPeriod(RollType.F, new Calendar(), t)).ToArray();
var deltaKs = new[] { -0.1, -0.25, -0.5, -0.75, -0.9 };
var smileVols = new[] { 0.32, 0.3, 0.29, 0.3, 0.32 };
var vols = Enumerable.Repeat(smileVols, expiries.Length).ToArray();
var volSurface = new GridVolSurface(origin, deltaKs, expiries, vols,
Core.Basic.StrikeType.ForwardDelta, Interpolator1DType.LinearFlatExtrap,
Interpolator1DType.LinearInVariance, DayCountBasis.Act365F);
var fwdCurve1 = new Func <double, double>(t => { return(1000); });
var fwdCurve2 = new Func <double, double>(t => { return(1000); });
var fwdCurve3 = new Func <double, double>(t => { return(1000); });
var assetA = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddYears(1),
volSurface: volSurface,
forwardCurve: fwdCurve1,
nTimeSteps: 365,
name: "TestAssetA"
);
var assetB = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddYears(1),
volSurface: volSurface,
forwardCurve: fwdCurve2,
nTimeSteps: 365,
name: "TestAssetB"
);
var assetC = new LVSingleAsset
(
startDate: origin,
expiryDate: origin.AddYears(1),
volSurface: volSurface,
forwardCurve: fwdCurve3,
nTimeSteps: 365,
name: "TestAssetC"
);
engine.AddPathProcess(assetA);
engine.AddPathProcess(assetB);
engine.AddPathProcess(assetC);
var correlAB = new Correlation("TestAssetA", "TestAssetB");
var correlAC = new Correlation("TestAssetA", "TestAssetC");
var correlBC = new Correlation("TestAssetB", "TestAssetC");
engine.AddPathProcess(correlAB);
engine.AddPathProcess(correlAC);
engine.AddPathProcess(correlBC);
engine.SetupFeatures();
engine.RunProcess();
Assert.Equal(correlationAB, correlAB.AverageResult, 2);
Assert.Equal(correlationAC, correlAC.AverageResult, 2);
Assert.Equal(correlationBC, correlBC.AverageResult, 2);
}
