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 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));
}
//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 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);
}
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);
}