public static object CreateConstantHazzardCurve(
[ExcelArgument(Description = "Object name")] string ObjectName,
[ExcelArgument(Description = "Hazzard rate")] double HazzardRate,
[ExcelArgument(Description = "Build date")] DateTime BuildDate,
[ExcelArgument(Description = "Basis, default Act365F")] object Basis)
{
return(ExcelHelper.Execute(_logger, () =>
{
var basis = Basis.OptionalExcel("Act365F");
if (!Enum.TryParse(basis, out DayCountBasis dayCountBasis))
{
throw new Exception($"Could not parse basis type - {basis}");
}
var cObj = new HazzardCurve(BuildDate, dayCountBasis, new ConstantHazzardInterpolator(HazzardRate))
{
ConstantPD = HazzardRate
};
var cache = ContainerStores.GetObjectCache <HazzardCurve>();
cache.PutObject(ObjectName, new SessionItem <HazzardCurve> {
Name = ObjectName, Value = cObj
});
return ObjectName + '¬' + cache.GetObject(ObjectName).Version;
}));
}
public double PV_LinearApprox(HazzardCurve hazzardCurve, IIrCurve discountCurve, double recoveryRate, bool payAccruedOnDefault = true)
{
var nodeDates = DatePeriodType.M.GenerateDateSchedule(hazzardCurve.OriginDate, FinalSensitivityDate);
var ts = nodeDates.Select(d => discountCurve.BuildDate.CalculateYearFraction(d, DayCountBasis.ACT365F)).ToArray();
var integrandD = new Func <DateTime, double> (d => discountCurve.GetDf(discountCurve.BuildDate, d) * -hazzardCurve.GetSurvivalProbabilitySlope(d));
var integrandT = new Func <double, double>(t => integrandD(OriginDate.AddYearFraction(t, DayCountBasis.ACT365F)));
//contingent leg
var pv = (1.0 - recoveryRate) * Notional * Integration.SimpsonsRuleExtended(integrandT, 0, ts.Last(), 100);
//fixed leg
foreach (var f in FixedSchedule.Flows)
{
pv -= f.Notional * f.YearFraction * Spread * discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate) * hazzardCurve.GetSurvivalProbability(f.SettleDate);
if (payAccruedOnDefault)
{
pv -= 0.5 * f.Notional * f.YearFraction * Spread
* hazzardCurve.GetDefaultProbability(f.AccrualPeriodStart, f.AccrualPeriodEnd)
* discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate);
}
}
return(pv);
}
public static (double CVA, double CCR) PvCapital_Split(DateTime originDate, DateTime[] EADDates, IAssetFxModel[] models,
Portfolio portfolio, HazzardCurve hazzardCurve, Currency reportingCurrency, IIrCurve discountCurve, double LGD, double partyCVAWeight, double riskWeight,
Dictionary <string, string> assetIdToHedgeMap, Dictionary <string, double> hedgeGroupCCFs, ICurrencyProvider currencyProvider, double[] epeProfile,
DateTime?B2B3ChangeDate = null, double[] eadProfile = null)
{
var pd = hazzardCurve.ConstantPD;
if (!B2B3ChangeDate.HasValue)
{
B2B3ChangeDate = DateTime.MaxValue;
}
var eads = eadProfile ?? EAD_Split(originDate, EADDates, epeProfile, models, portfolio, reportingCurrency, assetIdToHedgeMap, hedgeGroupCCFs, B2B3ChangeDate.Value, currencyProvider);
eads = eads.Select(e => e * riskWeight).ToArray();
var Ms = EADDates.Select(d => Max(1.0, portfolio.WeightedMaturity(d))).ToArray();
var dfs = Ms.Select(m => m == 0 ? 1.0 : (1.0 - Exp(-0.05 * m)) / (0.05 * m)).ToArray();
var ksCCR = eads.Select((e, ix) => BaselHelper.K(pd, LGD, Ms[ix]) * e).ToArray();
var ksCVA = eads.Select((e, ix) => XVACalculator.Capital_BaselII_CVA_SM(e * dfs[ix], Ms[ix], partyCVAWeight)).ToArray();
var pvCapitalCCR = PvProfile(originDate, EADDates, ksCCR, discountCurve);
var pvCapitalCVA = PvProfile(originDate, EADDates, ksCVA, discountCurve);
return(pvCapitalCVA, pvCapitalCCR);
}
public double PV_SmallSteps(HazzardCurve hazzardCurve, IIrCurve discountCurve, double recoveryRate, bool payAccruedOnDefault = true)
{
var nodeDates = DatePeriodType.M.GenerateDateSchedule(hazzardCurve.OriginDate, FinalSensitivityDate);
//contingent leg
var pv = 0.0;
for (var i = 1; i < nodeDates.Length; i++)
{
pv += discountCurve.GetDf(discountCurve.BuildDate, nodeDates[i])
* hazzardCurve.GetDefaultProbability(nodeDates[i - 1], nodeDates[i]);
}
pv *= (1.0 - recoveryRate) * Notional;
//fixed leg
foreach (var f in FixedSchedule.Flows)
{
pv -= f.Notional * f.YearFraction * Spread * discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate) * hazzardCurve.GetSurvivalProbability(f.SettleDate);
if (payAccruedOnDefault)
{
pv -= 0.5 * f.Notional * f.YearFraction * Spread
* hazzardCurve.GetDefaultProbability(f.AccrualPeriodStart, f.AccrualPeriodEnd)
* discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate);
}
}
return(pv);
}
private double[] ComputePVs()
{
var o = new double[_numberOfInstruments];
var hzCurve = new HazzardCurve(_buildDate, _basis, _currentCurve);
for (var i = 0; i < o.Length; i++)
{
o[i] = UseSmallSteps ?
_curveInstruments[i].PV_SmallSteps(hzCurve, _discountCurve, _recoveryRate, true) :
_curveInstruments[i].PV_PiecewiseFlat(hzCurve, _discountCurve, _recoveryRate, true);
}
return(o);
}
public static double PvCcrCapital_BII_SM(DateTime originDate, DateTime[] EADDates, IAssetFxModel[] models, Portfolio portfolio,
HazzardCurve hazzardCurve, Currency reportingCurrency, IIrCurve discountCurve, double LGD, Dictionary <string, string> assetIdToHedgeMap,
Dictionary <string, double> hedgeGroupCCFs, ICurrencyProvider currencyProvider, double[] epeProfile, double[] eadProfile = null)
{
var pd = hazzardCurve.ConstantPD;
var eads = eadProfile ?? EAD_BII_SM(originDate, EADDates, epeProfile, models, portfolio, reportingCurrency, assetIdToHedgeMap, hedgeGroupCCFs, currencyProvider);
var Ms = EADDates.Select(d => Max(1.0, portfolio.WeightedMaturity(d))).ToArray();
var ks = eads.Select((e, ix) => BaselHelper.K(pd, LGD, Ms[ix]) * e).ToArray();
var pvCapital = PvProfile(originDate, EADDates, ks, discountCurve);
return(pvCapital);
}
public void HazzardCurveFact()
{
var hzi = new Math.Interpolation.ConstantHazzardInterpolator(0.1);
var origin = new DateTime(2019, 05, 28);
var hz = new HazzardCurve(origin, Dates.DayCountBasis.Act365F, hzi);
Assert.Equal(1.0, hz.GetSurvivalProbability(origin, origin));
Assert.Equal(1.0, hz.GetSurvivalProbability(origin));
Assert.Equal(hzi.Interpolate(1.0 / 365.0), hz.GetSurvivalProbability(origin, origin.AddDays(1)));
var dfCurve = new ConstantRateIrCurve(0.05, origin, "zzz", TestProviderHelper.CurrencyProvider.GetCurrency("USD"));
var df = dfCurve.GetDf(origin, origin.AddDays(100));
Assert.Equal(df, hz.RiskyDiscountFactor(origin, origin.AddDays(100), dfCurve, 0.0));
Assert.Equal(df * (1.0 - (1.0 - hzi.Interpolate(100.0 / 365)) * 0.5), hz.RiskyDiscountFactor(origin, origin.AddDays(100), dfCurve, 0.5));
}
public static double SolveStrikeForGrossRoC(this Portfolio portfolio, IAssetFxModel model, double targetRoC, Currency reportingCurrency,
HazzardCurve hazzardCurve, double LGD, double xVA_LGD, double partyRiskWeight, double cvaCapitalWeight, IIrCurve discountCurve,
ICurrencyProvider currencyProvider, Dictionary <string, string> assetIdToHedgeMap, Dictionary <string, double> hedgeGroupCCFs)
{
var insList = portfolio.Instruments.Select(x => x as IAssetInstrument).ToList();
if (insList.Any(x => x == null))
{
throw new Exception("Not all instruments in the portfolio implement IAssetInstrument");
}
var rolledModels = new Dictionary <DateTime, IAssetFxModel>();
var d = model.BuildDate;
var lastModel = model;
while (d <= portfolio.LastSensitivityDate)
{
rolledModels.Add(d, lastModel);
d = d.AddDays(1);
lastModel = lastModel.RollModel(d, currencyProvider);
}
var targetFunc = new Func <double, double>(k =>
{
var newPf = new Portfolio()
{
Instruments = insList.Select(i => (IInstrument)i.SetStrike(k)).ToList()
};
var roc = newPf.GrossRoC(model, reportingCurrency, hazzardCurve, LGD, xVA_LGD, cvaCapitalWeight, partyRiskWeight, discountCurve, currencyProvider, rolledModels, assetIdToHedgeMap, hedgeGroupCCFs);
return(roc - targetRoC);
});
var firstGuess = insList.Average(i => i.ParRate(model));
var solvedStrike = Math.Solvers.Newton1D.MethodSolve(targetFunc, firstGuess, 1e-8, 1000, 1e-9);
if (System.Math.Abs(targetFunc(solvedStrike)) < 1e-8)
{
return(solvedStrike);
}
else
{
throw new Exception("Failed to find solution after 1000 itterations");
}
}
public static double CVA(DateTime originDate, ICube EPE, HazzardCurve hazzardCurve, IIrCurve discountCurve, double LGD)
{
if (!EPE.DataTypes.TryGetValue("ExposureDate", out var type) || type != typeof(DateTime))
{
throw new Exception("EPE cube input not valid");
}
var rows = EPE.GetAllRows();
var dateIx = EPE.GetColumnIndex("ExposureDate");
var epeDates = new DateTime[rows.Length];
var epeValues = new double[rows.Length];
for (var i = 0; i < rows.Length; i++)
{
epeDates[i] = (DateTime)rows[i].MetaData[dateIx];
epeValues[i] = rows[i].Value;
}
return(CVA(originDate, epeDates, epeValues, hazzardCurve, discountCurve, LGD));
}
public static object CreateConstantHazzardCurve(
[ExcelArgument(Description = "Object name")] string ObjectName,
[ExcelArgument(Description = "Hazzard rate")] double HazzardRate,
[ExcelArgument(Description = "Build date")] DateTime BuildDate,
[ExcelArgument(Description = "Basis, default Act365F")] object Basis)
{
return(ExcelHelper.Execute(_logger, () =>
{
var basis = Basis.OptionalExcel("Act365F");
if (!Enum.TryParse(basis, out DayCountBasis dayCountBasis))
{
throw new Exception($"Could not parse basis type - {basis}");
}
var cObj = new HazzardCurve(BuildDate, dayCountBasis, new ConstantHazzardInterpolator(HazzardRate))
{
ConstantPD = HazzardRate
};
return ExcelHelper.PushToCache(cObj, ObjectName);
}));
}
public void ComputeCVAFacts()
{
var hz = new HazzardCurve(DateTime.Today, DayCountBasis.Act365F, new DummyPointInterpolator(0.0));
var disco = new FlatIrCurve(0.0, ContainerStores.CurrencyProvider.GetCurrency("ZAR"), "disco");
ContainerStores.GetObjectCache <HazzardCurve>().PutObject("hz", new SessionItem <HazzardCurve>()
{
Name = "hz", Value = hz
});
ContainerStores.GetObjectCache <IIrCurve>().PutObject("disco", new SessionItem <IIrCurve>()
{
Name = "disco", Value = disco
});
Assert.Equal("Hazzard curve blash not found", CapitalFunctions.ComputeCVA("blash", DateTime.Today, "woo", null, 0.0));
Assert.Equal("Discount curve woo not found", CapitalFunctions.ComputeCVA("hz", DateTime.Today, "woo", null, 0.0));
Assert.Equal("Expected Nx2 array for EPE", CapitalFunctions.ComputeCVA("hz", DateTime.Today, "disco", new object[1, 1], 0.0));
Assert.Equal("EPE profile must be cube reference or Nx2 array", CapitalFunctions.ComputeCVA("hz", DateTime.Today, "disco", 7, 0.0));
Assert.Equal(0.0, CapitalFunctions.ComputeCVA("hz", DateTime.Today, "disco", new object[1, 2] {
{ DateTime.Today, 0.0 }
}, 0.0));
}
public void CDSBasicFacts_LinearApprox()
{
var origin = new DateTime(2020, 06, 15);
var hzi = new ConstantHazzardInterpolator(0.0);
var hz = new HazzardCurve(origin, DayCountBasis.ACT365F, hzi);
var usd = TestProviderHelper.CurrencyProvider.GetCurrency("USD");
var df = new ConstantRateIrCurve(0.00, origin, "LIBOR", usd);
var sut = new CDS()
{
Basis = DayCountBasis.ACT365F,
Currency = usd,
OriginDate = origin,
Tenor = new Frequency("1y"),
Spread = 0.01,
Notional = 1e6
};
sut.Init();
var pv = sut.PV_LinearApprox(hz, df, 0.4, false);
Assert.Equal(-sut.Notional * sut.Spread, pv);
}
//http://www.bnikolic.co.uk/cds/cdsvaluation.html
//var contingentLeg = (1.0 - recoveryRate) *
public double PV_PiecewiseFlat(HazzardCurve hazzardCurve, IIrCurve discountCurve, double recoveryRate, bool payAccruedOnDefault = true)
{
var nodeDates = FixedSchedule.Flows.Select(f => f.AccrualPeriodEnd).ToArray();
var pv = 0.0;
//contingent leg
var d = hazzardCurve.OriginDate;
foreach (var nd in nodeDates)
{
var deltaT = d.CalculateYearFraction(nd, hazzardCurve.Basis);
var s = hazzardCurve.GetSurvivalProbability(d);
var dd = discountCurve.GetDf(discountCurve.BuildDate, d);
var lambda = System.Math.Log(s / hazzardCurve.GetSurvivalProbability(nd)) / deltaT;
var f = System.Math.Log(dd / discountCurve.GetDf(discountCurve.BuildDate, nd)) / deltaT;
var term1 = (lambda == 0 && f == 0) ? 1.0 : lambda / (lambda + f);
pv += term1 * (1.0 - System.Math.Exp(-deltaT * (lambda + f))) * s * dd;
d = nd;
}
pv *= (1.0 - recoveryRate) * Notional;
//fixed leg
foreach (var f in FixedSchedule.Flows)
{
pv -= f.Notional * f.YearFraction * Spread * discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate) * hazzardCurve.GetSurvivalProbability(f.SettleDate);
if (payAccruedOnDefault)
{
pv -= 0.5 * f.Notional * f.YearFraction * Spread
* hazzardCurve.GetDefaultProbability(f.AccrualPeriodStart, f.AccrualPeriodEnd)
* discountCurve.GetDf(discountCurve.BuildDate, f.SettleDate);
}
}
return(pv);
}
//http://www.bnikolic.co.uk/cds/cdsvaluation.html //var contingentLeg = (1.0 - recoveryRate) * public double PV(HazzardCurve hazzardCurve, ICurve discountCurve, double recoveryRate, bool payAccruedOnDefault = true) => 0;
public static double CVA(DateTime originDate, ICube EPE, HazzardCurve hazzardCurve, IIrCurve discountCurve, double LGD)
{
(var epeDates, var epeValues) = CubeToExposures(EPE);
return(CVA(originDate, epeDates, epeValues, hazzardCurve, discountCurve, LGD));
}
public static double CVA_Approx(DateTime[] exposureDates, Portfolio portfolio, HazzardCurve hazzardCurve, IAssetFxModel model, IIrCurve discountCurve, double LGD, Currency reportingCurrency, ICurrencyProvider currencyProvider, Dictionary <DateTime, IAssetFxModel> models = null)
{
var exposures = EPE_Approx(exposureDates, portfolio, model, reportingCurrency, currencyProvider, models);
return(CVA(model.BuildDate, exposureDates, exposures, hazzardCurve, discountCurve, LGD));
}
public static double CVA(DateTime originDate, DateTime[] EPEDates, double[] EPEExposures, HazzardCurve hazzardCurve, IIrCurve discountCurve, double LGD)
{
if (EPEDates.Length != EPEExposures.Length)
{
throw new Exception("Number of EPE dates and EPE values must be equal");
}
var lastDate = originDate;
var cva = 0.0;
for (var i = 0; i < EPEDates.Length; i++)
{
if (EPEDates[i] < originDate)
{
continue;
}
var pDefault = hazzardCurve.GetDefaultProbability(lastDate, EPEDates[i]);
var df = discountCurve.GetDf(originDate, EPEDates[i]);
cva += EPEExposures[i] * pDefault * df * LGD;
lastDate = EPEDates[i];
}
return(-cva);
}
public static (double FBA, double FCA) FVA(DateTime originDate, ICube EPE, ICube ENE, HazzardCurve hazzardCurve, IIrCurve discountCurve, IIrCurve fundingCurve)
{
if (!EPE.DataTypes.TryGetValue("ExposureDate", out var type) || type != typeof(DateTime))
{
throw new Exception("EPE cube input not valid");
}
if (!ENE.DataTypes.TryGetValue("ExposureDate", out var type2) || type2 != typeof(DateTime))
{
throw new Exception("ENE cube input not valid");
}
var rowsEPE = EPE.GetAllRows();
var rowsENE = ENE.GetAllRows();
if (rowsEPE.Length != rowsENE.Length)
{
throw new Exception("EPE and ENE curves not of same size");
}
var dateIx = EPE.GetColumnIndex("ExposureDate");
var epeDates = new DateTime[rowsEPE.Length];
var epeValues = new double[rowsEPE.Length];
var eneValues = new double[rowsENE.Length];
for (var i = 0; i < rowsENE.Length; i++)
{
epeDates[i] = (DateTime)rowsEPE[i].MetaData[dateIx];
epeValues[i] = rowsEPE[i].Value;
eneValues[i] = rowsENE[i].Value;
}
return(FVA(originDate, epeDates, epeValues, eneValues, hazzardCurve, discountCurve, fundingCurve));
}
public static (double FBA, double FCA) FVA(DateTime originDate, DateTime[] ExEDates, double[] EPEExposures, double[] ENEExposures, HazzardCurve hazzardCurve, IIrCurve discountCurve, IIrCurve fundingCurve)
{
if (ExEDates.Length != EPEExposures.Length)
{
throw new Exception("Number of EPE dates and EPE values must be equal");
}
if (ExEDates.Length != ENEExposures.Length)
{
throw new Exception("Number of ENE dates and ENE values must be equal");
}
var lastDate = originDate;
var fba = 0.0;
var fca = 0.0;
for (var i = 0; i < ExEDates.Length; i++)
{
if (ExEDates[i] < originDate)
{
continue;
}
var pSurvival = hazzardCurve.GetSurvivalProbability(lastDate, ExEDates[i]);
var fwdDf = fundingCurve.GetDf(lastDate, ExEDates[i]) / discountCurve.GetDf(lastDate, ExEDates[i]);
var df = fundingCurve.GetDf(originDate, ExEDates[i]);
fba += ENEExposures[i] * pSurvival / fwdDf * df;
fca += EPEExposures[i] * pSurvival / fwdDf * df;
lastDate = ExEDates[i];
}
return(fba, fca);
}
public static double PVCapital_BII_IMM(DateTime originDate, ICube expectedEAD, HazzardCurve hazzardCurve, IIrCurve discountCurve, double LGD, Portfolio portfolio)
{
(var eadDates, var eadValues) = XVACalculator.CubeToExposures(expectedEAD);
return(PVCapital_BII_IMM(originDate, eadDates, eadValues, hazzardCurve, discountCurve, LGD, portfolio));
}
public static double PVCapital_BII_IMM(DateTime originDate, DateTime[] EADDates, double[] EADs, HazzardCurve hazzardCurve,
IIrCurve discountCurve, double LGD, Portfolio portfolio)
{
if (EADDates.Length != EADs.Length)
{
throw new Exception("Number of EPE dates and EPE values must be equal");
}
var pd = hazzardCurve.ConstantPD;
var epees = EADs.Select((d, ix) => EADs.Skip(ix).Max()).ToArray();
var Ms = EADDates.Select(d => Max(1.0, portfolio.WeightedMaturity(d))).ToArray();
var ks = epees.Select((e, ix) => BaselHelper.K(pd, LGD, Ms[ix]) * e * 1.4).ToArray();
var pvCapital = PvProfile(originDate, EADDates, ks, discountCurve);
return(pvCapital);
}
