public virtual void test_zeroRate()
{
LegalEntitySurvivalProbabilities test = LegalEntitySurvivalProbabilities.of(LEGAL_ENTITY, DFS);
double relativeYearFraction = ACT_365F.relativeYearFraction(VALUATION, DATE_AFTER);
double discountFactor = test.survivalProbability(DATE_AFTER);
double zeroRate = test.zeroRate(relativeYearFraction);
assertEquals(Math.Exp(-zeroRate * relativeYearFraction), discountFactor);
}
// computes protection leg pv per unit notional, without loss-given-default rate multiplied
internal virtual double protectionFull(ResolvedCds cds, CreditDiscountFactors discountFactors, LegalEntitySurvivalProbabilities survivalProbabilities, LocalDate referenceDate, LocalDate effectiveStartDate)
{
DoubleArray integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(discountFactors.relativeYearFraction(effectiveStartDate), discountFactors.relativeYearFraction(cds.ProtectionEndDate), discountFactors.ParameterKeys, survivalProbabilities.ParameterKeys);
double pv = 0d;
double ht0 = survivalProbabilities.zeroRate(integrationSchedule.get(0)) * integrationSchedule.get(0);
double rt0 = discountFactors.zeroRate(integrationSchedule.get(0)) * integrationSchedule.get(0);
double b0 = Math.Exp(-ht0 - rt0);
int n = integrationSchedule.size();
for (int i = 1; i < n; ++i)
{
double ht1 = survivalProbabilities.zeroRate(integrationSchedule.get(i)) * integrationSchedule.get(i);
double rt1 = discountFactors.zeroRate(integrationSchedule.get(i)) * integrationSchedule.get(i);
double b1 = Math.Exp(-ht1 - rt1);
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
// The formula has been modified from ISDA (but is equivalent) to avoid log(exp(x)) and explicitly
// calculating the time step - it also handles the limit
double dPV = 0d;
if (Math.Abs(dhrt) < SMALL)
{
dPV = dht * b0 * epsilon(-dhrt);
}
else
{
dPV = (b0 - b1) * dht / dhrt;
}
pv += dPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
// roll to the cash settle date
double df = discountFactors.discountFactor(referenceDate);
return(pv / df);
}
private Pair <double, PointSensitivityBuilder> singlePeriodAccrualOnDefaultSensitivity(CreditCouponPaymentPeriod coupon, LocalDate effectiveStartDate, DoubleArray integrationSchedule, CreditDiscountFactors discountFactors, LegalEntitySurvivalProbabilities survivalProbabilities)
{
LocalDate start = coupon.EffectiveStartDate.isBefore(effectiveStartDate) ? effectiveStartDate : coupon.EffectiveStartDate;
if (!start.isBefore(coupon.EffectiveEndDate))
{
return(Pair.of(0d, PointSensitivityBuilder.none())); //this coupon has already expired
}
DoubleArray knots = DoublesScheduleGenerator.truncateSetInclusive(discountFactors.relativeYearFraction(start), discountFactors.relativeYearFraction(coupon.EffectiveEndDate), integrationSchedule);
// pv
double pv = 0d;
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final int nItems = knots.size();
int nItems = knots.size();
double[] dhrtBar = new double[nItems - 1];
double[] dhtBar = new double[nItems - 1];
double[] bBar = new double[nItems];
double[] p = new double[nItems];
double[] q = new double[nItems];
double t = knots.get(0);
double ht0 = survivalProbabilities.zeroRate(t) * t;
double rt0 = discountFactors.zeroRate(t) * t;
q[0] = Math.Exp(-ht0);
p[0] = Math.Exp(-rt0);
double b0 = q[0] * p[0];
double effStart = discountFactors.relativeYearFraction(coupon.EffectiveStartDate);
double t0 = t - effStart + omega;
for (int i = 1; i < nItems; ++i)
{
t = knots.get(i);
double ht1 = survivalProbabilities.zeroRate(t) * t;
double rt1 = discountFactors.zeroRate(t) * t;
q[i] = Math.Exp(-ht1);
p[i] = Math.Exp(-rt1);
double b1 = q[i] * p[i];
double dt = knots.get(i) - knots.get(i - 1);
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
double tPv;
if (formula == AccrualOnDefaultFormula.MARKIT_FIX)
{
if (Math.Abs(dhrt) < SMALL)
{
double eps = epsilonP(-dhrt);
tPv = dht * dt * b0 * eps;
dhtBar[i - 1] = dt * b0 * eps;
dhrtBar[i - 1] = -dht *dt *b0 *epsilonPP(-dhrt);
bBar[i - 1] += dht * eps;
}
else
{
tPv = dht * dt / dhrt * ((b0 - b1) / dhrt - b1);
dhtBar[i - 1] = dt / dhrt * ((b0 - b1) / dhrt - b1);
dhrtBar[i - 1] = dht * dt / (dhrt * dhrt) * (b1 - 2d * (b0 - b1) / dhrt);
bBar[i - 1] += dht * dt / (dhrt * dhrt);
bBar[i] += -dht * dt / dhrt * (1d + 1d / dhrt);
}
}
else
{
double t1 = t - effStart + omega;
if (Math.Abs(dhrt) < SMALL)
{
double eps = epsilon(-dhrt);
double epsp = epsilonP(-dhrt);
tPv = dht * b0 * (t0 * eps + dt * epsp);
dhtBar[i - 1] = b0 * (t0 * eps + dt * epsp);
dhrtBar[i - 1] = -dht * b0 * (t0 * epsp + dt * epsilonPP(-dhrt));
bBar[i - 1] += dht * (t0 * eps + dt * epsp);
}
else
{
tPv = dht / dhrt * (t0 * b0 - t1 * b1 + dt / dhrt * (b0 - b1));
dhtBar[i - 1] = (t0 * b0 - t1 * b1 + dt / dhrt * (b0 - b1)) / dhrt;
dhrtBar[i - 1] = dht / (dhrt * dhrt) * (-2d * dt / dhrt * (b0 - b1) - t0 * b0 + t1 * b1);
bBar[i - 1] += dht / dhrt * (t0 + dt / dhrt);
bBar[i] += dht / dhrt * (-t1 - dt / dhrt);
}
t0 = t1;
}
pv += tPv;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
double yfRatio = coupon.YearFraction / discountFactors.DayCount.relativeYearFraction(coupon.StartDate, coupon.EndDate);
// pv sensitivity
PointSensitivityBuilder qSensiFirst = survivalProbabilities.zeroRatePointSensitivity(knots.get(0)).multipliedBy(yfRatio * ((dhrtBar[0] + dhtBar[0]) / q[0] + bBar[0] * p[0]));
PointSensitivityBuilder pSensiFirst = discountFactors.zeroRatePointSensitivity(knots.get(0)).multipliedBy(yfRatio * (dhrtBar[0] / p[0] + bBar[0] * q[0]));
PointSensitivityBuilder pvSensi = pSensiFirst.combinedWith(qSensiFirst);
for (int i = 1; i < nItems - 1; ++i)
{
PointSensitivityBuilder qSensi = survivalProbabilities.zeroRatePointSensitivity(knots.get(i)).multipliedBy(yfRatio * (-(dhrtBar[i - 1] + dhtBar[i - 1]) / q[i] + (dhrtBar[i] + dhtBar[i]) / q[i] + bBar[i] * p[i]));
PointSensitivityBuilder pSensi = discountFactors.zeroRatePointSensitivity(knots.get(i)).multipliedBy(yfRatio * (-dhrtBar[i - 1] / p[i] + dhrtBar[i] / p[i] + bBar[i] * q[i]));
pvSensi = pvSensi.combinedWith(pSensi).combinedWith(qSensi);
}
if (nItems > 1)
{
PointSensitivityBuilder qSensiLast = survivalProbabilities.zeroRatePointSensitivity(knots.get(nItems - 1)).multipliedBy(yfRatio * (-(dhrtBar[nItems - 2] + dhtBar[nItems - 2]) / q[nItems - 1] + bBar[nItems - 1] * p[nItems - 1]));
PointSensitivityBuilder pSensiLast = discountFactors.zeroRatePointSensitivity(knots.get(nItems - 1)).multipliedBy(yfRatio * (-dhrtBar[nItems - 2] / p[nItems - 1] + bBar[nItems - 1] * q[nItems - 1]));
pvSensi = pvSensi.combinedWith(pSensiLast).combinedWith(qSensiLast);
}
return(Pair.of(yfRatio * pv, pvSensi));
}
//-------------------------------------------------------------------------
internal virtual PointSensitivityBuilder protectionLegSensitivity(ResolvedCds cds, CreditDiscountFactors discountFactors, LegalEntitySurvivalProbabilities survivalProbabilities, LocalDate referenceDate, LocalDate effectiveStartDate, double recoveryRate)
{
DoubleArray integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(discountFactors.relativeYearFraction(effectiveStartDate), discountFactors.relativeYearFraction(cds.ProtectionEndDate), discountFactors.ParameterKeys, survivalProbabilities.ParameterKeys);
int n = integrationSchedule.size();
double[] dht = new double[n - 1];
double[] drt = new double[n - 1];
double[] dhrt = new double[n - 1];
double[] p = new double[n];
double[] q = new double[n];
// pv
double pv = 0d;
double ht0 = survivalProbabilities.zeroRate(integrationSchedule.get(0)) * integrationSchedule.get(0);
double rt0 = discountFactors.zeroRate(integrationSchedule.get(0)) * integrationSchedule.get(0);
p[0] = Math.Exp(-rt0);
q[0] = Math.Exp(-ht0);
double b0 = p[0] * q[0];
for (int i = 1; i < n; ++i)
{
double ht1 = survivalProbabilities.zeroRate(integrationSchedule.get(i)) * integrationSchedule.get(i);
double rt1 = discountFactors.zeroRate(integrationSchedule.get(i)) * integrationSchedule.get(i);
p[i] = Math.Exp(-rt1);
q[i] = Math.Exp(-ht1);
double b1 = p[i] * q[i];
dht[i - 1] = ht1 - ht0;
drt[i - 1] = rt1 - rt0;
dhrt[i - 1] = dht[i - 1] + drt[i - 1];
double dPv = 0d;
if (Math.Abs(dhrt[i - 1]) < SMALL)
{
double eps = epsilon(-dhrt[i - 1]);
dPv = dht[i - 1] * b0 * eps;
}
else
{
dPv = (b0 - b1) * dht[i - 1] / dhrt[i - 1];
}
pv += dPv;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
double df = discountFactors.discountFactor(referenceDate);
// pv sensitivity
double factor = (1d - recoveryRate) / df;
double eps0 = computeExtendedEpsilon(-dhrt[0], p[1], q[1], p[0], q[0]);
PointSensitivityBuilder pvSensi = discountFactors.zeroRatePointSensitivity(integrationSchedule.get(0)).multipliedBy(-dht[0] * q[0] * eps0 * factor);
pvSensi = pvSensi.combinedWith(survivalProbabilities.zeroRatePointSensitivity(integrationSchedule.get(0)).multipliedBy(factor * (drt[0] * p[0] * eps0 + p[0])));
for (int i = 1; i < n - 1; ++i)
{
double epsp = computeExtendedEpsilon(-dhrt[i], p[i + 1], q[i + 1], p[i], q[i]);
double epsm = computeExtendedEpsilon(dhrt[i - 1], p[i - 1], q[i - 1], p[i], q[i]);
PointSensitivityBuilder pSensi = discountFactors.zeroRatePointSensitivity(integrationSchedule.get(i)).multipliedBy(factor * (-dht[i] * q[i] * epsp - dht[i - 1] * q[i] * epsm));
PointSensitivityBuilder qSensi = survivalProbabilities.zeroRatePointSensitivity(integrationSchedule.get(i)).multipliedBy(factor * (drt[i - 1] * p[i] * epsm + drt[i] * p[i] * epsp));
pvSensi = pvSensi.combinedWith(pSensi).combinedWith(qSensi);
}
if (n > 1)
{
double epsLast = computeExtendedEpsilon(dhrt[n - 2], p[n - 2], q[n - 2], p[n - 1], q[n - 1]);
pvSensi = pvSensi.combinedWith(discountFactors.zeroRatePointSensitivity(integrationSchedule.get(n - 1)).multipliedBy(-dht[n - 2] * q[n - 1] * epsLast * factor));
pvSensi = pvSensi.combinedWith(survivalProbabilities.zeroRatePointSensitivity(integrationSchedule.get(n - 1)).multipliedBy(factor * (drt[n - 2] * p[n - 1] * epsLast - p[n - 1])));
}
PointSensitivityBuilder dfSensi = discountFactors.zeroRatePointSensitivity(referenceDate).multipliedBy(-pv * factor / df);
return(dfSensi.combinedWith(pvSensi));
}
// computes accrual-on-default pv per unit notional for a single payment period
private double singlePeriodAccrualOnDefault(CreditCouponPaymentPeriod coupon, LocalDate effectiveStartDate, DoubleArray integrationSchedule, CreditDiscountFactors discountFactors, LegalEntitySurvivalProbabilities survivalProbabilities)
{
LocalDate start = coupon.EffectiveStartDate.isBefore(effectiveStartDate) ? effectiveStartDate : coupon.EffectiveStartDate;
if (!start.isBefore(coupon.EffectiveEndDate))
{
return(0d); // this coupon has already expired
}
DoubleArray knots = DoublesScheduleGenerator.truncateSetInclusive(discountFactors.relativeYearFraction(start), discountFactors.relativeYearFraction(coupon.EffectiveEndDate), integrationSchedule);
double t0Knot = knots.get(0);
double ht0 = survivalProbabilities.zeroRate(t0Knot) * t0Knot;
double rt0 = discountFactors.zeroRate(t0Knot) * t0Knot;
double b0 = Math.Exp(-rt0 - ht0);
double effStart = discountFactors.relativeYearFraction(coupon.EffectiveStartDate);
double t0 = t0Knot - effStart + omega;
double pv = 0d;
//JAVA TO C# CONVERTER WARNING: The original Java variable was marked 'final':
//ORIGINAL LINE: final int nItems = knots.size();
int nItems = knots.size();
for (int j = 1; j < nItems; ++j)
{
double t = knots.get(j);
double ht1 = survivalProbabilities.zeroRate(t) * t;
double rt1 = discountFactors.zeroRate(t) * t;
double b1 = Math.Exp(-rt1 - ht1);
double dt = knots.get(j) - knots.get(j - 1);
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
double tPV;
if (formula == AccrualOnDefaultFormula.MARKIT_FIX)
{
if (Math.Abs(dhrt) < SMALL)
{
tPV = dht * dt * b0 * Epsilon.epsilonP(-dhrt);
}
else
{
tPV = dht * dt / dhrt * ((b0 - b1) / dhrt - b1);
}
}
else
{
double t1 = t - effStart + omega;
if (Math.Abs(dhrt) < SMALL)
{
tPV = dht * b0 * (t0 * epsilon(-dhrt) + dt * Epsilon.epsilonP(-dhrt));
}
else
{
tPV = dht / dhrt * (t0 * b0 - t1 * b1 + dt / dhrt * (b0 - b1));
}
t0 = t1;
}
pv += tPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
double yearFractionCurve = discountFactors.DayCount.relativeYearFraction(coupon.StartDate, coupon.EndDate);
return(coupon.YearFraction * pv / yearFractionCurve);
}