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 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[] accOnDefault(PiecewiseconstantHazardRate creditCurve)
{
double t = _knots[0];
double[] htAndSense = creditCurve.getRTandSensitivity(t, _creditCurveKnot);
double ht0 = htAndSense[0];
double rt0 = _rt[0];
double p0 = _p[0];
double q0 = Math.Exp(-ht0);
double b0 = p0 * q0; // this is the risky discount factor
double dqdr0 = -htAndSense[1] * q0;
double t0 = t - _coupon.getEffStart() + _omega;
double pv = 0.0;
double pvSense = 0.0;
for (int j = 1; j < _n; ++j)
{
t = _knots[j];
htAndSense = creditCurve.getRTandSensitivity(t, _creditCurveKnot);
double ht1 = htAndSense[0];
double rt1 = _rt[j];
double p1 = _p[j];
double q1 = Math.Exp(-ht1);
double b1 = p1 * q1;
double dqdr1 = -htAndSense[1] * q1;
double dt = _knots[j] - _knots[j - 1];
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
double tPV;
double tPvSense;
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 + dhrt) * w1 - dht * w2);
double dPVdq1 = b0 / q1 * (-w1 + dht * w2);
tPV = dht * b0 * w1;
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);
tPV = dht / dhrt * (t0 * b0 - t1 * b1 + dt / dhrt * (b0 - b1));
tPvSense = dPVdq0 * dqdr0 - dPVdq1 * dqdr1;
}
t0 = t1;
pv += tPV;
pvSense += tPvSense;
ht0 = ht1;
rt0 = rt1;
p0 = p1;
q0 = q1;
b0 = b1;
dqdr0 = dqdr1;
}
return(new double[] { _coupon.getYFRatio() *pv, _coupon.getYFRatio() *pvSense });
}
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);
}