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);
}
/**
* The value of the full (or dirty) annuity (or RPV01 - the premium leg per unit of coupon) today (t=0).
* The cash flows from premium payments and accrual-on-default are risky discounted to t=0
* The actual value of the leg is this multiplied by the notional and the fractional coupon
* (i.e. coupon in basis points divided by 10,000).
* <p>
* This is valid for both spot and forward starting CDS.
*
* @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 full (or dirty) annuity valued today. <b>Note</b> what is usually quoted is the clean annuity
*/
public double dirtyAnnuity(CDS cds,
YieldTermStructure yt, PiecewiseconstantHazardRate hazard)
{
DateTime tradedate = cds.tradedate;
List <DateTime> Jumps = yt.jumpDates_;
DateTime settlementDate = tradedate.AddDays(0);
double recoveryrate = cds.Recovery;
DateTime Stepindate = tradedate.AddDays(1);
double coupon = cds.PremiumRate;
OMLib.Conventions.DayCount.Actual360 dc = new OMLib.Conventions.DayCount.Actual360();
CdsCoupon[] cf = cds.getCoupons();
double notional = cds.Notional;
double ita = (double)365 / 360;
double totalNPV = 0.0;
for (int i = 0; i < cf.Length; ++i)
{
totalNPV += cf[i].getYearFrac() * notional * Math.Exp(-hazard.getRT_(cf[i].getEffEnd()))
* Math.Exp(-yt.getRT_(cf[i].getPaymentTime()));
}
double start = cds.getNumPayments() == 1 ? cds.getEffectiveProtectionStart() : cds.getAccStart();
double[] integrationSchedule = DoublesScheduleGenerator.getIntegrationsPoints(start, cds.getProtectionEnd(), yt, hazard);
double accPV = 0.0;
for (int i = 0; i < cf.Length; ++i)
{
accPV += calculateSinglePeriodAccrualOnDefault(cf[i], cds.getEffectiveProtectionStart(), integrationSchedule, yt, hazard);
}
totalNPV += accPV;
return(totalNPV);
}
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;
}
}
public double calculateSinglePeriodAccrualOnDefault(CDS cds,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve)
{
double Acc = 0;
List <double> Jumps = yieldCurve.t;
DateTime tradedate = cds.tradedate;
DateTime settlementDate = tradedate.AddDays(cds.Cashsettlement);
double recoveryrate = cds.Recovery;
DateTime Stepindate = tradedate.AddDays(1);
double notional = cds.Notional;
double coupon = cds.PremiumRate;
DateTime lastpayment = cds.formerpaymentdate;
DateTime effectiveStart = tradedate.AddDays(1);
CdsCoupon[] cc = cds.getCoupons();
for (int i = 0; i < cds.getNumPayments(); ++i)
{
//Accured on default
double t_0 = (i > 0) ? cc[i].getEffStart():0;
double T = cc[i].getEffEnd();
List <double> knots = new List <double>();
knots.Add(t_0);
for (int j = 0; j < Jumps.Count; j++)
{
if ((Jumps[j] < T) && (t_0 < Jumps[j]))
{
knots.Add(Jumps[j]);
}
}
knots.Add(T);
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
OMLib.Conventions.DayCount.Actual365 dc = new OMLib.Conventions.DayCount.Actual365();
double t0;
if (i == 0)
{
t0 = knots[0] - cc[0].getEffStart();
}
else
{
t0 = knots[0] - cc[i].getEffStart();
}
double pv = 0.0;
int nItems = knots.Count;
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 + 1e-50;
double tPV;
double t1;
if (i == 0)
{
t1 = knots[j] - cc[0].getEffStart();
}
else
{
t1 = knots[j] - cc[i].getEffStart();
}
if (Math.Abs(dhrt) < 1e-5)
{
tPV = dht * b0 * (t0 * (Math.Exp(-dhrt) - 1) / (-dhrt) + dt * ((-dhrt - 1) * (Math.Exp(-dhrt) - 1) - dhrt) / (dhrt * dhrt));
}
else
{
tPV = dht / dhrt * (t0 * b0 - t1 * b1 + dt / dhrt * (b0 - b1));
}
t0 = t1;
pv += tPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
Acc += pv;
}
return(Acc);
}
