Java tutorial
/** * Copyright (C) 2011 - present by OpenGamma Inc. and the OpenGamma group of companies * * Please see distribution for license. */ package com.opengamma.analytics.financial.interestrate.future.provider; import java.util.ArrayList; import java.util.HashMap; import java.util.List; import java.util.Map; import org.apache.commons.lang.Validate; import com.opengamma.analytics.financial.interestrate.annuity.derivative.AnnuityPaymentFixed; import com.opengamma.analytics.financial.interestrate.future.derivative.BondFuture; import com.opengamma.analytics.financial.model.interestrate.HullWhiteOneFactorPiecewiseConstantInterestRateModel; import com.opengamma.analytics.financial.model.interestrate.definition.HullWhiteOneFactorPiecewiseConstantParameters; import com.opengamma.analytics.financial.provider.calculator.discounting.CashFlowEquivalentCalculator; import com.opengamma.analytics.financial.provider.description.interestrate.HullWhiteIssuerProviderInterface; import com.opengamma.analytics.financial.provider.description.interestrate.IssuerProviderInterface; import com.opengamma.analytics.financial.provider.description.interestrate.MulticurveProviderDiscountingDecoratedIssuer; import com.opengamma.analytics.financial.provider.description.interestrate.MulticurveProviderInterface; import com.opengamma.analytics.financial.provider.sensitivity.multicurve.MulticurveSensitivity; import com.opengamma.analytics.financial.provider.sensitivity.multicurve.MultipleCurrencyMulticurveSensitivity; import com.opengamma.analytics.math.function.Function1D; import com.opengamma.analytics.math.rootfinding.BracketRoot; import com.opengamma.analytics.math.rootfinding.RidderSingleRootFinder; import com.opengamma.analytics.math.statistics.distribution.NormalDistribution; import com.opengamma.analytics.math.statistics.distribution.ProbabilityDistribution; import com.opengamma.util.ArgumentChecker; import com.opengamma.util.money.Currency; import com.opengamma.util.money.MultipleCurrencyAmount; import com.opengamma.util.tuple.DoublesPair; import com.opengamma.util.tuple.Pair; /** * Method to compute the price of bond future using the Hull-White one factor model to estimate the delivery option. * <P> Reference: Henrard, M. Bonds futures and their options: more than the cheapest-to-deliver; quality option and margining. Journal of Fixed Income, 2006, 16, 62-75 */ public final class BondFutureHullWhiteMethod extends BondFutureMethod { /** * Creates the method unique instance. */ private static final BondFutureHullWhiteMethod INSTANCE = new BondFutureHullWhiteMethod(); /** * Constructor. */ private BondFutureHullWhiteMethod() { } /** * Return the method unique instance. * @return The instance. */ public static BondFutureHullWhiteMethod getInstance() { return INSTANCE; } /** * The number of points used in the numerical integration process. */ private static final int DEFAULT_NB_POINTS = 81; /** * The normal distribution implementation. */ private static final ProbabilityDistribution<Double> NORMAL = new NormalDistribution(0, 1); /** * The cash flow equivalent calculator used in computations. */ private static final CashFlowEquivalentCalculator CFEC = CashFlowEquivalentCalculator.getInstance(); /** * The model used in computations. */ private static final HullWhiteOneFactorPiecewiseConstantInterestRateModel MODEL = new HullWhiteOneFactorPiecewiseConstantInterestRateModel(); /** * Computes the future price from the curves used to price the underlying bonds and a Hull-White one factor model. * @param future The future security. * @param data The curve and Hull-White parameters. * @param nbPoint The number of point in the numerical cross estimation. * @return The future price. */ public double price(final BondFuture future, final HullWhiteIssuerProviderInterface data, final int nbPoint) { ArgumentChecker.notNull(future, "Future"); ArgumentChecker.notNull(data, "Hull-White data bundle"); final Pair<String, Currency> issuerCcy = future.getDeliveryBasket()[0].getIssuerCcy(); ArgumentChecker.isTrue(data.getHullWhiteIssuerCurrency().equals(issuerCcy), "Incompatible data and futures"); final int nbBond = future.getDeliveryBasket().length; final String issuerName = future.getDeliveryBasket()[0].getIssuer(); final HullWhiteOneFactorPiecewiseConstantParameters parameters = data.getHullWhiteParameters(); final IssuerProviderInterface issuer = data.getIssuerProvider(); final MulticurveProviderInterface multicurvesDecorated = new MulticurveProviderDiscountingDecoratedIssuer( issuer, future.getCurrency(), issuerName); final double expiry = future.getNoticeLastTime(); final double delivery = future.getDeliveryLastTime(); final double dfdelivery = data.getIssuerProvider().getDiscountFactor(issuerCcy, delivery); // Constructing non-homogeneous point series for the numerical estimations. final int nbPtWing = ((int) Math.floor(nbPoint / 20.)); // Number of point on each wing. final int nbPtCenter = nbPoint - 2 * nbPtWing; final double prob = 1.0 / (2.0 * nbPtCenter); final double xStart = NORMAL.getInverseCDF(prob); final double[] x = new double[nbPoint]; for (int loopwing = 0; loopwing < nbPtWing; loopwing++) { x[loopwing] = xStart * (1.0 + (nbPtWing - loopwing) / 2.0); x[nbPoint - 1 - loopwing] = -xStart * (1.0 + (nbPtWing - loopwing) / 2.0); } for (int loopcent = 0; loopcent < nbPtCenter; loopcent++) { x[nbPtWing + loopcent] = xStart + loopcent * (-2.0 * xStart) / (nbPtCenter - 1); } // Figures for each bond final double[][] cfTime = new double[nbBond][]; final double[][] df = new double[nbBond][]; final double[][] alpha = new double[nbBond][]; final double[][] beta = new double[nbBond][]; final double[][] cfaAdjusted = new double[nbBond][]; final double[] e = new double[nbBond]; final double[][] pv = new double[nbPoint][nbBond]; final AnnuityPaymentFixed[] cf = new AnnuityPaymentFixed[nbBond]; for (int loopbnd = 0; loopbnd < nbBond; loopbnd++) { cf[loopbnd] = future.getDeliveryBasket()[loopbnd].accept(CFEC, multicurvesDecorated); final int nbCf = cf[loopbnd].getNumberOfPayments(); cfTime[loopbnd] = new double[nbCf]; df[loopbnd] = new double[nbCf]; alpha[loopbnd] = new double[nbCf]; beta[loopbnd] = new double[nbCf]; cfaAdjusted[loopbnd] = new double[nbCf]; for (int loopcf = 0; loopcf < nbCf; loopcf++) { cfTime[loopbnd][loopcf] = cf[loopbnd].getNthPayment(loopcf).getPaymentTime(); df[loopbnd][loopcf] = issuer.getDiscountFactor(issuerCcy, cfTime[loopbnd][loopcf]); alpha[loopbnd][loopcf] = MODEL.alpha(parameters, 0.0, expiry, delivery, cfTime[loopbnd][loopcf]); beta[loopbnd][loopcf] = MODEL.futuresConvexityFactor(parameters, expiry, cfTime[loopbnd][loopcf], delivery); cfaAdjusted[loopbnd][loopcf] = df[loopbnd][loopcf] / dfdelivery * beta[loopbnd][loopcf] * cf[loopbnd].getNthPayment(loopcf).getAmount() / future.getConversionFactor()[loopbnd]; for (int looppt = 0; looppt < nbPoint; looppt++) { pv[looppt][loopbnd] += cfaAdjusted[loopbnd][loopcf] * Math.exp(-alpha[loopbnd][loopcf] * alpha[loopbnd][loopcf] / 2.0 - alpha[loopbnd][loopcf] * x[looppt]); } } e[loopbnd] = future.getDeliveryBasket()[loopbnd].getAccruedInterest() / future.getConversionFactor()[loopbnd]; for (int looppt = 0; looppt < nbPoint; looppt++) { pv[looppt][loopbnd] -= e[loopbnd]; } } // Minimum: create a list of index of the CTD in each interval and a first estimate of the crossing point (x[]). final double[] pvMin = new double[nbPoint]; final int[] indMin = new int[nbPoint]; for (int looppt = 0; looppt < nbPoint; looppt++) { pvMin[looppt] = Double.POSITIVE_INFINITY; for (int loopbnd = 0; loopbnd < nbBond; loopbnd++) { if (pv[looppt][loopbnd] < pvMin[looppt]) { pvMin[looppt] = pv[looppt][loopbnd]; indMin[looppt] = loopbnd; } } } final ArrayList<Double> refx = new ArrayList<>(); final ArrayList<Integer> ctd = new ArrayList<>(); int lastInd = indMin[0]; ctd.add(indMin[0]); for (int looppt = 1; looppt < nbPoint; looppt++) { if (indMin[looppt] != lastInd) { ctd.add(indMin[looppt]); lastInd = indMin[looppt]; refx.add(x[looppt]); } } // Sum on each interval final int nbInt = ctd.size(); final double[] kappa = new double[nbInt - 1]; double price = 0.0; if (nbInt == 1) { for (int loopcf = 0; loopcf < cfaAdjusted[ctd.get(0)].length; loopcf++) { price += cfaAdjusted[ctd.get(0)][loopcf]; } price -= e[ctd.get(0)]; } else { // The intersections final BracketRoot bracketer = new BracketRoot(); final double accuracy = 1.0E-8; final RidderSingleRootFinder rootFinder = new RidderSingleRootFinder(accuracy); for (int loopint = 1; loopint < nbInt; loopint++) { final BondDifference cross = new BondDifference(cfaAdjusted[ctd.get(loopint - 1)], alpha[ctd.get(loopint - 1)], e[ctd.get(loopint - 1)], cfaAdjusted[ctd.get(loopint)], alpha[ctd.get(loopint)], e[ctd.get(loopint)]); final double[] range = bracketer.getBracketedPoints(cross, refx.get(loopint - 1) - 0.01, refx.get(loopint - 1) + 0.01); kappa[loopint - 1] = rootFinder.getRoot(cross, range[0], range[1]); } // From -infinity to first cross. for (int loopcf = 0; loopcf < cfaAdjusted[ctd.get(0)].length; loopcf++) { price += cfaAdjusted[ctd.get(0)][loopcf] * NORMAL.getCDF(kappa[0] + alpha[ctd.get(0)][loopcf]); } price -= e[ctd.get(0)] * NORMAL.getCDF(kappa[0]); // Between cross for (int loopint = 1; loopint < nbInt - 1; loopint++) { for (int loopcf = 0; loopcf < cfaAdjusted[ctd.get(loopint)].length; loopcf++) { price += cfaAdjusted[ctd.get(loopint)][loopcf] * (NORMAL.getCDF(kappa[loopint] + alpha[ctd.get(loopint)][loopcf]) - NORMAL.getCDF(kappa[loopint - 1] + alpha[ctd.get(loopint)][loopcf])); } price -= e[ctd.get(loopint)] * (NORMAL.getCDF(kappa[loopint]) - NORMAL.getCDF(kappa[loopint - 1])); } // From last cross to +infinity for (int loopcf = 0; loopcf < cfaAdjusted[ctd.get(nbInt - 1)].length; loopcf++) { price += cfaAdjusted[ctd.get(nbInt - 1)][loopcf] * (1.0 - NORMAL.getCDF(kappa[nbInt - 2] + alpha[ctd.get(nbInt - 1)][loopcf])); } price -= e[ctd.get(nbInt - 1)] * (1 - NORMAL.getCDF(kappa[nbInt - 2])); } return price; } /** * Computes the future price from the curves used to price the underlying bonds and a Hull-White one factor model. The default number of points is used for the numerical search. * @param future The future security. * @param data The curve and Hull-White parameters. * @return The future price. */ public double price(final BondFuture future, final HullWhiteIssuerProviderInterface data) { return price(future, data, DEFAULT_NB_POINTS); } /** * Computes the present value of future from the curves using the cheapest-to-deliver and computing the value as a forward. * @param future The future. * @param data The curve and Hull-White parameters. * @return The present value. */ public MultipleCurrencyAmount presentValue(final BondFuture future, final HullWhiteIssuerProviderInterface data) { final double futurePrice = price(future, data); return presentValueFromPrice(future, futurePrice); } /** * Computes the future price curve sensitivity. * @param future The future security. * @param data The curve and Hull-White parameters. * @param nbPoint The number of point in the numerical cross estimation. * @return The curve sensitivity. */ public MulticurveSensitivity priceCurveSensitivity(final BondFuture future, final HullWhiteIssuerProviderInterface data, final int nbPoint) { ArgumentChecker.notNull(future, "Future"); ArgumentChecker.notNull(data, "Hull-White data bundle"); final Currency ccy = future.getCurrency(); final Pair<String, Currency> issuerCcy = future.getDeliveryBasket()[0].getIssuerCcy(); ArgumentChecker.isTrue(data.getHullWhiteIssuerCurrency().equals(issuerCcy), "Incompatible data and futures"); final int nbBond = future.getDeliveryBasket().length; final String issuerName = future.getDeliveryBasket()[0].getIssuer(); final HullWhiteOneFactorPiecewiseConstantParameters parameters = data.getHullWhiteParameters(); final IssuerProviderInterface issuer = data.getIssuerProvider(); final MulticurveProviderInterface multicurvesDecorated = new MulticurveProviderDiscountingDecoratedIssuer( issuer, future.getCurrency(), issuerName); final double expiry = future.getNoticeLastTime(); final double delivery = future.getDeliveryLastTime(); final double dfdelivery = data.getIssuerProvider().getDiscountFactor(issuerCcy, delivery); // Constructing non-homogeneous point series for the numerical estimations. final int nbPtWing = ((int) Math.floor(nbPoint / 20.)); // Number of point on each wing. final int nbPtCenter = nbPoint - 2 * nbPtWing; final double prob = 1.0 / (2.0 * nbPtCenter); final double xStart = NORMAL.getInverseCDF(prob); final double[] x = new double[nbPoint]; for (int loopwing = 0; loopwing < nbPtWing; loopwing++) { x[loopwing] = xStart * (1.0 + (nbPtWing - loopwing) / 2.0); x[nbPoint - 1 - loopwing] = -xStart * (1.0 + (nbPtWing - loopwing) / 2.0); } for (int loopcent = 0; loopcent < nbPtCenter; loopcent++) { x[nbPtWing + loopcent] = xStart + loopcent * (-2.0 * xStart) / (nbPtCenter - 1); } // Figures for each bond final double[][] cfTime = new double[nbBond][]; final double[][] df = new double[nbBond][]; final double[][] alpha = new double[nbBond][]; final double[][] beta = new double[nbBond][]; final double[][] cfaAdjusted = new double[nbBond][]; final double[] e = new double[nbBond]; final double[][] pv = new double[nbPoint][nbBond]; final AnnuityPaymentFixed[] cf = new AnnuityPaymentFixed[nbBond]; for (int loopbnd = 0; loopbnd < nbBond; loopbnd++) { cf[loopbnd] = future.getDeliveryBasket()[loopbnd].accept(CFEC, multicurvesDecorated); final int nbCf = cf[loopbnd].getNumberOfPayments(); cfTime[loopbnd] = new double[nbCf]; df[loopbnd] = new double[nbCf]; alpha[loopbnd] = new double[nbCf]; beta[loopbnd] = new double[nbCf]; cfaAdjusted[loopbnd] = new double[nbCf]; for (int loopcf = 0; loopcf < nbCf; loopcf++) { cfTime[loopbnd][loopcf] = cf[loopbnd].getNthPayment(loopcf).getPaymentTime(); df[loopbnd][loopcf] = issuer.getDiscountFactor(issuerCcy, cfTime[loopbnd][loopcf]); alpha[loopbnd][loopcf] = MODEL.alpha(parameters, 0.0, expiry, delivery, cfTime[loopbnd][loopcf]); beta[loopbnd][loopcf] = MODEL.futuresConvexityFactor(parameters, expiry, cfTime[loopbnd][loopcf], delivery); cfaAdjusted[loopbnd][loopcf] = df[loopbnd][loopcf] / dfdelivery * beta[loopbnd][loopcf] * cf[loopbnd].getNthPayment(loopcf).getAmount() / future.getConversionFactor()[loopbnd]; for (int looppt = 0; looppt < nbPoint; looppt++) { pv[looppt][loopbnd] += cfaAdjusted[loopbnd][loopcf] * Math.exp(-alpha[loopbnd][loopcf] * alpha[loopbnd][loopcf] / 2.0 - alpha[loopbnd][loopcf] * x[looppt]); } } e[loopbnd] = future.getDeliveryBasket()[loopbnd].getAccruedInterest() / future.getConversionFactor()[loopbnd]; for (int looppt = 0; looppt < nbPoint; looppt++) { pv[looppt][loopbnd] -= e[loopbnd]; } } // Minimum: create a list of index of the CTD in each interval and a first estimate of the crossing point (x[]). final double[] pvMin = new double[nbPoint]; final int[] indMin = new int[nbPoint]; for (int looppt = 0; looppt < nbPoint; looppt++) { pvMin[looppt] = Double.POSITIVE_INFINITY; for (int loopbnd = 0; loopbnd < nbBond; loopbnd++) { if (pv[looppt][loopbnd] < pvMin[looppt]) { pvMin[looppt] = pv[looppt][loopbnd]; indMin[looppt] = loopbnd; } } } final ArrayList<Double> refx = new ArrayList<>(); final ArrayList<Integer> ctd = new ArrayList<>(); int lastInd = indMin[0]; ctd.add(indMin[0]); for (int looppt = 1; looppt < nbPoint; looppt++) { if (indMin[looppt] != lastInd) { ctd.add(indMin[looppt]); lastInd = indMin[looppt]; refx.add(x[looppt]); } } // Sum on each interval final int nbInt = ctd.size(); final double[] kappa = new double[nbInt - 1]; // double price = 0.0; if (nbInt != 1) { // The intersections final BracketRoot bracketer = new BracketRoot(); final double accuracy = 1.0E-8; final RidderSingleRootFinder rootFinder = new RidderSingleRootFinder(accuracy); for (int loopint = 1; loopint < nbInt; loopint++) { final BondDifference cross = new BondDifference(cfaAdjusted[ctd.get(loopint - 1)], alpha[ctd.get(loopint - 1)], e[ctd.get(loopint - 1)], cfaAdjusted[ctd.get(loopint)], alpha[ctd.get(loopint)], e[ctd.get(loopint)]); final double[] range = bracketer.getBracketedPoints(cross, refx.get(loopint - 1) - 0.01, refx.get(loopint - 1) + 0.01); kappa[loopint - 1] = rootFinder.getRoot(cross, range[0], range[1]); } } // === Backward Sweep === final double priceBar = 1.0; final double[][] cfaAdjustedBar = new double[nbBond][]; final double[][] dfBar = new double[nbBond][]; for (int loopbnd = 0; loopbnd < nbBond; loopbnd++) { final int nbCf = cf[loopbnd].getNumberOfPayments(); cfaAdjustedBar[loopbnd] = new double[nbCf]; dfBar[loopbnd] = new double[nbCf]; } double dfdeliveryBar = 0.0; final Map<String, List<DoublesPair>> resultMap = new HashMap<>(); final List<DoublesPair> listCredit = new ArrayList<>(); if (nbInt == 1) { for (int loopcf = 0; loopcf < cfaAdjusted[ctd.get(0)].length; loopcf++) { cfaAdjustedBar[ctd.get(0)][loopcf] = priceBar; dfBar[ctd.get(0)][loopcf] = beta[ctd.get(0)][loopcf] / dfdelivery * cf[ctd.get(0)].getNthPayment(loopcf).getAmount() / future.getConversionFactor()[ctd.get(0)] * cfaAdjustedBar[ctd.get(0)][loopcf]; listCredit.add(new DoublesPair(cfTime[ctd.get(0)][loopcf], -cfTime[ctd.get(0)][loopcf] * df[ctd.get(0)][loopcf] * dfBar[ctd.get(0)][loopcf])); dfdeliveryBar += -cfaAdjusted[ctd.get(0)][loopcf] / dfdelivery * cfaAdjustedBar[ctd.get(0)][loopcf]; } listCredit.add(new DoublesPair(delivery, -delivery * dfdelivery * dfdeliveryBar)); } else { // From -infinity to first cross. for (int loopcf = 0; loopcf < cfaAdjusted[ctd.get(0)].length; loopcf++) { cfaAdjustedBar[ctd.get(0)][loopcf] = NORMAL.getCDF(kappa[0] + alpha[ctd.get(0)][loopcf]) * priceBar; } // Between cross for (int loopint = 1; loopint < nbInt - 1; loopint++) { for (int loopcf = 0; loopcf < cfaAdjusted[ctd.get(loopint)].length; loopcf++) { cfaAdjustedBar[ctd.get( loopint)][loopcf] = (NORMAL.getCDF(kappa[loopint] + alpha[ctd.get(loopint)][loopcf]) - NORMAL.getCDF(kappa[loopint - 1] + alpha[ctd.get(loopint)][loopcf])) * priceBar; } } // From last cross to +infinity for (int loopcf = 0; loopcf < cfaAdjusted[ctd.get(nbInt - 1)].length; loopcf++) { cfaAdjustedBar[ctd.get(nbInt - 1)][loopcf] = (1.0 - NORMAL.getCDF(kappa[nbInt - 2] + alpha[ctd.get(nbInt - 1)][loopcf])) * priceBar; } for (int loopbnd = 0; loopbnd < nbBond; loopbnd++) { // Could be reduced to only the ctd intervals. for (int loopcf = 0; loopcf < cfaAdjusted[loopbnd].length; loopcf++) { dfBar[loopbnd][loopcf] = beta[loopbnd][loopcf] / dfdelivery * cf[loopbnd].getNthPayment(loopcf).getAmount() / future.getConversionFactor()[loopbnd] * cfaAdjustedBar[loopbnd][loopcf]; listCredit.add(new DoublesPair(cfTime[loopbnd][loopcf], -cfTime[loopbnd][loopcf] * df[loopbnd][loopcf] * dfBar[loopbnd][loopcf])); dfdeliveryBar += -cfaAdjusted[loopbnd][loopcf] / dfdelivery * cfaAdjustedBar[loopbnd][loopcf]; } } listCredit.add(new DoublesPair(delivery, -delivery * dfdelivery * dfdeliveryBar)); } resultMap.put(multicurvesDecorated.getName(ccy), listCredit); return MulticurveSensitivity.ofYieldDiscounting(resultMap); } /** * Computes the future price curve sensitivity. The default number of points is used for the numerical search. * @param future The future derivative. * @param data The curve and Hull-White parameters. * @return The curve sensitivity. */ public MulticurveSensitivity priceCurveSensitivity(final BondFuture future, final HullWhiteIssuerProviderInterface data) { return priceCurveSensitivity(future, data, DEFAULT_NB_POINTS); } /** * Compute the present value sensitivity to rates of a bond future by discounting. * @param future The future. * @param data The curve and Hull-White parameters. * @return The present value rate sensitivity. */ public MultipleCurrencyMulticurveSensitivity presentValueCurveSensitivity(final BondFuture future, final HullWhiteIssuerProviderInterface data) { Validate.notNull(future, "Future"); final MulticurveSensitivity priceSensitivity = priceCurveSensitivity(future, data); final MultipleCurrencyMulticurveSensitivity transactionSensitivity = MultipleCurrencyMulticurveSensitivity .of(future.getCurrency(), priceSensitivity.multipliedBy(future.getNotional())); return transactionSensitivity; } /** * Internal class to estimate the price difference between two bonds. */ private static final class BondDifference extends Function1D<Double, Double> { private final double[] _cfa1; private final double[] _alpha1; private final double _e1; private final double[] _cfa2; private final double[] _alpha2; private final double _e2; public BondDifference(final double[] cfa1, final double[] alpha1, final double e1, final double[] cfa2, final double[] alpha2, final double e2) { _cfa1 = cfa1; _alpha1 = alpha1; _e1 = e1; _cfa2 = cfa2; _alpha2 = alpha2; _e2 = e2; } @Override public Double evaluate(final Double x) { double pv = 0.0; for (int loopcf = 0; loopcf < _cfa1.length; loopcf++) { pv += _cfa1[loopcf] * Math.exp(-_alpha1[loopcf] * _alpha1[loopcf] / 2.0 - _alpha1[loopcf] * x); } pv -= _e1; for (int loopcf = 0; loopcf < _cfa2.length; loopcf++) { pv -= _cfa2[loopcf] * Math.exp(-_alpha2[loopcf] * _alpha2[loopcf] / 2.0 - _alpha2[loopcf] * x); } pv += _e2; return pv; } } }