public PremiumLegElement(double protectionStart, CdsCoupon coupon, YieldTermStructure yieldCurve, int creditCurveKnot, double[] knots, AccrualOnDefaultFormulae formula) : base(coupon, yieldCurve, creditCurveKnot)
{
_coupon = coupon;
_creditCurveKnot = creditCurveKnot;
_formula = formula;
if (formula == AccrualOnDefaultFormulae.ORIGINAL_ISDA)
{
_omega = 1.0 / 730;
}
else
{
_omega = 0.0;
}
_knots = DoublesScheduleGenerator.truncateSetInclusive(Math.Max(_coupon.getEffStart(), protectionStart), _coupon.getEffEnd(), knots);
_n = _knots.Length;
_rt = new double[_n];
_p = new double[_n];
for (int i = 0; i < _n; i++)
{
_rt[i] = yieldCurve.getRT_(_knots[i]);
_p[i] = Math.Exp(-_rt[i]);
}
}
private double calculateSinglePeriodAccrualOnDefault(
CdsCoupon coupon,
double effectiveStart,
double[] integrationPoints,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve)
{
double start = Math.Max(coupon.getEffStart(), effectiveStart);
if (start >= coupon.getEffEnd())
{
return(0.0); //this coupon has already expired
}
double[] knots = DoublesScheduleGenerator.truncateSetInclusive(start, coupon.getEffEnd(), integrationPoints);
double t = knots[0];
double ht0 = creditCurve.getRT_(t);
double rt0 = yieldCurve.getRT_(t);
double b0 = Math.Exp(-rt0 - ht0); // this is the risky discount factor
double t0 = t - coupon.getEffStart() + _omega;
double pv = 0.0;
int nItems = knots.Length;
for (int j = 1; j < nItems; ++j)
{
t = knots[j];
double ht1 = creditCurve.getRT_(t);
double rt1 = yieldCurve.getRT_(t);
double b1 = Math.Exp(-rt1 - ht1);
double dt = knots[j] - knots[j - 1];
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
double tPV;
double t1 = t - coupon.getEffStart() + _omega;
if (Math.Abs(dhrt) < 1e-5)
{
tPV = dht * b0 * (t0 * Maths.Epsilon.epsilon(-dhrt) + dt * Maths.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;
}
return(coupon.getYFRatio() * pv);
}
public CDS(double Coupon, double notional, DateTime maturity, DateTime firstpaymentday, DateTime tradedate,
DateTime formerpaymentday, string frequency, double recovery, int settlement, int Cashsettlement)
{
// Product Setup
OMLib.Conventions.DayCount.Actual360 AccuralDCC = new OMLib.Conventions.DayCount.Actual360();
OMLib.Conventions.DayCount.Actual365 curveDCC = new OMLib.Conventions.DayCount.Actual365();
Calendar calendar = new UnitedStates();
formerpaymentday = calendar.adjust(formerpaymentday, BusinessDayConvention.Following);
int accrued = AccuralDCC.DayCount(formerpaymentday, calendar.adjust(tradedate, BusinessDayConvention.Following)) + 1;
this.accruedday = accrued;
this.marketvalue = new double();
this.accruedamt = notional * Coupon * accrued / 360;
this.Notional = notional;
this._payAccOnDefault = true;
OMLib.Conventions.BusinessDayConvention convention = new OMLib.Conventions.BusinessDayConvention(Enums.BusinessDayConvention.ModifiedFollowing, tradedate);
this.tradedate = calendar.adjust(tradedate, BusinessDayConvention.ModifiedFollowing); /*convention.AdjustedDate;*/
this.Recovery = recovery;
convention = new OMLib.Conventions.BusinessDayConvention(Enums.BusinessDayConvention.ModifiedFollowing, firstpaymentday);
this.firstpaymentdate = CdsAnalyticFactory.getNextIMMDate(tradedate); /*convention.AdjustedDate;*/
convention = new OMLib.Conventions.BusinessDayConvention(Enums.BusinessDayConvention.ModifiedFollowing, formerpaymentday);
this.formerpaymentdate = CdsAnalyticFactory.getPrevIMMDate(tradedate);//calendar.adjust(formerpaymentday,BusinessDayConvention.ModifiedFollowing); /*convention.AdjustedDate;*/
this.Maturity = maturity;
this.PremiumRate = Coupon;
this.Frequency = frequency;
this.Cashsettlement = Cashsettlement;
DateTime valueDate = calendar.adjust(tradedate.AddDays(Cashsettlement));
convention = new OMLib.Conventions.BusinessDayConvention(Enums.BusinessDayConvention.ModifiedFollowing, tradedate.AddDays(3));
this.evalDate = calendar.adjust(tradedate.AddDays(settlement), BusinessDayConvention.ModifiedFollowing); /*convention.AdjustedDate;*/
this.Payment_Schedule = PremiumDates(this.Maturity, CdsAnalyticFactory.getNextIMMDate(tradedate), this.Frequency);
QLNet.Calendar.OrthodoxImpl cal = new Calendar.OrthodoxImpl();
IsdaPremiumLegSchedule paymentSchedule = new IsdaPremiumLegSchedule(formerpaymentdate, maturity, payment_interval, StubConvention.SHORT_INITIAL, QLNet.BusinessDayConvention.ModifiedFollowing, cal, true);
_coupons = CdsCoupon.makeCoupons(tradedate, paymentSchedule, true, ACT_360, ACT_365);
OMLib.Conventions.DayCount.Actual365 CurveDCC = new OMLib.Conventions.DayCount.Actual365();
DateTime effectiveStartDate = tradedate;
_accStart = DateTime.Compare(formerpaymentdate, tradedate) < 0 ?-CurveDCC.YearFraction(formerpaymentdate, tradedate) :
CurveDCC.YearFraction(tradedate, formerpaymentdate);
_cashSettlementTime = CurveDCC.YearFraction(tradedate, valueDate);
_effectiveProtectionStart = DateTime.Compare(effectiveStartDate, tradedate) < 0 ?
-CurveDCC.YearFraction(effectiveStartDate, tradedate) :
CurveDCC.YearFraction(tradedate, effectiveStartDate);
_protectionEnd = CurveDCC.YearFraction(tradedate, maturity);
DateTime accStart = paymentSchedule.getAccStartDate(0);
}
public double pvPremiumLegCreditSensitivity(
CDS cds,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve,
int creditCurveNode)
{
if (cds.getProtectionEnd() <= 0.0)
{ //short cut already expired CDSs
return(0.0);
}
int n = cds.getNumPayments();
double pvSense = 0.0;
for (int i = 0; i < n; i++)
{
CdsCoupon c = cds.getCoupon(i);
double paymentTime = c.getPaymentTime();
double creditObsTime = c.getEffEnd();
double dqdh = creditCurve.getSingleNodeDiscountFactorSensitivity(creditObsTime, creditCurveNode);
if (dqdh == 0)
{
continue;
}
double p = Math.Exp(-yieldCurve.getRT_(paymentTime));
pvSense += c.getYearFrac() * p * dqdh;
}
if (cds.isPayAccOnDefault())
{
double start = cds.getNumPayments() == 1 ? cds.getEffectiveProtectionStart() : cds.getAccStart();
double[] integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(start, cds.getProtectionEnd(), yieldCurve, creditCurve);
double accPVSense = 0.0;
for (int i = 0; i < n; i++)
{
accPVSense += calculateSinglePeriodAccrualOnDefaultCreditSensitivity(
cds.getCoupon(i),
cds.getEffectiveProtectionStart(), integrationSchedule, yieldCurve, creditCurve, creditCurveNode);
}
pvSense += accPVSense;
}
double df = Math.Exp(-yieldCurve.getRT_(cds.getCashSettleTime()));
pvSense /= df;
return(pvSense);
}
public CouponOnlyElement(CdsCoupon coupon, YieldTermStructure yieldCurve, int creditCurveKnot)
{
_riskLessValue = coupon.getYearFrac() * Math.Exp(-yieldCurve.getRT_(coupon.getPaymentTime()));
_effEnd = coupon.getEffEnd();
_creditCurveKnot = creditCurveKnot;
}
public CreditCurveCalibrator(MultiCdsAnalytic multiCDS, YieldTermStructure yieldCurve, AccrualOnDefaultFormulae formula)
{
_nCDS = multiCDS.getNumMaturities();
_t = new double[_nCDS];
_lgd = new double[_nCDS];
_unitAccured = new double[_nCDS];
for (int i = 0; i < _nCDS; i++)
{
_t[i] = multiCDS.getProtectionEnd(i);
_lgd[i] = multiCDS.getLGD();
_unitAccured[i] = multiCDS.getAccruedPremiumPerUnitSpread(i);
}
_valuationDF = Math.Exp(-yieldCurve.getRT_(multiCDS.getCashSettleTime()));
//This is the global set of knots - it will be truncated down for the various leg elements
//TODO this will not match ISDA C for forward starting (i.e. accStart > tradeDate) CDS, and will give different answers
//if the Markit 'fix' is used in that case
double[] knots = DoublesScheduleGenerator.getIntegrationsPoints(
multiCDS.getEffectiveProtectionStart(), _t[_nCDS - 1], yieldCurve.t.ToArray(), _t.ToArray());
//The protection leg
_protElems = new ProtectionLegElement[_nCDS];
for (int i = 0; i < _nCDS; i++)
{
_protElems[i] = new ProtectionLegElement(
i == 0 ? multiCDS.getEffectiveProtectionStart() : _t[i - 1], _t[i], yieldCurve, i, knots);
}
_cds2CouponsMap = new int[_nCDS][];
_cdsCouponsUpdateMap = new int[_nCDS][];
_knot2CouponsMap = new int[_nCDS][];
List <CdsCoupon> allCoupons = new List <CdsCoupon>(_nCDS + multiCDS.getTotalPayments() - 1);
allCoupons.AddRange(multiCDS.getStandardCoupons().ToList());
allCoupons.Add(multiCDS.getTerminalCoupon(_nCDS - 1));
int[] temp = new int[multiCDS.getTotalPayments()];
for (int i = 0; i < multiCDS.getTotalPayments(); i++)
{
temp[i] = i;
}
_cds2CouponsMap[_nCDS - 1] = temp;
//complete the list of unique coupons and fill out the cds2CouponsMap
for (int i = 0; i < _nCDS - 1; i++)
{
CdsCoupon c = multiCDS.getTerminalCoupon(i);
int nPayments = Math.Max(0, multiCDS.getPaymentIndexForMaturity(i)) + 1;
_cds2CouponsMap[i] = new int[nPayments];
for (int jj = 0; jj < nPayments - 1; jj++)
{
_cds2CouponsMap[i][jj] = jj;
}
//because of business-day adjustment, a terminal coupon can be identical to a standard coupon,
//in which case it is not added again
int index = allCoupons.IndexOf(c);
if (index == -1)
{
index = allCoupons.Count;
allCoupons.Add(c);
}
_cds2CouponsMap[i][nPayments - 1] = index;
}
//loop over the coupons to populate the couponUpdateMap
_nCoupons = allCoupons.Count;
int[] sizes = new int[_nCDS];
int[] map = new int[_nCoupons];
for (int i = 0; i < _nCoupons; i++)
{
CdsCoupon c = allCoupons[i];
int index = Array.BinarySearch(_t, c.getEffEnd());
if (index < 0)
{
index = -(index + 1);
}
sizes[index]++;
map[i] = index;
}
//make the protection leg elements
if (multiCDS.isPayAccOnDefault())
{
_premElems = new PremiumLegElement[_nCoupons];
for (int i = 0; i < _nCoupons; i++)
{
_premElems[i] = new PremiumLegElement(multiCDS.getEffectiveProtectionStart(), allCoupons[i], yieldCurve, map[i],
knots, formula);
}
}
else
{
_premElems = new CouponOnlyElement[_nCoupons];
for (int i = 0; i < _nCoupons; i++)
{
_premElems[i] = new CouponOnlyElement(allCoupons[i], yieldCurve, map[i]);
}
}
//sort a map from coupon to curve node, to a map from curve node to coupons
for (int i = 0; i < _nCDS; i++)
{
_knot2CouponsMap[i] = new int[sizes[i]];
}
int[] indexes = new int[_nCDS];
for (int i = 0; i < _nCoupons; i++)
{
int index = map[i];
_knot2CouponsMap[index][indexes[index]++] = i;
}
//the cdsCouponsUpdateMap is the intersection of the cds2CouponsMap and knot2CouponsMap
for (int i = 0; i < _nCDS; i++)
{
_cdsCouponsUpdateMap[i] = intersection(_knot2CouponsMap[i], _cds2CouponsMap[i]);
}
}
public CreditCurveCalibrator(CDS[] cds, YieldTermStructure yieldCurve, AccrualOnDefaultFormulae formula)
{
_nCDS = cds.Length;
Boolean payAccOnDefault = cds[0].isPayAccOnDefault();
double accStart = cds[0].getAccStart();
double effectProtStart = cds[0].getEffectiveProtectionStart();
double cashSettleTime = cds[0].getCashSettleTime();
_t = new double[_nCDS];
_t[0] = cds[0].getProtectionEnd();
//Check all the CDSs match
for (int i = 1; i < _nCDS; i++)
{
_t[i] = cds[i].getProtectionEnd();
}
_valuationDF = Math.Exp(-yieldCurve.getRT_(cashSettleTime));
_lgd = new double[_nCDS];
_unitAccured = new double[_nCDS];
for (int i = 0; i < _nCDS; i++)
{
_lgd[i] = cds[i].getLGD();
_unitAccured[i] = cds[i].getAccruedYearFraction();
}
//This is the global set of knots - it will be truncated down for the various leg elements
//TODO this will not match ISDA C for forward starting (i.e. accStart > tradeDate) CDS, and will give different answers
//if the Markit 'fix' is used in that case
double[] knots = DoublesScheduleGenerator.
getIntegrationsPoints(effectProtStart, _t[_nCDS - 1], yieldCurve.t.ToArray(), _t);
//The protection leg
_protElems = new ProtectionLegElement[_nCDS];
for (int i = 0; i < _nCDS; i++)
{
_protElems[i] = new ProtectionLegElement(i == 0 ? effectProtStart : _t[i - 1], _t[i], yieldCurve, i, knots);
}
_cds2CouponsMap = new int[_nCDS][];
_cdsCouponsUpdateMap = new int[_nCDS][];
_knot2CouponsMap = new int[_nCDS][];
int nPaymentsFinalCDS = cds[_nCDS - 1].getNumPayments();
List <CdsCoupon> allCoupons = new List <CdsCoupon>(_nCDS + nPaymentsFinalCDS - 1);
allCoupons.AddRange(cds[_nCDS - 1].getCoupons());
int[] temp = new int[nPaymentsFinalCDS];
for (int i = 0; i < nPaymentsFinalCDS; i++)
{
temp[i] = i;
}
_cds2CouponsMap[_nCDS - 1] = temp;
//complete the list of unique coupons and fill out the cds2CouponsMap
for (int i = 0; i < _nCDS - 1; i++)
{
CdsCoupon[] c = cds[i].getCoupons();
int nPayments = c.Length;
_cds2CouponsMap[i] = new int[nPayments];
for (int k = 0; k < nPayments; k++)
{
int index = -1;
for (int j = 0; j < allCoupons.Count; j++)
{
if (allCoupons[j].Equals(c[k]))
{
index = j;
break;
}
}
if (index == -1)
{
index = allCoupons.Count;
allCoupons.Add(c[k]);
}
_cds2CouponsMap[i][k] = index;
}
}
//loop over the coupons to populate the couponUpdateMap
_nCoupons = allCoupons.Count;
int[] sizes = new int[_nCDS];
int[] map = new int[_nCoupons];
for (int i = 0; i < _nCoupons; i++)
{
CdsCoupon c = allCoupons[i];
int index = Array.BinarySearch(_t, c.getEffEnd());
if (index < 0)
{
index = -(index + 1);
}
sizes[index]++;
map[i] = index;
}
//make the protection leg elements
if (payAccOnDefault)
{
_premElems = new PremiumLegElement[_nCoupons];
for (int i = 0; i < _nCoupons; i++)
{
_premElems[i] = new PremiumLegElement(effectProtStart, allCoupons[i], yieldCurve, map[i], knots, formula);
}
}
else
{
_premElems = new CouponOnlyElement[_nCoupons];
for (int i = 0; i < _nCoupons; i++)
{
_premElems[i] = new CouponOnlyElement(allCoupons[i], yieldCurve, map[i]);
}
}
//sort a map from coupon to curve node, to a map from curve node to coupons
for (int i = 0; i < _nCDS; i++)
{
_knot2CouponsMap[i] = new int[sizes[i]];
}
int[] indexes = new int[_nCDS];
for (int i = 0; i < _nCoupons; i++)
{
int index = map[i];
_knot2CouponsMap[index][indexes[index]++] = i;
}
//the cdsCouponsUpdateMap is the intersection of the cds2CouponsMap and knot2CouponsMap
for (int i = 0; i < _nCDS; i++)
{
_cdsCouponsUpdateMap[i] = intersection(_knot2CouponsMap[i], _cds2CouponsMap[i]);
}
}
/**
* Set up a strip of increasing maturity CDSs that have some coupons in common. The trade date, step-in date and valuation date and
* accrual start date are all common, as is the payment frequency. The maturities are expressed as integer multiples of the
* payment interval from a reference date (the next IMM date after the trade date for standard CDSs) - this guarantees that premiums
* will be the same across several CDSs.
* @param tradeDate The trade date
* @param stepinDate (aka Protection Effective sate or assignment date). Date when party assumes ownership. This is usually T+1. This is when protection
* (and risk) starts in terms of the model. Note, this is sometimes just called the Effective Date, however this can cause
* confusion with the legal effective date which is T-60 or T-90.
* @param cashSettlementDate The cash settlement date. The date that values are PVed to. Is is normally today + 3 business days.
* @param accStartDate Accrual Start Date. This is when the CDS nominally starts in terms of premium payments. i.e. the number
* of days in the first period (and thus the amount of the first premium payment) is counted from this date.
* @param maturityReferanceDate A reference date that maturities are measured from. For standard CDSSs, this is the next IMM date after
* the trade date, so the actually maturities will be some fixed periods after this.
* @param maturityIndexes The maturities are fixed integer multiples of the payment interval, so for 6M, 1Y and 2Y tenors with a 3M
* payment interval, would require 2, 4, and 8 as the indices
* @param payAccOnDefault Is the accrued premium paid in the event of a default
* @param paymentInterval The nominal step between premium payments (e.g. 3 months, 6 months).
* @param stubType the stub convention
* @param protectStart If protectStart = true, then protections starts at the beginning of the day, otherwise it is at the end.
* @param recoveryRate The recovery rate
* @param businessdayAdjustmentConvention How are adjustments for non-business days made
* @param calendar HolidayCalendar defining what is a non-business day
* @param accrualDayCount Day count used for accrual
* @param curveDayCount Day count used on curve (NOTE ISDA uses ACT/365 and it is not recommended to change this)
*/
public MultiCdsAnalytic(
DateTime tradeDate,
DateTime stepinDate,
DateTime cashSettlementDate,
DateTime accStartDate,
DateTime maturityReferanceDate,
int[] maturityIndexes,
Boolean payAccOnDefault,
int paymentInterval,
StubConvention stubType,
Boolean protectStart,
double recoveryRate,
QLNet.BusinessDayConvention businessdayAdjustmentConvention,
QLNet.Calendar calendar,
Enums.DayCount accrualDayCount,
Enums.DayCount curveDayCount)
{
OMLib.Conventions.DayCount.Thirty360 swapDCC = new OMLib.Conventions.DayCount.Thirty360();
OMLib.Conventions.DayCount.Actual360 moneyMarketDCC = new OMLib.Conventions.DayCount.Actual360();
OMLib.Conventions.DayCount.Actual365 curveDCC = new OMLib.Conventions.DayCount.Actual365();
_nMaturities = maturityIndexes.Length;
_payAccOnDefault = payAccOnDefault;
_accStart = DateTime.Compare(accStartDate, tradeDate) < 0 ?
-curveDCC.YearFraction(accStartDate, tradeDate) :
curveDCC.YearFraction(tradeDate, accStartDate);
DateTime temp = DateTime.Compare(stepinDate, accStartDate) > 0 ? stepinDate : accStartDate;
DateTime effectiveStartDate = protectStart ? temp.AddDays(-1) : temp;
_cashSettlementTime = curveDCC.YearFraction(tradeDate, cashSettlementDate);
_effectiveProtectionStart = curveDCC.YearFraction(tradeDate, effectiveStartDate);
_lgd = 1 - recoveryRate;
DateTime[] maturities = new DateTime[_nMaturities];
_protectionEnd = new double[_nMaturities];
int period = paymentInterval;
for (int i = 0; i < _nMaturities; i++)
{
int tStep = period * maturityIndexes[i];
maturities[i] = maturityReferanceDate.AddMonths(tStep);
_protectionEnd[i] = curveDCC.YearFraction(tradeDate, maturities[i]);
}
IsdaPremiumLegSchedule fullPaymentSchedule = new IsdaPremiumLegSchedule(accStartDate, maturities[_nMaturities - 1], period,
stubType, businessdayAdjustmentConvention, calendar, protectStart);
//remove already expired coupons
IsdaPremiumLegSchedule paymentSchedule = fullPaymentSchedule.truncateSchedule(stepinDate);
int couponOffset = fullPaymentSchedule.getNumPayments() - paymentSchedule.getNumPayments();
_totalPayments = paymentSchedule.getNumPayments();
_standardCoupons = new CdsCoupon[_totalPayments - 1];
for (int i = 0; i < (_totalPayments - 1); i++)
{ //The last coupon is actually a terminal coupon, so not included here
_standardCoupons[i] = new CdsCoupon(
tradeDate, paymentSchedule.getAccPaymentDateTriplet(i), protectStart, accrualDayCount, curveDayCount);
}
//find the terminal coupons
_terminalCoupons = new CdsCoupon[_nMaturities];
_matIndexToPayments = new int[_nMaturities];
_accruedDays = new int[_nMaturities];
_accrued = new double[_nMaturities];
long secondJulianDate = stepinDate.Ticks;
for (int i = 0; i < _nMaturities; i++)
{
int index = fullPaymentSchedule.getNominalPaymentDateIndex(maturities[i]);
//maturity is unadjusted, but if protectionStart=true (i.e. standard CDS) there is effectively an extra day of accrued interest
DateTime accEnd = protectStart ? maturities[i].AddDays(1) : maturities[i];
_terminalCoupons[i] = new CdsCoupon(
tradeDate, fullPaymentSchedule.getAccStartDate(index), accEnd,
fullPaymentSchedule.getPaymentDate(index), protectStart);
_matIndexToPayments[i] = index - couponOffset;
//This will only matter for the edge case when the trade date is 1 day before maturity
DateTime tDate2 = _matIndexToPayments[i] < 0 ?
fullPaymentSchedule.getAccStartDate(couponOffset - 1) : paymentSchedule.getAccStartDate(0);
long firstJulianDate = tDate2.Ticks;
_accruedDays[i] = secondJulianDate > firstJulianDate ? (int)(secondJulianDate - firstJulianDate) : 0;
_accrued[i] = DateTime.Compare(tDate2, stepinDate) < 0 ? swapDCC.YearFraction(tDate2, stepinDate) : 0.0;
}
}
private double calculateSinglePeriodAccrualOnDefaultCreditSensitivity(
CdsCoupon coupon,
double effStart,
double[] integrationPoints,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve,
int creditCurveNode)
{
double start = Math.Max(coupon.getEffStart(), effStart);
if (start >= coupon.getEffEnd())
{
return(0.0);
}
double[] knots = DoublesScheduleGenerator.truncateSetInclusive(start, coupon.getEffEnd(), integrationPoints);
double t = knots[0];
double ht0 = creditCurve.getRT_(t);
double rt0 = yieldCurve.getRT_(t);
double p0 = Math.Exp(-rt0);
double q0 = Math.Exp(-ht0);
double b0 = p0 * q0; // this is the risky discount factor
double dqdr0 = creditCurve.getSingleNodeDiscountFactorSensitivity(t, creditCurveNode);
double t0 = t - coupon.getEffStart() + _omega;
double pvSense = 0.0;
int nItems = knots.Length;
for (int j = 1; j < nItems; ++j)
{
t = knots[j];
double ht1 = creditCurve.getRT_(t);
double rt1 = yieldCurve.getRT_(t);
double p1 = Math.Exp(-rt1);
double q1 = Math.Exp(-ht1);
double b1 = p1 * q1;
double dqdr1 = creditCurve.getSingleNodeDiscountFactorSensitivity(t, creditCurveNode);
double dt = knots[j] - knots[j - 1];
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt + 1e-50; // to keep consistent with ISDA c code
double tPvSense;
// TODO once the maths is written up in a white paper, check these formula again,
// since tests again finite difference could miss some subtle error
if (_formula == AccrualOnDefaultFormulae.MARKIT_FIX)
{
if (Math.Abs(dhrt) < 1e-5)
{
double eP = Maths.Epsilon.epsilonP(-dhrt);
double ePP = Maths.Epsilon.epsilonPP(-dhrt);
double dPVdq0 = p0 * dt * ((1 + dht) * eP - dht * ePP);
double dPVdq1 = b0 * dt / q1 * (-eP + dht * ePP);
tPvSense = dPVdq0 * dqdr0 + dPVdq1 * dqdr1;
}
else
{
double w1 = (b0 - b1) / dhrt;
double w2 = w1 - b1;
double w3 = dht / dhrt;
double w4 = dt / dhrt;
double w5 = (1 - w3) * w2;
double dPVdq0 = w4 / q0 * (w5 + w3 * (b0 - w1));
double dPVdq1 = w4 / q1 * (w5 + w3 * (b1 * (1 + dhrt) - w1));
tPvSense = dPVdq0 * dqdr0 - dPVdq1 * dqdr1;
}
}
else
{
double t1 = t - coupon.getEffStart() + _omega;
if (Math.Abs(dhrt) < 1e-5)
{
double e = Maths.Epsilon.epsilon(-dhrt);
double eP = Maths.Epsilon.epsilonP(-dhrt);
double ePP = Maths.Epsilon.epsilonPP(-dhrt);
double w1 = t0 * e + dt * eP;
double w2 = t0 * eP + dt * ePP;
double dPVdq0 = p0 * ((1 + dht) * w1 - dht * w2);
double dPVdq1 = b0 / q1 * (-w1 + dht * w2);
tPvSense = dPVdq0 * dqdr0 + dPVdq1 * dqdr1;
}
else
{
double w1 = dt / dhrt;
double w2 = dht / dhrt;
double w3 = (t0 + w1) * b0 - (t1 + w1) * b1;
double w4 = (1 - w2) / dhrt;
double w5 = w1 / dhrt * (b0 - b1);
double dPVdq0 = w4 * w3 / q0 + w2 * ((t0 + w1) * p0 - w5 / q0);
double dPVdq1 = w4 * w3 / q1 + w2 * ((t1 + w1) * p1 - w5 / q1);
tPvSense = dPVdq0 * dqdr0 - dPVdq1 * dqdr1;
}
t0 = t1;
}
pvSense += tPvSense;
ht0 = ht1;
rt0 = rt1;
p0 = p1;
q0 = q1;
b0 = b1;
dqdr0 = dqdr1;
}
return(coupon.getYFRatio() * pvSense);
}
