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 ProtectionLegElement(double start, double end, YieldTermStructure yieldCurve, int creditCurveKnot, double[] knots)
{
_knots = DoublesScheduleGenerator.truncateSetInclusive(start, end, 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]);
}
_creditCurveKnot = creditCurveKnot;
}
/**
* 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);
}
/**
* CDS value for the payer of premiums (i.e. the buyer of protection) at the specified valuation time.
*
* @param cds 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 fractionalSpread the <b>fraction</b> spread
* @param cleanOrDirty the clean or dirty price
* @param valuationTime the valuation time, if time is zero, leg is valued today,
* value often quoted for cash-settlement date
* @return the value of a unit notional payer CDS at the specified valuation time
*/
public double pv(
CDS cds,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve,
double fractionalSpread,
CdsPriceType cleanOrDirty,
double valuationTime)
{
if (cds.getProtectionEnd() <= 0.0)
{ //short cut already Expired CDSs
return(0.0);
}
double rpv01 = annuity(cds, yieldCurve, creditCurve, cleanOrDirty, 0.0);
double proLeg = protectionLeg(cds, yieldCurve, creditCurve, 0.0);
double df = Math.Exp(-yieldCurve.getRT_(valuationTime));
return((proLeg - fractionalSpread * rpv01) / df);
}
/**
* 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 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]);
}
}
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;
}
}
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);
}
/**
* 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);
}
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);
}
public double protectionLeg(CDS cds, YieldTermStructure yt, PiecewiseconstantHazardRate hazard,
double valuationTime)
{
List <double> Jumps = yt.t;
List <double> tenor = hazard.t;
List <double> result = new List <double>();
int index = 0, indexj = 0, lastIndex = 0;
while (index < Jumps.Count || indexj < tenor.Count)
{
if (lastIndex > 0)
{
if (index >= Jumps.Count)
{
if (!DateTime.Equals(result.Last(), tenor[indexj]))
{
result.Add(tenor[indexj]);
lastIndex++;
}
indexj++;
continue;
}
if (indexj >= tenor.Count)
{
if (!DateTime.Equals(result.Last(), Jumps[index]))
{
result.Add(Jumps[index]);
lastIndex++;
}
index++;
continue;
}
}
double smallestVal = tenor.Last();
// Choose the smaller of a or b
if (Jumps[index] < tenor[indexj])
{
smallestVal = Jumps[index++];
}
else
{
smallestVal = tenor[indexj++];
}
// Don't insert duplicates
if (lastIndex > 0)
{
if (result.Last() != smallestVal)
{
result.Add(smallestVal);
lastIndex++;
}
}
else
{
result.Add(smallestVal);
lastIndex++;
}
}
DateTime tradedate = cds.tradedate;
DateTime settlementDate = tradedate.AddDays((int)valuationTime * 365);
double recoveryrate = cds.Recovery;
DateTime Stepindate = tradedate.AddDays(1);
OMLib.Conventions.DayCount.Actual360 dc = new OMLib.Conventions.DayCount.Actual360();
CdsCoupon[] cf = cds.getCoupons();
double notional = cds.Notional;
DateTime t0 = tradedate;
double T = cf.Last().getEffEnd();
List <double> JumpNodes = new List <double>();
JumpNodes.Add(0);
for (int j = 0; j < result.Count; j++)
{
if (result[j] < T)
{
JumpNodes.Add(result[j]);
}
}
JumpNodes.Add(T);
double ht0 = hazard.getRT_(JumpNodes[0]);
double rt0 = yt.getRT_(JumpNodes[0]);
double b0 = Math.Exp(-ht0 - rt0); // risky discount factor
double pv = 0.0;
double dPV = 0.0;
for (int i = 1; i < JumpNodes.Count; ++i)
{
double ht1 = hazard.getRT_(JumpNodes[i]);
double rt1 = yt.getRT_(JumpNodes[i]);
double b1 = Math.Exp(-ht1 - rt1);
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
// The formula has been modified from ISDA (but is equivalent) to avoid log(exp(x)) and explicitly
// calculating the time step - it also handles the limit
if (Math.Abs(dhrt) < 1e-5)
{
dPV = dht * b0 * Maths.Epsilon.epsilon(-dhrt) / (-dhrt);
}
else
{
dPV = (b0 - b1) * dht / dhrt;
}
pv += dPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
pv = pv * notional * (1 - recoveryrate);
return(pv / yt.discount(settlementDate));
}
