/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.option.pricing.fourier;
import static org.testng.AssertJUnit.assertEquals;
import static org.testng.AssertJUnit.assertTrue;
import org.testng.annotations.Test;
import com.opengamma.analytics.math.number.ComplexNumber;
/**
*
*/
public class TimeChangeTest {
private static final double FORWARD = 1.0;
private static final double T = 3.0;
private static final double DF = 0.93;
private static final double SIGMA = 0.2;
private static final double KAPPA = 0.7; // mean reversion speed
private static final double THETA = SIGMA * SIGMA; // reversion level
private static final double VOL0 = THETA; // start level
private static final double OMEGA = 0.2; // vol-of-vol
private static final double RH0 = -0.0; // correlation
private static double ALPHA = -0.5;
private static final double MAX_LOG_MONEYNESS = 0.1;
private static final double EPS = 1e-6;
private static final MartingaleCharacteristicExponent HESTON = new HestonCharacteristicExponent(KAPPA, THETA, VOL0, OMEGA, RH0);
private static final StocasticClockCharcteristicExponent CIR = new IntegratedCIRTimeChangeCharacteristicExponent(KAPPA, THETA / VOL0, OMEGA / Math.sqrt(VOL0));
private static final MartingaleCharacteristicExponent NORMAL = new GaussianMartingaleCharacteristicExponent(Math.sqrt(VOL0));
private static final CharacteristicExponent NORMAL_CIR = new TimeChangedCharacteristicExponent(NORMAL, CIR);
private static final FFTPricer FFT_PRICER = new FFTPricer();
@Test
public void testAgainstHeston() {
final int n = 21;
final double[][] heston_strikeNprice = FFT_PRICER.price(FORWARD, DF, T, true, HESTON, n, MAX_LOG_MONEYNESS, SIGMA, ALPHA, 0.01 * EPS);
final double[][] normalCIR_strikeNprice = FFT_PRICER.price(FORWARD, DF, T, true, HESTON, n, MAX_LOG_MONEYNESS, SIGMA, ALPHA, 0.01 * EPS);
for (int i = 0; i < n; i++) {
assertEquals(heston_strikeNprice[i][0], normalCIR_strikeNprice[i][0], 1e-12);//should have the same strikes
assertEquals(heston_strikeNprice[i][1], normalCIR_strikeNprice[i][1], 1e-12);//should have the same price
}
}
@Test
public void testCE() {
for (int i = 0; i < 101; i++) {
final double x = 10.0 * i / 100.0;
final ComplexNumber z = new ComplexNumber(x, -(1 + ALPHA));
final ComplexNumber res1 = NORMAL_CIR.getFunction(T).evaluate(z);
final ComplexNumber res2 = NORMAL.getFunction(1).evaluate(z);
final ComplexNumber res3 = HESTON.getFunction(T).evaluate(z);
assertTrue(Math.abs(res1.getImaginary()) < EPS);
assertTrue(Math.abs(res2.getImaginary()) < EPS);
assertTrue(Math.abs(res3.getImaginary()) < EPS);
assertEquals(res1.getReal(), res3.getReal(), EPS);
}
}
}