/**
* This is the present value of the premium leg per unit coupon, seen at the cash-settlement date.
* It is equal to 10,000 times the RPV01 (Risky PV01). The actual PV of the leg is this multiplied by the
* notional and the fractional spread (i.e. coupon in basis points divided by 10,000).
*
* @param cds the analytic description of a CDS traded at a certain time
* @param yieldCurve the yield (or discount) curve
* @param creditCurve the credit (or survival) curve
* @param cleanOrDirty the clean or dirty price
* @return 10,000 times the RPV01 (on a notional of 1)
* @see #annuity
* @see #dirtyAnnuity
*/
public double annuity(
CDS cds,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve,
CdsPriceType cleanOrDirty)
{
return(annuity(cds, yieldCurve, creditCurve, cleanOrDirty, cds.getCashSettleTime()));
}
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);
}
/**
* Compute the present value of the protection leg with a notional of 1, which is given by the integral
* $\frac{1-R}{P(T_{v})} \int_{T_a} ^{T_b} P(t) \frac{dQ(t)}{dt} dt$ where $P(t)$ and $Q(t)$ are the discount
* and survival curves respectively, $T_a$ and $T_b$ are the start and end of the protection respectively,
* $T_v$ is the valuation time (all measured from $t = 0$, 'today') and $R$ is the recovery rate.
*
* @param cds the analytic description of a CDS traded at a certain time
* @param yieldCurve the yield (or discount) curve
* @param creditCurve the credit (or survival) curve
* @param valuationTime the valuation time, if time is zero, leg is valued today,
* value often quoted for cash-settlement date
* @return the value of the protection leg (on a unit notional)
*/
public double annuity(
CDS cds,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve,
CdsPriceType cleanOrDirty,
double valuationTime)
{
double pv = dirtyAnnuity(cds, yieldCurve, creditCurve);
double valDF = Math.Exp(-yieldCurve.getRT_(valuationTime));
if (cleanOrDirty == CdsPriceType.CLEAN)
{
double csTime = cds.getCashSettleTime();
double protStart = cds.getEffectiveProtectionStart();
double csDF = valuationTime == csTime ? valDF :Math.Exp(-yieldCurve.getRT_(csTime));
double q = protStart == 0 ? 1.0 : Math.Exp(-creditCurve.getRT_(protStart));
double acc = cds.getAccruedYearFraction();
pv -= acc * csDF * q; //subtract the accrued risky discounted to today
}
pv /= valDF; //roll forward to valuation date
return(pv);
}
public Pricer(
CDS cds,
YieldTermStructure yieldCurve,
double[] creditCurveKnots,
double fractionalSpread,
double pointsUpfront)
{
_cds = cds;
_fracSpread = fractionalSpread;
_pointsUpfront = pointsUpfront;
// protection leg
_proLegIntPoints = DoublesScheduleGenerator.getIntegrationsPoints(
cds.getEffectiveProtectionStart(),
cds.getProtectionEnd(),
yieldCurve.t.ToArray(),
creditCurveKnots);
_nProPoints = _proLegIntPoints.Length;
double lgd = cds.getLGD();
_valuationDF = Math.Exp(-yieldCurve.getRT_(cds.getCashSettleTime()));
_lgdDF = lgd / _valuationDF;
_proYieldCurveRT = new double[_nProPoints];
_proDF = new double[_nProPoints];
for (int i = 0; i < _nProPoints; i++)
{
_proYieldCurveRT[i] = yieldCurve.getRT_(_proLegIntPoints[i]);
_proDF[i] = Math.Exp(-_proYieldCurveRT[i]);
}
// premium leg
_nPayments = cds.getNumPayments();
_paymentDF = new double[_nPayments];
for (int i = 0; i < _nPayments; i++)
{
_paymentDF[i] = Math.Exp(-yieldCurve.getRT_(cds.getCoupon(i).getPaymentTime()));
}
if (cds.isPayAccOnDefault())
{
double tmp = cds.getNumPayments() == 1 ? cds.getEffectiveProtectionStart() : cds.getAccStart();
double[] integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(
tmp, cds.getProtectionEnd(), yieldCurve.t.ToArray(), creditCurveKnots);
_accRate = new double[_nPayments];
_offsetAccStart = new double[_nPayments];
_premLegIntPoints = new double[_nPayments][];
_premDF = new double[_nPayments][];
_rt = new double[_nPayments][];
_premDt = new double[_nPayments][];
for (int i = 0; i < _nPayments; i++)
{
CdsCoupon c = cds.getCoupon(i);
_offsetAccStart[i] = c.getEffStart();
double offsetAccEnd = c.getEffEnd();
_accRate[i] = c.getYFRatio();
double start = Math.Max(_offsetAccStart[i], cds.getEffectiveProtectionStart());
if (start >= offsetAccEnd)
{
continue;
}
_premLegIntPoints[i] = DoublesScheduleGenerator.truncateSetInclusive(start, offsetAccEnd, integrationSchedule);
int n = _premLegIntPoints[i].Length;
_rt[i] = new double[n];
_premDF[i] = new double[n];
for (int k = 0; k < n; k++)
{
_rt[i][k] = yieldCurve.getRT_(_premLegIntPoints[i][k]);
_premDF[i][k] = Math.Exp(-_rt[i][k]);
}
_premDt[i] = new double[n - 1];
for (int k = 1; k < n; k++)
{
double dt = _premLegIntPoints[i][k] - _premLegIntPoints[i][k - 1];
_premDt[i][k - 1] = dt;
}
}
}
else
{
_accRate = null;
_offsetAccStart = null;
_premDF = null;
_premDt = null;
_rt = null;
_premLegIntPoints = null;
}
}
/**
* The sensitivity of the PV of the protection leg to the zero rate of a given node (knot) of the yield curve.
*
* @param cds the analytic description of a CDS traded at a certain time
* @param yieldCurve the yield (or discount) curve
* @param creditCurve the credit (or survival) curve
* @param yieldCurveNode the yield curve node
* @return the sensitivity (on a unit notional)
*/
public double protectionLegYieldSensitivity(
CDS cds,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve,
int yieldCurveNode)
{
if ((yieldCurveNode != 0 && cds.getProtectionEnd() <= yieldCurve.t[yieldCurveNode - 1]) ||
(yieldCurveNode != creditCurve.getNumberOfKnots() - 1 &&
cds.getEffectiveProtectionStart() >= yieldCurve.t[yieldCurveNode + 1]))
{
return(0.0); // can't have any sensitivity in this case
}
if (cds.getProtectionEnd() <= 0.0)
{ //short cut already expired CDSs
return(0.0);
}
double[] integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(
cds.getEffectiveProtectionStart(), cds.getProtectionEnd(), yieldCurve, creditCurve);
double t = integrationSchedule[0];
double ht0 = creditCurve.getRT_(t);
double rt0 = yieldCurve.getRT_(t);
double dpdr0 = yieldCurve.getSingleNodeDiscountFactorSensitivity(t, yieldCurveNode);
double q0 = Math.Exp(-ht0);
double p0 = Math.Exp(-rt0);
double pvSense = 0.0;
int n = integrationSchedule.Length;
for (int i = 1; i < n; ++i)
{
t = integrationSchedule[i];
double ht1 = creditCurve.getRT_(t);
double dpdr1 = yieldCurve.getSingleNodeDiscountFactorSensitivity(t, yieldCurveNode);
double rt1 = yieldCurve.getRT_(t);
double q1 = Math.Exp(-ht1);
double p1 = Math.Exp(-rt1);
if (dpdr0 == 0.0 && dpdr1 == 0.0)
{
ht0 = ht1;
rt0 = rt1;
p0 = p1;
q0 = q1;
continue;
}
double hBar = ht1 - ht0;
double fBar = rt1 - rt0;
double fhBar = hBar + fBar;
double dPVSense;
double e = Maths.Epsilon.epsilon(-fhBar);
double eP = Maths.Epsilon.epsilonP(-fhBar);
double dPVdp0 = q0 * hBar * (e - eP);
double dPVdp1 = hBar * p0 * q0 / p1 * eP;
dPVSense = dPVdp0 * dpdr0 + dPVdp1 * dpdr1;
pvSense += dPVSense;
ht0 = ht1;
dpdr0 = dpdr1;
rt0 = rt1;
p0 = p1;
q0 = q1;
}
pvSense *= cds.getLGD();
// Compute the discount factor discounting the upfront payment made on the cash settlement date back to the valuation date
double df = Math.Exp(-yieldCurve.getRT_(cds.getCashSettleTime()));
pvSense /= df;
//TODO this was put in quickly the get the right sensitivity to the first node
double dfSense = yieldCurve.getSingleNodeDiscountFactorSensitivity(cds.getCashSettleTime(), yieldCurveNode);
if (dfSense != 0.0)
{
double pro = protectionLeg(cds, yieldCurve, creditCurve);
pvSense -= pro / df * dfSense;
}
return(pvSense);
}
public double protectionLegCreditSensitivity(
CDS cds,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve,
int creditCurveNode)
{
if ((creditCurveNode != 0 && cds.getProtectionEnd() <= creditCurve.getTimeAtIndex(creditCurveNode - 1)) ||
(creditCurveNode != creditCurve.t.Count - 1 &&
cds.getEffectiveProtectionStart() >= creditCurve.getTimeAtIndex(creditCurveNode + 1)))
{
return(0.0); // can't have any sensitivity in this case
}
if (cds.getProtectionEnd() <= 0.0)
{ //short cut already expired CDSs
return(0.0);
}
double[] integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(
cds.getEffectiveProtectionStart(), cds.getProtectionEnd(), yieldCurve, creditCurve);
double t = integrationSchedule[0];
double ht0 = creditCurve.getRT_(t);
double rt0 = yieldCurve.getRT_(t);
double dqdr0 = creditCurve.getSingleNodeDiscountFactorSensitivity(t, creditCurveNode);
double q0 = Math.Exp(-ht0);
double p0 = Math.Exp(-rt0);
double pvSense = 0.0;
int n = integrationSchedule.Length;
for (int i = 1; i < n; ++i)
{
t = integrationSchedule[i];
double ht1 = creditCurve.getRT_(t);
double dqdr1 = creditCurve.getSingleNodeDiscountFactorSensitivity(t, creditCurveNode);
double rt1 = yieldCurve.getRT_(t);
double q1 = Math.Exp(-ht1);
double p1 = Math.Exp(-rt1);
if (dqdr0 == 0.0 && dqdr1 == 0.0)
{
ht0 = ht1;
rt0 = rt1;
p0 = p1;
q0 = q1;
continue;
}
double hBar = ht1 - ht0;
double fBar = rt1 - rt0;
double fhBar = hBar + fBar;
double dPVSense;
if (Math.Abs(fhBar) < 1e-5)
{
double e = Maths.Epsilon.epsilon(-fhBar);
double eP = Maths.Epsilon.epsilonP(-fhBar);
double dPVdq0 = p0 * ((1 + hBar) * e - hBar * eP);
double dPVdq1 = -p0 * q0 / q1 * (e - hBar * eP);
dPVSense = dPVdq0 * dqdr0 + dPVdq1 * dqdr1;
}
else
{
double w = fBar / fhBar * (p0 * q0 - p1 * q1);
dPVSense = ((w / q0 + hBar * p0) / fhBar) * dqdr0 - ((w / q1 + hBar * p1) / fhBar) * dqdr1;
}
pvSense += dPVSense;
ht0 = ht1;
dqdr0 = dqdr1;
rt0 = rt1;
p0 = p1;
q0 = q1;
}
pvSense *= cds.getLGD();
// Compute the discount factor discounting the upfront payment made on the cash settlement date back to the valuation date
double df = Math.Exp(-yieldCurve.getRT_(cds.getCashSettleTime()));
pvSense /= df;
return(pvSense);
}
/**
* Compute the present value of the protection leg with a notional of 1, which is given by the integral
* $\frac{1-R}{P(T_{v})} \int_{T_a} ^{T_b} P(t) \frac{dQ(t)}{dt} dt$ where $P(t)$ and $Q(t)$ are the discount
* and survival curves respectively, $T_a$ and $T_b$ are the start and end of the protection respectively,
* $T_v$ is the valuation time (all measured from $t = 0$, 'today') and $R$ is the recovery rate.
*
* @param cds the analytic description of a CDS traded at a certain time
* @param yieldCurve the yield (or discount) curve
* @param creditCurve the credit (or survival) curve
* @return the value of the protection leg (on a unit notional)
*/
public double protectionLeg(CDS cds, YieldTermStructure yieldCurve, PiecewiseconstantHazardRate creditCurve)
{
return(protectionLeg(cds, yieldCurve, creditCurve, cds.getCashSettleTime()));
}
