/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.finitedifference;
import static org.testng.AssertJUnit.assertEquals;
import org.apache.commons.lang.Validate;
import org.testng.annotations.Test;
import com.opengamma.analytics.financial.model.option.pricing.fourier.FFTPricer;
import com.opengamma.analytics.financial.model.option.pricing.fourier.HestonCharacteristicExponent;
import com.opengamma.analytics.financial.model.option.pricing.fourier.MartingaleCharacteristicExponent;
import com.opengamma.analytics.math.cube.Cube;
import com.opengamma.analytics.math.cube.FunctionalDoublesCube;
import com.opengamma.analytics.math.function.Function;
import com.opengamma.analytics.math.interpolation.Interpolator1D;
import com.opengamma.analytics.math.interpolation.Interpolator1DFactory;
import com.opengamma.analytics.math.interpolation.data.Interpolator1DDataBundle;
import com.opengamma.analytics.math.surface.FunctionalDoublesSurface;
import com.opengamma.util.test.TestGroup;
/**
* @deprecated This class tests deprecated functionality
*/
@Deprecated
@Test(groups = TestGroup.UNIT)
public class HestonPDETestCase {
private static BoundaryCondition2D F_LOWER;
private static BoundaryCondition2D F_UPPER;
private static BoundaryCondition2D V_LOWER;
private static BoundaryCondition2D V_UPPER;
private static final double F0 = 0.05;
private static final double V0 = 0.01;
private static final double KAPPA = 0.2;// changed from 0.2
private static final double THETA = 0.07;
private static final double OMEGA = 0.2;
private static final double RHO = -0.50;// changed from -0.5
private static final double STRIKE = 0.06;
private static final double T = 1.0;
private static final double RATE = 0.0;
// private static final ZonedDateTime DATE = DateUtil.getUTCDate(2010, 7, 1);
// private static final OptionDefinition OPTION;
private static final ConvectionDiffusion2DPDEDataBundle DATA;
private static Cube<Double, Double, Double, Double> A;
private static Cube<Double, Double, Double, Double> B;
private static Cube<Double, Double, Double, Double> C;
private static Cube<Double, Double, Double, Double> D;
private static Cube<Double, Double, Double, Double> E;
private static Cube<Double, Double, Double, Double> F;
static {
// final Function<Double, Double> volZeroBoundary = new Function<Double, Double>() {
// @Override
// public Double evaluate(final Double... tx) {
// Validate.isTrue(tx.length == 2);
// double x = tx[1];
// return Math.max(x - STRIKE, 0);
// }
// };
//
// final Function<Double, Double> volInfiniteBoundary = new Function<Double, Double>() {
// @Override
// public Double evaluate(final Double... tx) {
// Validate.isTrue(tx.length == 2);
// double x = tx[1];
// return x;
// }
// };
F_LOWER = new DirichletBoundaryCondition2D(0.0, 0.0); // option worth zero if spot is zero
F_UPPER = new SecondDerivativeBoundaryCondition2D(0.0, 5 * F0); // option price linear in spot for spot -> infinity
V_LOWER = new SecondDerivativeBoundaryCondition2D(0.0, 0.0);
V_UPPER = new SecondDerivativeBoundaryCondition2D(0.0, 5 * V0);
// F_UPPER = new DirichletBoundaryCondition2D(0.0, 5 * F0); // a knock-out barrier
// V_LOWER = new DirichletBoundaryCondition2D(0.0, 0.0);
// V_UPPER = new DirichletBoundaryCondition2D(0.0, 5 * V0);
// TODO these more sophisticated boundary conditions don't work
// V_LOWER = new DirichletBoundaryCondition2D(FunctionalDoublesSurface.from(volZeroBoundary), 0); // TODO should be solving the convection PDE on this boundary
// V_UPPER = new DirichletBoundaryCondition2D(FunctionalDoublesSurface.from(volInfiniteBoundary), 5 * V0); // option the same as underlying for vol -> infinity
final Function<Double, Double> a = new Function<Double, Double>() {
@Override
public Double evaluate(final Double... txy) {
Validate.isTrue(txy.length == 3);
final double x = txy[1];
final double y = txy[2];
return -0.5 * x * x * y;
}
};
A = FunctionalDoublesCube.from(a);
final Function<Double, Double> b = new Function<Double, Double>() {
@Override
public Double evaluate(final Double... txy) {
Validate.isTrue(txy.length == 3);
final double x = txy[1];
return -x * RATE;
}
};
B = FunctionalDoublesCube.from(b);
final Function<Double, Double> c = new Function<Double, Double>() {
@Override
public Double evaluate(final Double... txy) {
Validate.isTrue(txy.length == 3);
return RATE;
}
};
C = FunctionalDoublesCube.from(c);
final Function<Double, Double> d = new Function<Double, Double>() {
@Override
public Double evaluate(final Double... txy) {
Validate.isTrue(txy.length == 3);
final double y = txy[2];
return -0.5 * OMEGA * OMEGA * y;
}
};
D = FunctionalDoublesCube.from(d);
final Function<Double, Double> e = new Function<Double, Double>() {
@Override
public Double evaluate(final Double... txy) {
Validate.isTrue(txy.length == 3);
final double x = txy[1];
final double y = txy[2];
return -x * y * OMEGA * RHO;
}
};
E = FunctionalDoublesCube.from(e);
final Function<Double, Double> f = new Function<Double, Double>() {
@Override
public Double evaluate(final Double... txy) {
Validate.isTrue(txy.length == 3);
final double y = txy[2];
return -KAPPA * (THETA - y);
}
};
F = FunctionalDoublesCube.from(f);
final Function<Double, Double> payoff = new Function<Double, Double>() {
@Override
public Double evaluate(final Double... xy) {
Validate.isTrue(xy.length == 2);
final double x = xy[0];
return Math.max(x - STRIKE, 0);
}
};
DATA = new ConvectionDiffusion2DPDEDataBundle(A, B, C, D, E, F, FunctionalDoublesSurface.from(payoff));
}
public void testCallPrice(final ConvectionDiffusionPDESolver2D solver, final int timeSteps, final int spotSteps, final int volSqrSteps, final boolean print) {
final double deltaX = (F_UPPER.getLevel() - F_LOWER.getLevel()) / spotSteps;
final double deltaY = (V_UPPER.getLevel() - V_LOWER.getLevel()) / volSqrSteps;
final double[][] res = solver.solve(DATA, timeSteps, spotSteps, volSqrSteps, T, F_LOWER, F_UPPER, V_LOWER, V_UPPER);
if (print) {
final int xSteps = res.length - 1;
final int ySteps = res[0].length - 1;
for (int j = 0; j <= ySteps; j++) {
System.out.print("\t" + (V_LOWER.getLevel() + j * deltaY));
}
System.out.print("\n");
for (int i = 0; i <= xSteps; i++) {
System.out.print(F_LOWER.getLevel() + i * deltaX);
for (int j = 0; j <= ySteps; j++) {
System.out.print("\t" + res[i][j]);
}
System.out.print("\n");
}
}
// TODO There is no guarantee that F0 and V0 are grid points (it depends on the chosen step sizes), so we should do a surface interpolation (what fun!)
final double pdfPrice = res[(int) (F0 / deltaX)][(int) (V0 / deltaY)];
// System.out.print("\n");
final FFTPricer pricer = new FFTPricer();
final MartingaleCharacteristicExponent heston = new HestonCharacteristicExponent(KAPPA, THETA, V0, OMEGA, RHO);
final int n = 51;
final double alpha = -0.5;
final double tol = 1e-12;
final double[][] strikeNprice = pricer.price(F0, 1.0, T, true, heston, STRIKE / 2, STRIKE * 2, n, 0.2, alpha, tol);
final int nStrikes = strikeNprice.length;
final double[] k = new double[nStrikes];
final double[] price = new double[nStrikes];
for (int i = 0; i < nStrikes; i++) {
k[i] = strikeNprice[i][0];
price[i] = strikeNprice[i][1];
}
final Interpolator1D interpolator = Interpolator1DFactory.getInterpolator("DoubleQuadratic");
final Interpolator1DDataBundle dataBundle = interpolator.getDataBundleFromSortedArrays(k, price);
final double fftPrice = interpolator.interpolate(dataBundle, STRIKE);
// System.out.println(fftPrice + "\t" + pdfPrice);
assertEquals(fftPrice, pdfPrice, 2e-6);
// for (int i = 0; i < strikeNprice.length; i++) {
// System.out.println(strikeNprice[i][0] + "\t" + strikeNprice[i][1]);
// }
}
}