//-------------------------------------------------------------------------
/**
* The sensitivity of the PV of a CDS to the zero hazard rates at the knots of the credit curve.
*
* @param cds the CDS
* @param coupon the coupon
* @param creditCurve the credit Curve
* @param yieldCurve the yield curve
* @return vector of sensitivities
*/
public double[] getCurveSensitivities(
CDS cds,
double coupon,
PiecewiseconstantHazardRate creditCurve,
YieldTermStructure yieldCurve)
{
int n = creditCurve.getNumberOfKnots();
double[] CurveSen = new double[n];
for (int i = 0; i < n; i++)
{
CurveSen[i] = _pricer.pvCreditSensitivity(cds, yieldCurve, creditCurve, coupon, i);
}
return(CurveSen);
}
/**
* The sensitivity of a set of CDSs to the zero hazard rates at the knots of the credit curve.
* The element (i,j) is the sensitivity of the PV of the jth CDS to the ith knot.
*
* @param cds the set of CDSs
* @param coupons the coupons of the CDSs
* @param creditCurve the credit Curve
* @param yieldCurve the yield curve
* @return matrix of sensitivities
*/
public double[,] getCurveSensitivities(
CDS[] cds,
double[] coupons,
PiecewiseconstantHazardRate creditCurve,
YieldTermStructure yieldCurve)
{
int nCDS = cds.Length;
int nKnots = creditCurve.getNumberOfKnots();
double[,] sense = new double[nKnots, nCDS];
for (int i = 0; i < nCDS; i++)
{
for (int j = 0; j < nKnots; j++)
{
sense[j, i] = _pricer.pvCreditSensitivity(cds[i], yieldCurve, creditCurve, coupons[i], j);
}
}
return(sense);
}
/**
* 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);
}
