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 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 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]);
}
}
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]);
}
}
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);
}