/** Tests solve AX = B from A and B. */
public void solveMatrix() {
final CholeskyDecompositionResult result = CDOG.evaluate(A5);
double[][] b = new double[][] {{1.0, 2.0}, {2.0, 3.0}, {3.0, 4.0}, {4.0, -2.0}, {-1.0, -1.0}};
DoubleMatrix2D x = result.solve(new DoubleMatrix2D(b));
DoubleMatrix2D ax = (DoubleMatrix2D) ALGEBRA.multiply(A5, x);
ArrayAsserts.assertArrayEquals(
"Cholesky decomposition OpenGamma - solve", b[0], ax.getData()[0], 1.0E-10);
ArrayAsserts.assertArrayEquals(
"Cholesky decomposition OpenGamma - solve", b[1], ax.getData()[1], 1.0E-10);
}
@Test
/** Tests the gamma method. */
public void gamma() {
final double theta0 = 0.25;
final double theta1 = 2.5;
final double[][] gamma = MODEL_G2PP.gamma(MODEL_PARAMETERS, theta0, theta1);
final double[][] gammaExpected =
new double[][] {{0.00032338, 0.000335543}, {0.000335543, 0.000349741}};
ArrayAsserts.assertArrayEquals("G2++: gamma", gammaExpected[0], gamma[0], 1.0E-7);
ArrayAsserts.assertArrayEquals("G2++: gamma", gammaExpected[1], gamma[1], 1.0E-7);
}
/** Tests solve Ax = b from A and b. */
public void solveVector() {
final CholeskyDecompositionResult result = CDOG.evaluate(A5);
double[] b = new double[] {1.0, 2.0, 3.0, 4.0, -1.0};
double[] x = result.solve(b);
DoubleMatrix1D ax = (DoubleMatrix1D) ALGEBRA.multiply(A5, new DoubleMatrix1D(x));
ArrayAsserts.assertArrayEquals(
"Cholesky decomposition OpenGamma - solve", b, ax.getData(), 1.0E-10);
}
@Test
/** Tests the volatilityMaturityPart method. */
public void volatilityMaturityPart() {
final double u = 0.75;
final double[] v = new double[] {2.0, 4.0, 7.0};
final double[][] h = MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, u, v);
final double[][] hExpected =
new double[][] {
{1.232938151, 3.173861567, 6.013423491}, {0.832348609, 1.657740023, 2.253532635}
};
ArrayAsserts.assertArrayEquals(
"G2++: maturity dependent volatility part", hExpected[0], h[0], 1.0E-7);
ArrayAsserts.assertArrayEquals(
"G2++: maturity dependent volatility part", hExpected[1], h[1], 1.0E-7);
final double[] hVector = MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, u, v[0]);
assertEquals("G2++: maturity dependent volatility part", hExpected[0][0], hVector[0], 1.0E-7);
assertEquals("G2++: maturity dependent volatility part", hExpected[1][0], hVector[1], 1.0E-7);
}
@Test(dataProvider = "coordinateData")
public void convertToEuclidean(Coordinate latLng)
throws NoninvertibleTransformException, TransformException {
final Coordinate xy = GeoUtils.convertToEuclidean(latLng);
final MathTransform transform = GeoUtils.getTransform(latLng);
final Coordinate latLngAgain = GeoUtils.convertToLatLon(transform, xy);
ArrayAsserts.assertArrayEquals(
new double[] {latLng.x, latLng.y}, new double[] {latLngAgain.x, latLngAgain.y}, 1e-4);
}
@Test
/** Tests the class setters. */
public void setter() {
final double[] volReplaced = new double[] {0.02, 0.01};
MODEL_PARAMETERS.setLastVolatilities(volReplaced);
ArrayAsserts.assertArrayEquals(
"G2++: setter", volReplaced, MODEL_PARAMETERS.getLastVolatilities(), 1.0E-10);
MODEL_PARAMETERS.setLastVolatilities(
new double[] {
VOLATILITY[0][VOLATILITY[0].length - 1], VOLATILITY[1][VOLATILITY[0].length - 1]
});
for (int loopperiod = 0; loopperiod < VOLATILITY[0].length; loopperiod++) {
assertEquals(
"G2++: setter " + loopperiod,
VOLATILITY[0][loopperiod],
MODEL_PARAMETERS.getVolatility()[0].get(loopperiod));
assertEquals(
"G2++: setter " + loopperiod,
VOLATILITY[1][loopperiod],
MODEL_PARAMETERS.getVolatility()[1].get(loopperiod));
}
}
@Test
public void swapRateDdcf() {
final double theta = 1.99;
final double rhog2pp = MODEL_PARAMETERS.getCorrelation();
final double[][] gamma = MODEL_G2PP.gamma(MODEL_PARAMETERS, 0, theta);
double[][] alphaFixed = new double[T_FIXED.length][2];
double[] tau2Fixed = new double[T_FIXED.length];
final double[][] alphaIbor = new double[T_IBOR.length][2];
final double[] tau2Ibor = new double[T_IBOR.length];
final double[][] hthetaFixed =
MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, theta, T_FIXED);
alphaFixed = new double[2][T_FIXED.length];
tau2Fixed = new double[T_FIXED.length];
for (int loopcf = 0; loopcf < T_FIXED.length; loopcf++) {
alphaFixed[loopcf][0] = Math.sqrt(gamma[0][0]) * hthetaFixed[0][loopcf];
alphaFixed[loopcf][1] = Math.sqrt(gamma[1][1]) * hthetaFixed[1][loopcf];
tau2Fixed[loopcf] =
alphaFixed[loopcf][0] * alphaFixed[loopcf][0]
+ alphaFixed[loopcf][1] * alphaFixed[loopcf][1]
+ 2 * rhog2pp * gamma[0][1] * hthetaFixed[0][loopcf] * hthetaFixed[1][loopcf];
}
final double[][] hthetaIbor =
MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, theta, T_IBOR);
for (int loopcf = 0; loopcf < T_IBOR.length; loopcf++) {
alphaIbor[loopcf][0] = Math.sqrt(gamma[0][0]) * hthetaIbor[0][loopcf];
alphaIbor[loopcf][1] = Math.sqrt(gamma[1][1]) * hthetaIbor[1][loopcf];
tau2Ibor[loopcf] =
alphaIbor[loopcf][0] * alphaIbor[loopcf][0]
+ alphaIbor[loopcf][1] * alphaIbor[loopcf][1]
+ 2 * rhog2pp * gamma[0][1] * hthetaIbor[0][loopcf] * hthetaIbor[1][loopcf];
}
final double shift = 1.0E-8;
final double[] x = {0.0, 0.1};
final double[] ddcffExpected = new double[DCF_FIXED.length];
for (int loopcf = 0; loopcf < DCF_FIXED.length; loopcf++) {
final double[] dsf_bumped = DCF_FIXED.clone();
dsf_bumped[loopcf] += shift;
final double swapRatePlus =
MODEL_G2PP.swapRate(x, dsf_bumped, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
dsf_bumped[loopcf] -= 2 * shift;
final double swapRateMinus =
MODEL_G2PP.swapRate(x, dsf_bumped, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
ddcffExpected[loopcf] = (swapRatePlus - swapRateMinus) / (2 * shift);
}
final double[] ddcffComputed =
MODEL_G2PP.swapRateDdcff1(
x, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
ArrayAsserts.assertArrayEquals(
"Hull-White model: swap rate", ddcffExpected, ddcffComputed, TOLERANCE_RATE_DELTA);
final double[] ddcfiExpected = new double[DCF_IBOR.length];
for (int loopcf = 0; loopcf < DCF_IBOR.length; loopcf++) {
final double[] dsf_bumped = DCF_IBOR.clone();
dsf_bumped[loopcf] += shift;
final double swapRatePlus =
MODEL_G2PP.swapRate(x, DCF_FIXED, alphaFixed, tau2Fixed, dsf_bumped, alphaIbor, tau2Ibor);
dsf_bumped[loopcf] -= 2 * shift;
final double swapRateMinus =
MODEL_G2PP.swapRate(x, DCF_FIXED, alphaFixed, tau2Fixed, dsf_bumped, alphaIbor, tau2Ibor);
ddcfiExpected[loopcf] = (swapRatePlus - swapRateMinus) / (2 * shift);
}
final double[] ddcfiComputed =
MODEL_G2PP.swapRateDdcfi1(
x, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
ArrayAsserts.assertArrayEquals(
"Hull-White model: swap rate", ddcfiExpected, ddcfiComputed, TOLERANCE_RATE_DELTA);
}
@Test
/** Tests swap rate first derivative */
public void swapRateD1and2() {
final double theta = 1.99;
final double rhog2pp = MODEL_PARAMETERS.getCorrelation();
final double[][] gamma = MODEL_G2PP.gamma(MODEL_PARAMETERS, 0, theta);
double[][] alphaFixed = new double[T_FIXED.length][2];
double[] tau2Fixed = new double[T_FIXED.length];
final double[][] alphaIbor = new double[T_IBOR.length][2];
final double[] tau2Ibor = new double[T_IBOR.length];
final double[][] hthetaFixed =
MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, theta, T_FIXED);
alphaFixed = new double[2][T_FIXED.length];
tau2Fixed = new double[T_FIXED.length];
for (int loopcf = 0; loopcf < T_FIXED.length; loopcf++) {
alphaFixed[loopcf][0] = Math.sqrt(gamma[0][0]) * hthetaFixed[0][loopcf];
alphaFixed[loopcf][1] = Math.sqrt(gamma[1][1]) * hthetaFixed[1][loopcf];
tau2Fixed[loopcf] =
alphaFixed[loopcf][0] * alphaFixed[loopcf][0]
+ alphaFixed[loopcf][1] * alphaFixed[loopcf][1]
+ 2 * rhog2pp * gamma[0][1] * hthetaFixed[0][loopcf] * hthetaFixed[1][loopcf];
}
final double[][] hthetaIbor =
MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, theta, T_IBOR);
for (int loopcf = 0; loopcf < T_IBOR.length; loopcf++) {
alphaIbor[loopcf][0] = Math.sqrt(gamma[0][0]) * hthetaIbor[0][loopcf];
alphaIbor[loopcf][1] = Math.sqrt(gamma[1][1]) * hthetaIbor[1][loopcf];
tau2Ibor[loopcf] =
alphaIbor[loopcf][0] * alphaIbor[loopcf][0]
+ alphaIbor[loopcf][1] * alphaIbor[loopcf][1]
+ 2 * rhog2pp * gamma[0][1] * hthetaIbor[0][loopcf] * hthetaIbor[1][loopcf];
}
// First derivative
final double[][] x = new double[][] {{0.0, 0.0}, {1.0, 0.0}, {0.5, -0.5}};
final double shift = 1.0E-4;
final double[] swapRateD1 = new double[2];
for (final double[] element : x) {
MODEL_G2PP.swapRate(
element, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor, swapRateD1);
for (int loop = 0; loop < 2; loop++) {
final double[] xP = element.clone();
xP[loop] += shift;
final double[] xM = element.clone();
xM[loop] -= shift;
final double swapRateP1 =
MODEL_G2PP.swapRate(
xP, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
final double swapRateM1 =
MODEL_G2PP.swapRate(
xM, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
assertEquals(
"G2++: swap rate", (swapRateP1 - swapRateM1) / (2 * shift), swapRateD1[loop], 1.0E-7);
}
}
// Second derivative
final double[] swapRateD1Expected = new double[2];
final double[][] swapRateD2 = new double[2][2];
for (final double[] element : x) {
MODEL_G2PP.swapRate(
element,
DCF_FIXED,
alphaFixed,
tau2Fixed,
DCF_IBOR,
alphaIbor,
tau2Ibor,
swapRateD1Expected);
MODEL_G2PP.swapRate(
element,
DCF_FIXED,
alphaFixed,
tau2Fixed,
DCF_IBOR,
alphaIbor,
tau2Ibor,
swapRateD1,
swapRateD2);
final double[][] swapRateD2Expected = new double[2][2];
for (int loop1 = 0; loop1 < 2; loop1++) {
for (int loop2 = 0; loop2 < 2; loop2++) {
final double[] xPP = element.clone();
final double[] xMM = element.clone();
final double[] xMP = element.clone();
final double[] xPM = element.clone();
xPP[loop1] += shift;
xPP[loop2] += shift;
xMM[loop1] -= shift;
xMM[loop2] -= shift;
xMP[loop1] -= shift;
xMP[loop2] += shift;
xPM[loop1] += shift;
xPM[loop2] -= shift;
final double swapRatePP =
MODEL_G2PP.swapRate(
xPP, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
final double swapRateMM =
MODEL_G2PP.swapRate(
xMM, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
final double swapRateMP =
MODEL_G2PP.swapRate(
xMP, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
final double swapRatePM =
MODEL_G2PP.swapRate(
xPM, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
swapRateD2Expected[loop1][loop2] =
(swapRatePP + swapRateMM - swapRateMP - swapRatePM) / (4 * shift * shift);
assertEquals(
"G2++: swap rate",
swapRateD2Expected[loop1][loop2],
swapRateD2[loop1][loop2],
1.0E-7);
}
}
ArrayAsserts.assertArrayEquals("G2++: gamma", swapRateD1Expected, swapRateD1, 1.0E-7);
}
}