/**
* 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.method;
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.CashFlowEquivalentCalculator;
import com.opengamma.analytics.financial.interestrate.InstrumentDerivative;
import com.opengamma.analytics.financial.interestrate.InterestRateCurveSensitivity;
import com.opengamma.analytics.financial.interestrate.YieldCurveBundle;
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.curve.YieldAndDiscountCurve;
import com.opengamma.analytics.financial.model.interestrate.definition.HullWhiteOneFactorPiecewiseConstantDataBundle;
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.money.CurrencyAmount;
import com.opengamma.util.tuple.DoublesPair;
/**
* 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
* @deprecated Use {@link com.opengamma.analytics.financial.interestrate.future.provider.BondFutureHullWhiteMethod}
*/
@Deprecated
public final class BondFutureHullWhiteMethod extends BondFutureMethod {
/**
* 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();
/**
* Creates the method unique instance.
*/
private static final BondFutureHullWhiteMethod INSTANCE = new BondFutureHullWhiteMethod();
/**
* Return the method unique instance.
* @return The instance.
*/
public static BondFutureHullWhiteMethod getInstance() {
return INSTANCE;
}
/**
* Constructor.
*/
private BondFutureHullWhiteMethod() {
}
/**
* 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 hwData 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 HullWhiteOneFactorPiecewiseConstantDataBundle hwData, final int nbPoint) {
Validate.notNull(future, "Future");
Validate.notNull(hwData, "Hull-White data bundle");
final int nbBond = future.getDeliveryBasket().length;
final YieldAndDiscountCurve bndCurve = hwData.getCurve(future.getDeliveryBasket()[0].getDiscountingCurveName());
final double expiry = future.getNoticeLastTime();
final double delivery = future.getDeliveryLastTime();
final double dfdelivery = bndCurve.getDiscountFactor(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, hwData);
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] = bndCurve.getDiscountFactor(cfTime[loopbnd][loopcf]);
alpha[loopbnd][loopcf] = MODEL.alpha(hwData.getHullWhiteParameter(), 0.0, expiry, delivery, cfTime[loopbnd][loopcf]);
beta[loopbnd][loopcf] = MODEL.futuresConvexityFactor(hwData.getHullWhiteParameter(), 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 hwData The curve and Hull-White parameters.
* @return The future price.
*/
public double price(final BondFuture future, final HullWhiteOneFactorPiecewiseConstantDataBundle hwData) {
return price(future, hwData, 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 curves The yield curves. Should contain the credit and repo curves associated to the instrument.
* @return The present value.
*/
public CurrencyAmount presentValue(final BondFuture future, final HullWhiteOneFactorPiecewiseConstantDataBundle curves) {
Validate.notNull(future, "Future");
final double futurePrice = price(future, curves);
return presentValueFromPrice(future, futurePrice);
}
/**
* Computes the present value of future from the curves using the cheapest-to-deliver and computing the value as a forward.
* @param instrument The future.
* @param curves The yield curves. Should contain the credit and repo curves associated to the instrument.
* @return The present value.
*/
@Override
public CurrencyAmount presentValue(final InstrumentDerivative instrument, final YieldCurveBundle curves) {
Validate.isTrue(instrument instanceof BondFuture, "Bond future");
Validate.isTrue(curves instanceof HullWhiteOneFactorPiecewiseConstantDataBundle, "Bundle should contain Hull-White data");
return presentValue((BondFuture) instrument, (HullWhiteOneFactorPiecewiseConstantDataBundle) curves);
}
/**
* Computes the future price curve sensitivity.
* @param future The future security.
* @param hwData The curve and Hull-White parameters.
* @param nbPoint The number of point in the numerical cross estimation.
* @return The curve sensitivity.
*/
public InterestRateCurveSensitivity priceCurveSensitivity(final BondFuture future, final HullWhiteOneFactorPiecewiseConstantDataBundle hwData, final int nbPoint) {
Validate.notNull(future, "Future");
Validate.notNull(hwData, "Hull-White data bundle");
final int nbBond = future.getDeliveryBasket().length;
final YieldAndDiscountCurve bndCurve = hwData.getCurve(future.getDeliveryBasket()[0].getDiscountingCurveName());
final double expiry = future.getNoticeLastTime();
final double delivery = future.getDeliveryLastTime();
final double dfdelivery = bndCurve.getDiscountFactor(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, hwData);
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] = bndCurve.getDiscountFactor(cfTime[loopbnd][loopcf]);
alpha[loopbnd][loopcf] = MODEL.alpha(hwData.getHullWhiteParameter(), 0.0, expiry, delivery, cfTime[loopbnd][loopcf]);
beta[loopbnd][loopcf] = MODEL.futuresConvexityFactor(hwData.getHullWhiteParameter(), 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(DoublesPair.of(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(DoublesPair.of(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(DoublesPair.of(cfTime[loopbnd][loopcf], -cfTime[loopbnd][loopcf] * df[loopbnd][loopcf] * dfBar[loopbnd][loopcf]));
dfdeliveryBar += -cfaAdjusted[loopbnd][loopcf] / dfdelivery * cfaAdjustedBar[loopbnd][loopcf];
}
}
listCredit.add(DoublesPair.of(delivery, -delivery * dfdelivery * dfdeliveryBar));
}
resultMap.put(future.getDeliveryBasket()[0].getDiscountingCurveName(), listCredit);
final InterestRateCurveSensitivity result = new InterestRateCurveSensitivity(resultMap);
return result;
}
/**
* Computes the future price curve sensitivity. The default number of points is used for the numerical search.
* @param future The future derivative.
* @param hwData The curve and Hull-White parameters.
* @return The curve sensitivity.
*/
public InterestRateCurveSensitivity priceCurveSensitivity(final BondFuture future, final HullWhiteOneFactorPiecewiseConstantDataBundle hwData) {
return priceCurveSensitivity(future, hwData, DEFAULT_NB_POINTS);
}
/**
* Compute the present value sensitivity to rates of a bond future by discounting.
* @param future The future.
* @param curves The yield curves. Should contain the credit and repo curves associated.
* @return The present value rate sensitivity.
*/
public InterestRateCurveSensitivity presentValueCurveSensitivity(final BondFuture future, final HullWhiteOneFactorPiecewiseConstantDataBundle curves) {
Validate.notNull(future, "Future");
final InterestRateCurveSensitivity priceSensitivity = priceCurveSensitivity(future, curves);
final InterestRateCurveSensitivity transactionSensitivity = priceSensitivity.multipliedBy(future.getNotional());
return transactionSensitivity;
}
public InterestRateCurveSensitivity presentValueCurveSensitivity(final InstrumentDerivative instrument, final YieldCurveBundle curves) {
Validate.isTrue(instrument instanceof BondFuture, "Bond future");
Validate.isTrue(curves instanceof HullWhiteOneFactorPiecewiseConstantDataBundle, "Bundle should contain Hull-White data");
return presentValueCurveSensitivity((BondFuture) instrument, (HullWhiteOneFactorPiecewiseConstantDataBundle) curves);
}
/**
* 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;
}
}
}