/**
* Copyright (C) 2009 - 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 java.util.BitSet;
import org.apache.commons.lang.Validate;
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.VolatilityFunctionProvider;
import com.opengamma.analytics.math.FunctionUtils;
import com.opengamma.analytics.math.function.Function1D;
import com.opengamma.analytics.math.matrix.DoubleMatrix1D;
import com.opengamma.analytics.math.matrix.DoubleMatrix2D;
import com.opengamma.analytics.math.minimization.BrentMinimizer1D;
import com.opengamma.analytics.math.minimization.ConjugateDirectionVectorMinimizer;
import com.opengamma.analytics.math.minimization.DoubleRangeLimitTransform;
import com.opengamma.analytics.math.minimization.ParameterLimitsTransform;
import com.opengamma.analytics.math.minimization.ParameterLimitsTransform.LimitType;
import com.opengamma.analytics.math.minimization.ScalarMinimizer;
import com.opengamma.analytics.math.minimization.SingleRangeLimitTransform;
import com.opengamma.analytics.math.minimization.UncoupledParameterTransforms;
import com.opengamma.analytics.math.statistics.leastsquare.LeastSquareResults;
import com.opengamma.analytics.math.statistics.leastsquare.LeastSquareResultsWithTransform;
import com.opengamma.util.CompareUtils;
/**
*
*/
public class SABRConjugateGradientLeastSquareFitter extends LeastSquareSmileFitter {
private static final int N_PARAMETERS = 4;
private static final ParameterLimitsTransform[] TRANSFORMS;
static {
TRANSFORMS = new ParameterLimitsTransform[4];
TRANSFORMS[0] = new SingleRangeLimitTransform(0, LimitType.GREATER_THAN); // alpha > 0
TRANSFORMS[1] = new DoubleRangeLimitTransform(0, 2.0); // 0 <= beta <= 2
TRANSFORMS[2] = new SingleRangeLimitTransform(0, LimitType.GREATER_THAN); // nu > 0
TRANSFORMS[3] = new DoubleRangeLimitTransform(-1.0, 1.0); // -1 <= rho <= 1
}
private final VolatilityFunctionProvider<SABRFormulaData> _formula;
public SABRConjugateGradientLeastSquareFitter(final VolatilityFunctionProvider<SABRFormulaData> formula) {
Validate.notNull(formula, "SABR formula");
_formula = formula;
}
@Override
public LeastSquareResultsWithTransform getFitResult(final EuropeanVanillaOption[] options, final BlackFunctionData[] data, final double[] initialFitParameters, final BitSet fixed) {
throw new UnsupportedOperationException("Cannot calculate SABR parameters using conjugate gradient method without error estimates for the black volatilities");
}
@Override
public LeastSquareResultsWithTransform getFitResult(final EuropeanVanillaOption[] options, final BlackFunctionData[] data, final double[] errors, final double[] initialFitParameters,
final BitSet fixed) {
testData(options, data, errors, initialFitParameters, fixed, N_PARAMETERS);
final int n = options.length;
final double forward = data[0].getForward();
final double maturity = options[0].getTimeToExpiry();
for (int i = 1; i < n; i++) {
Validate.isTrue(CompareUtils.closeEquals(options[i].getTimeToExpiry(), maturity),
"All options must have the same maturity " + maturity + "; have one with maturity " + options[i].getTimeToExpiry());
}
final UncoupledParameterTransforms transforms = new UncoupledParameterTransforms(new DoubleMatrix1D(initialFitParameters), TRANSFORMS, fixed);
final Function1D<DoubleMatrix1D, Double> function = new Function1D<DoubleMatrix1D, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final DoubleMatrix1D fp) {
final DoubleMatrix1D mp = transforms.inverseTransform(fp);
final double alpha = mp.getEntry(0);
final double beta = mp.getEntry(1);
final double nu = mp.getEntry(2);
final double rho = mp.getEntry(3);
double chiSqr = 0;
final SABRFormulaData sabrFormulaData = new SABRFormulaData(alpha, beta, rho, nu);
for (int i = 0; i < n; i++) {
chiSqr += FunctionUtils.square((data[i].getBlackVolatility() - _formula.getVolatilityFunction(options[i], forward).evaluate(sabrFormulaData)) / errors[i]);
}
return chiSqr;
}
};
final ScalarMinimizer lineMinimizer = new BrentMinimizer1D();
final ConjugateDirectionVectorMinimizer minimzer = new ConjugateDirectionVectorMinimizer(lineMinimizer, 1e-6, 10000);
final DoubleMatrix1D fp = transforms.transform(new DoubleMatrix1D(initialFitParameters));
final DoubleMatrix1D minPos = minimzer.minimize(function, fp);
final double chiSquare = function.evaluate(minPos);
final DoubleMatrix1D res = transforms.inverseTransform(minPos);
return new LeastSquareResultsWithTransform(new LeastSquareResults(chiSquare, res, new DoubleMatrix2D(new double[N_PARAMETERS][N_PARAMETERS])), transforms);
// return new LeastSquareResults(chiSquare, res, new DoubleMatrix2D(new double[N_PARAMETERS][N_PARAMETERS]));
}
//TODO add method that recovers ATM vol
}