public double protectionLeg(IsdaCompliantCreditCurve creditCurve) {
double ht0 = creditCurve.getRT(_proLegIntPoints[0]);
double rt0 = _proYieldCurveRT[0];
double b0 = _proDF[0] * Math.exp(-ht0);
double pv = 0.0;
for (int i = 1; i < _nProPoints; ++i) {
double ht1 = creditCurve.getRT(_proLegIntPoints[i]);
double rt1 = _proYieldCurveRT[i];
double b1 = _proDF[i] * Math.exp(-ht1);
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
// this is equivalent to the ISDA code without explicitly calculating the time step - it
// also handles the limit
double dPV;
if (Math.abs(dhrt) < 1e-5) {
dPV = dht * b0 * epsilon(-dhrt);
} else {
dPV = (b0 - b1) * dht / dhrt;
}
pv += dPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
pv *= _lgdDF; // multiply by LGD and adjust to valuation date
return pv;
}
private double calculateSinglePeriodAccrualOnDefault(
int paymentIndex, IsdaCompliantCreditCurve creditCurve) {
double[] knots = _premLegIntPoints[paymentIndex];
if (knots == null) {
return 0.0;
}
double[] df = _premDF[paymentIndex];
double[] deltaT = _premDt[paymentIndex];
double[] rt = _rt[paymentIndex];
double accRate = _accRate[paymentIndex];
double accStart = _offsetAccStart[paymentIndex];
double t = knots[0];
double ht0 = creditCurve.getRT(t);
double rt0 = rt[0];
double b0 = df[0] * Math.exp(-ht0);
double t0 = t - accStart + _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 = rt[j];
double b1 = df[j] * Math.exp(-ht1);
double dt = deltaT[j - 1];
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt + 1e-50; // to keep consistent with ISDA c code
double tPV;
if (getAccOnDefaultFormula() == AccrualOnDefaultFormulae.MARKIT_FIX) {
if (Math.abs(dhrt) < 1e-5) {
tPV = dht * dt * b0 * epsilonP(-dhrt);
} else {
tPV = dht * dt / dhrt * ((b0 - b1) / dhrt - b1);
}
} else {
double t1 = t - accStart + _omega;
if (Math.abs(dhrt) < 1e-5) {
tPV = dht * b0 * (t0 * epsilon(-dhrt) + dt * 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 accRate * pv;
}
public double rpv01(IsdaCompliantCreditCurve creditCurve, CdsPriceType cleanOrDirty) {
double pv = 0.0;
for (int i = 0; i < _nPayments; i++) {
CdsCoupon c = _cds.getCoupon(i);
double q = creditCurve.getDiscountFactor(c.getEffEnd());
pv += c.getYearFrac() * _paymentDF[i] * q;
}
if (_cds.isPayAccOnDefault()) {
double accPV = 0.0;
for (int i = 0; i < _nPayments; i++) {
accPV += calculateSinglePeriodAccrualOnDefault(i, creditCurve);
}
pv += accPV;
}
pv /= _valuationDF;
if (cleanOrDirty == CdsPriceType.CLEAN) {
pv -= _cds.getAccruedYearFraction();
}
return pv;
}
/** {@inheritDoc} */
@Override
public IsdaCompliantCreditCurve calibrateCreditCurve(
CdsAnalytic[] cds,
double[] premiums,
IsdaCompliantYieldCurve yieldCurve,
double[] pointsUpfront) {
ArgChecker.noNulls(cds, "null CDSs");
ArgChecker.notEmpty(premiums, "empty fractionalSpreads");
ArgChecker.notEmpty(pointsUpfront, "empty pointsUpfront");
ArgChecker.notNull(yieldCurve, "null yieldCurve");
int n = cds.length;
ArgChecker.isTrue(n == premiums.length, "Number of CDSs does not match number of spreads");
ArgChecker.isTrue(
n == pointsUpfront.length, "Number of CDSs does not match number of pointsUpfront");
double proStart = cds[0].getEffectiveProtectionStart();
for (int i = 1; i < n; i++) {
ArgChecker.isTrue(
proStart == cds[i].getEffectiveProtectionStart(),
"all CDSs must has same protection start");
ArgChecker.isTrue(
cds[i].getProtectionEnd() > cds[i - 1].getProtectionEnd(),
"protection end must be ascending");
}
// use continuous premiums as initial guess
double[] guess = new double[n];
double[] t = new double[n];
for (int i = 0; i < n; i++) {
t[i] = cds[i].getProtectionEnd();
guess[i] = (premiums[i] + pointsUpfront[i] / t[i]) / cds[i].getLGD();
}
IsdaCompliantCreditCurve creditCurve = new IsdaCompliantCreditCurve(t, guess);
for (int i = 0; i < n; i++) {
Pricer pricer = new Pricer(cds[i], yieldCurve, t, premiums[i], pointsUpfront[i]);
Function1D<Double, Double> func = pricer.getPointFunction(i, creditCurve);
switch (getArbHanding()) {
case Ignore:
{
try {
double[] bracket =
BRACKER.getBracketedPoints(
func,
0.8 * guess[i],
1.25 * guess[i],
Double.NEGATIVE_INFINITY,
Double.POSITIVE_INFINITY);
double zeroRate =
bracket[0] > bracket[1]
? ROOTFINDER.getRoot(func, bracket[1], bracket[0])
: ROOTFINDER.getRoot(func, bracket[0], bracket[1]); // Negative guess handled
creditCurve = creditCurve.withRate(zeroRate, i);
} catch (
MathException e) { // handling bracketing failure due to small survival probability
if (Math.abs(func.evaluate(creditCurve.getZeroRateAtIndex(i - 1))) < 1.e-12) {
creditCurve = creditCurve.withRate(creditCurve.getZeroRateAtIndex(i - 1), i);
} else {
throw new MathException(e);
}
}
break;
}
case Fail:
{
double minValue =
i == 0 ? 0.0 : creditCurve.getRTAtIndex(i - 1) / creditCurve.getTimeAtIndex(i);
if (i > 0 && func.evaluate(minValue) > 0.0) { // can never fail on the first spread
StringBuilder msg = new StringBuilder();
if (pointsUpfront[i] == 0.0) {
msg.append("The par spread of " + premiums[i] + " at index " + i);
} else {
msg.append(
"The premium of "
+ premiums[i]
+ "and points up-front of "
+ pointsUpfront[i]
+ " at index "
+ i);
}
msg.append(
" is an arbitrage; cannot fit a curve with positive forward hazard rate. ");
throw new IllegalArgumentException(msg.toString());
}
guess[i] = Math.max(minValue, guess[i]);
double[] bracket =
BRACKER.getBracketedPoints(
func, guess[i], 1.2 * guess[i], minValue, Double.POSITIVE_INFINITY);
double zeroRate = ROOTFINDER.getRoot(func, bracket[0], bracket[1]);
creditCurve = creditCurve.withRate(zeroRate, i);
break;
}
case ZeroHazardRate:
{
double minValue =
i == 0 ? 0.0 : creditCurve.getRTAtIndex(i - 1) / creditCurve.getTimeAtIndex(i);
if (i > 0 && func.evaluate(minValue) > 0.0) { // can never fail on the first spread
creditCurve = creditCurve.withRate(minValue, i);
} else {
guess[i] = Math.max(minValue, guess[i]);
double[] bracket =
BRACKER.getBracketedPoints(
func, guess[i], 1.2 * guess[i], minValue, Double.POSITIVE_INFINITY);
double zeroRate = ROOTFINDER.getRoot(func, bracket[0], bracket[1]);
creditCurve = creditCurve.withRate(zeroRate, i);
}
break;
}
default:
throw new IllegalArgumentException("unknow case " + getArbHanding());
}
}
return creditCurve;
}
