/**
* Copyright (C) 2011 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.interestrate;
import static org.testng.AssertJUnit.assertEquals;
import static org.testng.internal.junit.ArrayAsserts.assertArrayEquals;
import org.testng.annotations.Test;
import org.testng.internal.junit.ArrayAsserts;
import com.opengamma.analytics.financial.model.interestrate.definition.G2ppPiecewiseConstantParameters;
import com.opengamma.analytics.financial.model.interestrate.definition.HullWhiteOneFactorPiecewiseConstantParameters;
import com.opengamma.util.tuple.Pair;
/**
* Tests related to the construction of the G2++ model with piecewise constant volatility. The computation of several model related factors are also tested.
*/
public class G2ppPiecewiseConstantModelTest {
private static final double[] MEAN_REVERSION = new double[] {0.01, 0.30 };
private static final double[][] VOLATILITY = new double[][] { {0.01, 0.011, 0.012, 0.013, 0.014 }, {0.01, 0.009, 0.008, 0.007, 0.006 } };
private static final double[] VOLATILITY_TIME = new double[] {0.5, 1.0, 2.0, 5.0 };
private static final double CORRELATION = -0.50;
private static final G2ppPiecewiseConstantParameters MODEL_PARAMETERS = new G2ppPiecewiseConstantParameters(MEAN_REVERSION, VOLATILITY, VOLATILITY_TIME, CORRELATION);
private static final G2ppPiecewiseConstantModel MODEL_G2PP = new G2ppPiecewiseConstantModel();
private static final HullWhiteOneFactorPiecewiseConstantInterestRateModel MODEL_HW = new HullWhiteOneFactorPiecewiseConstantInterestRateModel();
private static final double[] DCF_FIXED = new double[] {1.0, 1.0 };
private static final double[] T_FIXED = new double[] {3.0, 4.0 };
private static final double[] DCF_IBOR = new double[] {1.001, 0.001, 0.001, 0.001, -1.0 };
private static final double[] T_IBOR = new double[] {2.0, 2.5, 3.0, 3.5, 4.0 };
private static final double TOLERANCE_FACTOR = 1.0E-6;
private static final double TOLERANCE_RATE_DELTA = 1.0E-8;
private static final double TOLERANCE_RATE_DELTA2 = 1.0E-7;
@Test
/**
* Tests the class getters.
*/
public void getter() {
assertArrayEquals(MEAN_REVERSION, MODEL_PARAMETERS.getMeanReversion(), 1e-10);
assertEquals(CORRELATION, MODEL_PARAMETERS.getCorrelation());
for (int loopperiod = 0; loopperiod < VOLATILITY[0].length; loopperiod++) {
assertEquals(VOLATILITY[0][loopperiod], MODEL_PARAMETERS.getVolatility()[0].get(loopperiod));
assertEquals(VOLATILITY[1][loopperiod], MODEL_PARAMETERS.getVolatility()[1].get(loopperiod));
}
final double[] volTime = MODEL_PARAMETERS.getVolatilityTime();
for (int loopperiod = 0; loopperiod < VOLATILITY_TIME.length; loopperiod++) {
assertEquals(VOLATILITY_TIME[loopperiod], volTime[loopperiod + 1]);
}
}
@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
/**
* 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
/**
* Tests the volatilityMaturityPart method for arrays.
*/
public void volatilityMaturityPartArray() {
final double u = 0.75;
final double[][] v = new double[][] { {2.0, 4.0, 7.0 }, {5.0, 3.0 } };
final double[][][] h = MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, u, v);
final double[][] h0 = MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, u, v[0]);
final double[][] h1 = MODEL_G2PP.volatilityMaturityPart(MODEL_PARAMETERS, u, v[1]);
for (int loop = 0; loop < v[0].length; loop++) {
assertEquals("G2++: maturity dependent volatility part", h[0][0][loop], h0[0][loop], 1.0E-7);
assertEquals("G2++: maturity dependent volatility part", h[1][0][loop], h0[1][loop], 1.0E-7);
}
for (int loop = 0; loop < v[1].length; loop++) {
assertEquals("G2++: maturity dependent volatility part", h[0][1][loop], h1[0][loop], 1.0E-7);
assertEquals("G2++: maturity dependent volatility part", h[1][1][loop], h1[1][loop], 1.0E-7);
}
}
@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);
}
@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);
}
}
@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(enabled = true)
public void swapRateDx2Ddcf() {
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-7;
final double[] x = {0.0, 0.1 };
final Pair<double[][][], double[][][]> dx2ddcfComputed = MODEL_G2PP.swapRateDdcfDx2(x, DCF_FIXED, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor);
final double[][][] dx2DdcffExpected = new double[DCF_FIXED.length][2][2];
for (int loopcf = 0; loopcf < DCF_FIXED.length; loopcf++) {
final double[] dsf_bumped = DCF_FIXED.clone();
dsf_bumped[loopcf] += shift;
final double[] d1Plus = new double[2];
final double[][] d2Plus = new double[2][2];
MODEL_G2PP.swapRate(x, dsf_bumped, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor, d1Plus, d2Plus);
dsf_bumped[loopcf] -= 2 * shift;
final double[] d1Minus = new double[2];
final double[][] d2Minus = new double[2][2];
MODEL_G2PP.swapRate(x, dsf_bumped, alphaFixed, tau2Fixed, DCF_IBOR, alphaIbor, tau2Ibor, d1Minus, d2Minus);
for (int loopd1 = 0; loopd1 < 2; loopd1++) {
for (int loopd2 = loopd1; loopd2 < 2; loopd2++) {
dx2DdcffExpected[loopcf][loopd1][loopd2] = (d2Plus[loopd1][loopd2] - d2Minus[loopd1][loopd2]) / (2 * shift);
assertEquals("Hull-White model: swap rate", dx2DdcffExpected[loopcf][loopd1][loopd2], dx2ddcfComputed.getFirst()[loopcf][loopd1][loopd2], TOLERANCE_RATE_DELTA2);
}
}
}
final double[][][] dx2DdcfiExpected = new double[DCF_IBOR.length][2][2];
for (int loopcf = 0; loopcf < DCF_IBOR.length; loopcf++) {
final double[] dsf_bumped = DCF_IBOR.clone();
dsf_bumped[loopcf] += shift;
final double[] d1Plus = new double[2];
final double[][] d2Plus = new double[2][2];
MODEL_G2PP.swapRate(x, DCF_FIXED, alphaFixed, tau2Fixed, dsf_bumped, alphaIbor, tau2Ibor, d1Plus, d2Plus);
dsf_bumped[loopcf] -= 2 * shift;
final double[] d1Minus = new double[2];
final double[][] d2Minus = new double[2][2];
MODEL_G2PP.swapRate(x, DCF_FIXED, alphaFixed, tau2Fixed, dsf_bumped, alphaIbor, tau2Ibor, d1Minus, d2Minus);
for (int loopd1 = 0; loopd1 < 2; loopd1++) {
for (int loopd2 = loopd1; loopd2 < 2; loopd2++) {
dx2DdcfiExpected[loopcf][loopd1][loopd2] = (d2Plus[loopd1][loopd2] - d2Minus[loopd1][loopd2]) / (2 * shift);
assertEquals("Hull-White model: swap rate", dx2DdcfiExpected[loopcf][loopd1][loopd2], dx2ddcfComputed.getSecond()[loopcf][loopd1][loopd2], TOLERANCE_RATE_DELTA2);
}
}
}
}
@Test
public void futuresConvexityFactor() {
// Compare with Hull-White one-factor
final double[] volTime = new double[0];
final double[][] vol10 = new double[][] { {0.01 }, {0.00 } };
final double[][] vol01 = new double[][] { {0.00 }, {0.01 } };
final double expiryTime = 1.0;
final double u = 1.02;
final double v = 1.27;
final HullWhiteOneFactorPiecewiseConstantParameters hw10 = new HullWhiteOneFactorPiecewiseConstantParameters(MEAN_REVERSION[0], vol10[0], volTime);
final G2ppPiecewiseConstantParameters g2pp10 = new G2ppPiecewiseConstantParameters(MEAN_REVERSION, vol10, volTime, CORRELATION);
final double adjHW10 = MODEL_HW.futuresConvexityFactor(hw10, expiryTime, u, v);
final double adjG210 = MODEL_G2PP.futuresConvexityFactor(g2pp10, expiryTime, u, v);
assertEquals("G2++: swap rate", adjHW10, adjG210, TOLERANCE_FACTOR);
final HullWhiteOneFactorPiecewiseConstantParameters hw01 = new HullWhiteOneFactorPiecewiseConstantParameters(MEAN_REVERSION[1], vol01[1], volTime);
final G2ppPiecewiseConstantParameters g2pp01 = new G2ppPiecewiseConstantParameters(MEAN_REVERSION, vol01, volTime, CORRELATION);
final double adjHW01 = MODEL_HW.futuresConvexityFactor(hw01, expiryTime, u, v);
final double adjG201 = MODEL_G2PP.futuresConvexityFactor(g2pp01, expiryTime, u, v);
assertEquals("G2++: swap rate", adjHW01, adjG201, TOLERANCE_FACTOR);
// TODO: full two-factor test
}
}