@Test
public void test() {
RealSingleRootFinder finder = getRootFinder();
assertEquals(finder.getRoot(F, 2.5, 3.5), 3, EPS);
assertEquals(finder.getRoot(F, 1.5, 2.5), 2, EPS);
assertEquals(finder.getRoot(F, -1.5, 0.5), -1, EPS);
}
private double getCriticalValue(
final OptionDefinition definition, final StandardOptionDataBundle data, final double k) {
final Function1D<Double, Double> f =
new Function1D<Double, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final Double x) {
return k - BSM.getPricingFunction(definition).evaluate(data.withSpot(x));
}
};
return ROOT_FINDER.getRoot(f, 0., 10000.);
}
/** {@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;
}