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);
}
public static double KVA(DateTime originDate, ICube ExpectedCapital, IIrCurve fundingCurve)
{
if (!ExpectedCapital.DataTypes.TryGetValue("ExposureDate", out var type) || type != typeof(DateTime))
{
throw new Exception("ExpectedCapital cube input not valid");
}
var rows = ExpectedCapital.GetAllRows();
var dateIx = ExpectedCapital.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(KVA(originDate, epeDates, epeValues, fundingCurve));
}
//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);
}
public static double KVA(DateTime originDate, DateTime[] ExEDates, double[] CapExposures, IIrCurve fundingCurve)
{
if (ExEDates.Length != CapExposures.Length)
{
throw new Exception("Number of exposure dates and values must be equal");
}
var lastDate = originDate;
var kva = 0.0;
for (var i = 0; i < ExEDates.Length; i++)
{
if (ExEDates[i] < originDate)
{
continue;
}
var fwdDf = fundingCurve.GetDf(lastDate, ExEDates[i]);
var df = fundingCurve.GetDf(originDate, ExEDates[i]);
kva += CapExposures[i] / fwdDf * df;
lastDate = ExEDates[i];
}
return(kva);
}
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 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 IPriceCurve Solve(List <AsianSwapStrip> instruments, List <DateTime> pillars, IIrCurve discountCurve, DateTime buildDate, ICurrencyProvider currencyProvider)
{
_currencyProvider = currencyProvider;
_curveInstruments = instruments;
_pillars = pillars.ToArray();
_numberOfInstruments = _curveInstruments.Count;
_numberOfPillars = pillars.Count;
_discountCurve = discountCurve;
_buildDate = buildDate;
_currentGuess = Enumerable.Repeat(instruments.Average(x => x.Swaplets.Average(s => s.Strike)), _numberOfPillars).ToArray();
_currentCurve = new SparsePriceCurve(_buildDate, _pillars, _currentGuess, SparsePriceCurveType.Coal, currencyProvider, null);
_currentPVs = ComputePVs();
ComputeJacobian();
for (var i = 0; i < MaxItterations; i++)
{
ComputeNextGuess();
_currentCurve = new SparsePriceCurve(_buildDate, _pillars, _currentGuess, SparsePriceCurveType.Coal, _currencyProvider);
_currentPVs = ComputePVs();
if (_currentPVs.Max(x => System.Math.Abs(x)) < Tollerance)
{
UsedItterations = i + 1;
break;
}
ComputeJacobian();
}
return(_currentCurve);
}
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 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 void ImplyVols(List <ListedOptionSettlementRecord> optionSettlements, Dictionary <string, double> futuresPrices, IIrCurve discountCurve = null)
{
var o = new Dictionary <DateTime, IInterpolator1D>();
foreach (var s in optionSettlements)
{
if (!futuresPrices.TryGetValue(s.UnderlyingFuturesCode, out var fut))
{
throw new Exception($"No future price found for contract {s}");
}
var t = s.ValDate.CalculateYearFraction(s.ExpiryDate, DayCountBasis.ACT365F);
var r = 0.0;
if (s.MarginType == OptionMarginingType.Regular)
{
if (discountCurve == null)
{
throw new Exception("To strip vols from options with regular margining, a discount curve must be supplied");
}
r = discountCurve.GetRate(s.ExpiryDate);
}
if (s.ExerciseType == OptionExerciseType.European || s.MarginType == OptionMarginingType.FuturesStyle)
{
s.ImpliedVol = BlackFunctions.BlackImpliedVol(fut, s.Strike, r, t, s.PV, s.CallPut);
}
else if (s.ExerciseType == OptionExerciseType.American)
{
s.ImpliedVol = BinomialTree.AmericanFuturesOptionImpliedVol(fut, s.Strike, r, t, s.PV, s.CallPut);
}
else
{
throw new Exception("Unable to handle option in stripper");
}
}
}
public static double KVA(DateTime originDate, ICube ExpectedCapital, IIrCurve fundingCurve)
{
(var epeDates, var epeValues) = CubeToExposures(ExpectedCapital);
return(KVA(originDate, epeDates, epeValues, fundingCurve));
}
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, 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 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 static double PvProfile(DateTime originDate, DateTime[] exposureDates, double[] exposures, IIrCurve discountCurve)
{
var capital = 0.0;
var time = 0.0;
if (exposureDates.Length != exposures.Length || exposures.Length < 1)
{
throw new DataMisalignedException();
}
if (exposureDates.Length == 1)
{
return(discountCurve.GetDf(originDate, exposureDates[0]) * exposures[0]);
}
for (var i = 0; i < exposureDates.Length - 1; i++)
{
var exposure = (exposures[i] + exposures[i + 1]) / 2.0;
var df = discountCurve.GetDf(originDate, exposureDates[i + 1]);
var dt = exposureDates[i].CalculateYearFraction(exposureDates[i + 1], DayCountBasis.ACT365F);
capital += exposure * dt * df;
time += dt;
}
return(capital / time);
}
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 IrCurve StripFxBasisCurve(string cmeFwdFileName, string ccyPair, Currency curveCcy, string curveName, DateTime valDate, IIrCurve baseCurve)
{
var fwds = GetFwdFxRatesFromFwdFile(cmeFwdFileName, ccyPair);
var dfs = fwds.ToDictionary(f => f.Key, f => fwds[valDate] / f.Value * baseCurve.GetDf(valDate, f.Key));
if (ccyPair.EndsWith("USD")) //flip dfs
{
dfs = dfs.ToDictionary(x => x.Key, x => 1.0 / x.Value);
}
var pillars = dfs.Keys.OrderBy(k => k).ToArray();
var dfsValues = pillars.Select(p => dfs[p]).ToArray();
var curve = new IrCurve(pillars, dfsValues, valDate, curveName, Interpolator1DType.Linear, curveCcy, null, RateType.DF);
return(curve);
}
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(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 double GetFloatRate(this CashFlow cashFlow, IIrCurve curve, DayCountBasis basis) => curve.GetForwardRate(cashFlow.AccrualPeriodStart, cashFlow.AccrualPeriodEnd, RateType.Linear, basis);
public BasisPriceCurve(List <IAssetInstrument> instruments, List <DateTime> pillars, IIrCurve discountCurve, IPriceCurve baseCurve, DateTime buildDate, PriceCurveType curveType, INewtonRaphsonAssetBasisCurveSolver solver, List <string> pillarLabels = null)
{
Instruments = instruments;
Pillars = pillars;
DiscountCurve = discountCurve;
BaseCurve = baseCurve;
CurveType = curveType;
Solver = solver;
BuildDate = buildDate;
PillarLabels = pillarLabels ?? pillars.Select(x => x.ToString("yyyy-MM-dd")).ToList();
Curve = solver.SolveCurve(Instruments, Pillars, DiscountCurve, BaseCurve, BuildDate, CurveType);
}
