/**
* Copyright (C) 2011 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.financial.model.volatility.smile.fitting;
import static org.testng.AssertJUnit.assertEquals;
import static org.testng.AssertJUnit.assertTrue;
import java.util.Arrays;
import java.util.BitSet;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import org.testng.annotations.Test;
import cern.jet.random.engine.MersenneTwister;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.BlackFunctionData;
import com.opengamma.analytics.financial.model.option.pricing.analytic.formula.EuropeanVanillaOption;
import com.opengamma.analytics.financial.model.volatility.smile.function.SABRFormulaData;
import com.opengamma.analytics.financial.model.volatility.smile.function.SABRHaganVolatilityFunction;
import com.opengamma.analytics.financial.model.volatility.smile.function.VolatilityFunctionProvider;
import com.opengamma.analytics.math.matrix.DoubleMatrix1D;
import com.opengamma.analytics.math.statistics.distribution.NormalDistribution;
import com.opengamma.analytics.math.statistics.distribution.ProbabilityDistribution;
import com.opengamma.analytics.math.statistics.leastsquare.LeastSquareResultsWithTransform;
import com.opengamma.util.monitor.OperationTimer;
import com.opengamma.util.test.TestGroup;
/**
* Test.
*/
@Test(groups = TestGroup.UNIT)
public class SABRModelFitterTest {
protected Logger _logger = LoggerFactory.getLogger(SABRModelFitterTest.class);
protected int _hotspotWarmupCycles = 0;
protected int _benchmarkCycles = 1;
private static final double F = 0.03;
private static final double T = 7.0;
private static final double ALPHA = 0.05;
private static final double BETA = 0.5;
private static double RHO = -0.3;
private static double NU = 0.2;
private static final EuropeanOptionMarketData[] MARKETDATA;
private static final EuropeanOptionMarketData[] NOISY_MARKETDATA;
private static double[] STRIKES;
private static double[] CLEAN_VOLS;
private static double[] NOISY_VOLS;
private static double[] ERRORS;
private static final SABRFormulaData SABR_DATA = new SABRFormulaData(ALPHA, BETA, RHO, NU);
private static VolatilityFunctionProvider<SABRFormulaData> SABR = new SABRHaganVolatilityFunction();
private static ProbabilityDistribution<Double> RANDOM = new NormalDistribution(0, 1, new MersenneTwister(12));
private static SmileModelFitter<SABRFormulaData> FITTER;
private static SmileModelFitter<SABRFormulaData> NOISY_FITTER;
static {
STRIKES = new double[] {0.005, 0.01, 0.02, 0.03, 0.04, 0.05, 0.07 };
final int n = STRIKES.length;
MARKETDATA = new EuropeanOptionMarketData[n];
NOISY_MARKETDATA = new EuropeanOptionMarketData[n];
CLEAN_VOLS = new double[n];
NOISY_VOLS = new double[n];
ERRORS = new double[n];
Arrays.fill(ERRORS, 0.0001); // 1bps error
for (int i = 0; i < n; i++) {
final EuropeanVanillaOption option = new EuropeanVanillaOption(STRIKES[i], T, true);
CLEAN_VOLS[i] = SABR.getVolatilityFunction(option, F).evaluate(SABR_DATA);
NOISY_VOLS[i] = CLEAN_VOLS[i] + RANDOM.nextRandom() * ERRORS[i];
}
FITTER = new SABRModelFitter(F, STRIKES, T, CLEAN_VOLS, ERRORS, SABR);
NOISY_FITTER = new SABRModelFitter(F, STRIKES, T, NOISY_VOLS, ERRORS, SABR);
}
@Test
public void testExactFit() {
final double[] start = new double[] {0.1, 0.7, 0.0, 0.3 };
final LeastSquareResultsWithTransform results = FITTER.solve(new DoubleMatrix1D(start));
final double[] res = results.getModelParameters().getData();
final double eps = 1e-6;
assertEquals(ALPHA, res[0], eps);
assertEquals(BETA, res[1], eps);
assertEquals(RHO, res[2], eps);
assertEquals(NU, res[3], eps);
assertEquals(0.0, results.getChiSq(), eps);
}
@Test
public void testExactFitOddStart() {
final double[] start = new double[] {0.01, 0.99, 0.9, 0.4 };
final LeastSquareResultsWithTransform results = FITTER.solve(new DoubleMatrix1D(start));
final double[] res = results.getModelParameters().getData();
final double eps = 1e-6;
assertEquals(ALPHA, res[0], eps);
assertEquals(BETA, res[1], eps);
assertEquals(RHO, res[2], eps);
assertEquals(NU, res[3], eps);
assertEquals(0.0, results.getChiSq(), eps);
}
@Test
public void testExactFitWithFixedBeta() {
final double[] start = new double[] {0.1, 0.5, 0.0, 0.3 };
final BitSet fixed = new BitSet();
fixed.set(1);
final LeastSquareResultsWithTransform results = FITTER.solve(new DoubleMatrix1D(start), fixed);
final double[] res = results.getModelParameters().getData();
final double eps = 1e-6;
assertEquals(ALPHA, res[0], eps);
assertEquals(BETA, res[1], eps);
assertEquals(RHO, res[2], eps);
assertEquals(NU, res[3], eps);
assertEquals(0.0, results.getChiSq(), eps);
}
@Test
public void testFitWithFixedWrongBeta() {
final double[] start = new double[] {0.1, 0.8, 0.0, 0.3 };
final BitSet fixed = new BitSet();
fixed.set(1);
final LeastSquareResultsWithTransform results = FITTER.solve(new DoubleMatrix1D(start), fixed);
final double[] res = results.getModelParameters().getData();
final double eps = 1e-6;
assertEquals(0.8, res[1], eps);
final double bpError = 35.0; // 35 bps error
final int n = MARKETDATA.length;
final double exChi2 = bpError * bpError * n;
assertTrue("chi^2 " + results.getChiSq(), results.getChiSq() < exChi2);
}
@Test
public void testNoisyFit() {
final double[] start = new double[] {0.1, 0.7, 0.0, 0.3 };
final LeastSquareResultsWithTransform results = NOISY_FITTER.solve(new DoubleMatrix1D(start));
final double[] res = results.getModelParameters().getData();
final double eps = 1e-2;
assertEquals(ALPHA, res[0], eps);
assertEquals(BETA, res[1], eps);
assertEquals(RHO, res[2], eps);
assertEquals(NU, res[3], eps);
assertTrue(results.getChiSq() < 7);
}
// SABRModelFitterTest - 813ms-processing 1000 cycles fitting SABR smile
// Disable test before commit
@Test(enabled = false)
public void fitTimeTest() {
final int hotspotWarmupCycles = 200;
final int benchmarkCycles = 1000;
for (int i = 0; i < hotspotWarmupCycles; i++) {
testNoisyFit();
}
if (benchmarkCycles > 0) {
final OperationTimer timer = new OperationTimer(_logger, "processing {} cycles fitting SABR smile", benchmarkCycles);
for (int i = 0; i < benchmarkCycles; i++) {
testNoisyFit();
}
timer.finished();
}
}
// SABRModelFitterTest - 1555ms-processing 1000 cycles fitting SABR smile - old
@SuppressWarnings("deprecation")
@Test
public void testOldMethod() {
// set to 1 and 0 before commit
final int hotspotWarmupCycles = 1;
final int benchmarkCycles = 0;
final double[] start = new double[] {0.1, 0.7, 0.0, 0.3 };
final BitSet fixed = new BitSet();
final SABRNonLinearLeastSquareFitter fitter = new SABRNonLinearLeastSquareFitter(SABR);
final int n = NOISY_MARKETDATA.length;
final EuropeanVanillaOption[] options = new EuropeanVanillaOption[n];
final BlackFunctionData[] data = new BlackFunctionData[n];
for (int i = 0; i < n; i++) {
options[i] = new EuropeanVanillaOption(STRIKES[i], T, true);
data[i] = new BlackFunctionData(F, 1.0, CLEAN_VOLS[i]);
}
for (int i = 0; i < hotspotWarmupCycles; i++) {
doOldTest(options, data, start, fixed, fitter);
}
if (benchmarkCycles > 0) {
final OperationTimer timer = new OperationTimer(_logger, "processing {} cycles fitting SABR smile - old", benchmarkCycles);
for (int i = 0; i < benchmarkCycles; i++) {
doOldTest(options, data, start, fixed, fitter);
}
timer.finished();
}
}
@SuppressWarnings("deprecation")
private void doOldTest(final EuropeanVanillaOption[] options, final BlackFunctionData[] data, final double[] start, final BitSet fixed, final SABRNonLinearLeastSquareFitter fitter) {
final LeastSquareResultsWithTransform lsRes = fitter.getFitResult(options, data, ERRORS, start, fixed);
final double[] res = lsRes.getModelParameters().getData();
final double eps = 1e-2;
assertEquals(ALPHA, res[0], eps);
assertEquals(BETA, res[1], eps);
assertEquals(RHO, res[2], eps);
assertEquals(NU, res[3], eps);
assertTrue(lsRes.getChiSq() < 7);
}
}