@Override
public Map<String, List<DoublesPair>> visitForwardRateAgreement(
final ForwardRateAgreement fra, final YieldCurveBundle curves) {
final ForwardRateAgreementDiscountingMethod method =
ForwardRateAgreementDiscountingMethod.getInstance();
return method.presentValueCurveSensitivity(fra, curves).getSensitivities();
}
/**
* For ForwardRateAgreement the ParSpread is the spread to be added to the fixed rate to obtain a
* present value of zero.
*
* @param fra The forward rate agreement.
* @param curves The yield curve bundle.
* @return The par spread.
*/
@Override
public Double visitForwardRateAgreement(
final ForwardRateAgreement fra, final YieldCurveBundle curves) {
Validate.notNull(curves);
Validate.notNull(fra);
return METHOD_FRA.parSpread(fra, curves);
}
/**
* Compute the spread to be added to the rate of the instrument for which the present value of the
* instrument is zero. The "rate" can be a "rate" or a "yield" and will depend of each instrument.
*
* @deprecated {@link YieldCurveBundle} is deprecated
*/
@Deprecated
public final class ParSpreadRateCalculator
extends InstrumentDerivativeVisitorAdapter<YieldCurveBundle, Double> {
/** The unique instance of the calculator. */
private static final ParSpreadRateCalculator INSTANCE = new ParSpreadRateCalculator();
/**
* Gets the calculator instance.
*
* @return The calculator.
*/
public static ParSpreadRateCalculator getInstance() {
return INSTANCE;
}
/** Constructor. */
private ParSpreadRateCalculator() {}
/** The methods and calculators. */
private static final PresentValueMCACalculator PVMCC = PresentValueMCACalculator.getInstance();
private static final PresentValueBasisPointCalculator PVBPC =
PresentValueBasisPointCalculator.getInstance();
private static final CashDiscountingMethod METHOD_DEPOSIT = CashDiscountingMethod.getInstance();
private static final DepositZeroDiscountingMethod METHOD_DEPOSIT_ZERO =
DepositZeroDiscountingMethod.getInstance();
private static final ForwardRateAgreementDiscountingMethod METHOD_FRA =
ForwardRateAgreementDiscountingMethod.getInstance();
// private static final InterestRateFutureTransactionDiscountingMethod
// METHOD_IR_FUTURES_TRANSACTION = InterestRateFutureTransactionDiscountingMethod.getInstance();
private static final InterestRateFutureSecurityDiscountingMethod METHOD_IR_FUTURES_SECURITY =
InterestRateFutureSecurityDiscountingMethod.getInstance();
@Override
public Double visitCash(final Cash deposit, final YieldCurveBundle curves) {
return METHOD_DEPOSIT.parSpread(deposit, curves);
}
@Override
public Double visitDepositZero(final DepositZero deposit, final YieldCurveBundle curves) {
return METHOD_DEPOSIT_ZERO.parSpread(deposit, curves);
}
/**
* For swaps the ParSpread is the spread to be added on each coupon of the first leg to obtain a
* present value of zero. It is computed as the opposite of the present value of the swap divided
* by the present value of a basis point of the first leg (as computed by the
* PresentValueBasisPointCalculator).
*
* @param swap The swap.
* @param curves The yield curve bundle.
* @return The par spread.
*/
@Override
public Double visitSwap(final Swap<?, ?> swap, final YieldCurveBundle curves) {
Validate.notNull(curves);
Validate.notNull(swap);
return -curves
.getFxRates()
.convert(swap.accept(PVMCC, curves), swap.getFirstLeg().getCurrency())
.getAmount()
/ swap.getFirstLeg().accept(PVBPC, curves);
}
@Override
public Double visitFixedCouponSwap(final SwapFixedCoupon<?> swap, final YieldCurveBundle curves) {
return visitSwap(swap, curves);
}
/**
* For ForwardRateAgreement the ParSpread is the spread to be added to the fixed rate to obtain a
* present value of zero.
*
* @param fra The forward rate agreement.
* @param curves The yield curve bundle.
* @return The par spread.
*/
@Override
public Double visitForwardRateAgreement(
final ForwardRateAgreement fra, final YieldCurveBundle curves) {
Validate.notNull(curves);
Validate.notNull(fra);
return METHOD_FRA.parSpread(fra, curves);
}
/**
* For InterestRateFutures the ParSpread is the spread to be added to the reference price to
* obtain a present value of zero.
*
* @param future The futures.
* @param curves The yield curve bundle.
* @return The par spread.
*/
@Override
public Double visitInterestRateFutureTransaction(
final InterestRateFutureTransaction future, final YieldCurveBundle curves) {
return -(METHOD_IR_FUTURES_SECURITY.price(future.getUnderlying(), curves)
- future.getReferencePrice());
}
// /**
// * For InterestRateFutures the ParSpread is the spread to be added to the reference price to
// obtain a present value of zero.
// * @param future The futures.
// * @param curves The yield curve bundle.
// * @return The par spread.
// */
// @Override
// public Double visitInterestRateFutureSecurity(final InterestRateFutureSecurity future, final
// YieldCurveBundle curves) {
// return -(METHOD_IR_FUTURES_SECURITY.presentValue(future, curves).getAmount());
// }
}
@Test
public void curveSensitivityFRA() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final double deltaShift = 1.0E-8;
final double pv = FRA_METHOD.presentValue(FRA, curves).getAmount();
// 1. Forward curve sensitivity
final String bumpedCurveName = "Bumped Curve";
final String[] bumpedCurvesForwardName = {FUNDING_CURVE_NAME, bumpedCurveName};
final ForwardRateAgreement fraBumpedForward =
(ForwardRateAgreement) FRA_DEFINITION.toDerivative(REFERENCE_DATE, bumpedCurvesForwardName);
final YieldAndDiscountCurve curveForward = curves.getCurve(FORWARD_CURVE_NAME);
final double[] timeForward = new double[2];
timeForward[0] = FRA.getFixingPeriodStartTime();
timeForward[1] = FRA.getFixingPeriodEndTime();
final int nbForwardDate = timeForward.length;
final double[] yieldsForward = new double[nbForwardDate + 1];
final double[] nodeTimesForward = new double[nbForwardDate + 1];
yieldsForward[0] = curveForward.getInterestRate(0.0);
for (int i = 0; i < nbForwardDate; i++) {
nodeTimesForward[i + 1] = timeForward[i];
yieldsForward[i + 1] = curveForward.getInterestRate(nodeTimesForward[i + 1]);
}
final YieldAndDiscountCurve tempCurveForward =
YieldCurve.from(
InterpolatedDoublesCurve.fromSorted(
nodeTimesForward, yieldsForward, new LinearInterpolator1D()));
final double[] sensiPvForwardFD = new double[nbForwardDate];
for (int i = 0; i < nbForwardDate; i++) {
final YieldAndDiscountCurve bumpedCurveForward =
tempCurveForward.withSingleShift(nodeTimesForward[i + 1], deltaShift);
final YieldCurveBundle curvesBumpedForward = new YieldCurveBundle();
curvesBumpedForward.addAll(curves);
curvesBumpedForward.setCurve("Bumped Curve", bumpedCurveForward);
final double bumpedPv =
FRA_METHOD.presentValue(fraBumpedForward, curvesBumpedForward).getAmount();
sensiPvForwardFD[i] = (bumpedPv - pv) / deltaShift;
}
final double[] nodeTimesForwardMethod =
new double[] {FRA.getFixingPeriodStartTime(), FRA.getFixingPeriodEndTime()};
final double[] sensiForwardMethod =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardMethod.length);
for (int loopnode = 0; loopnode < sensiForwardMethod.length; loopnode++) {
assertEquals(
"Sensitivity finite difference method: node sensitivity",
sensiPvForwardFD[loopnode],
sensiForwardMethod[loopnode]);
}
// 2. Funding curve sensitivity
final String[] bumpedCurvesFundingName = {bumpedCurveName, FORWARD_CURVE_NAME};
final ForwardRateAgreement fraBumped =
(ForwardRateAgreement) FRA_DEFINITION.toDerivative(REFERENCE_DATE, bumpedCurvesFundingName);
final YieldAndDiscountCurve curveFunding = curves.getCurve(FUNDING_CURVE_NAME);
final double[] yieldsFunding = new double[2];
final double[] nodeTimesFunding = new double[2];
yieldsFunding[0] = curveFunding.getInterestRate(0.0);
nodeTimesFunding[1] = FRA.getPaymentTime();
yieldsFunding[1] = curveFunding.getInterestRate(nodeTimesFunding[1]);
final YieldAndDiscountCurve tempCurveFunding =
YieldCurve.from(
InterpolatedDoublesCurve.fromSorted(
nodeTimesFunding, yieldsFunding, new LinearInterpolator1D()));
final YieldAndDiscountCurve bumpedCurve =
tempCurveFunding.withSingleShift(nodeTimesFunding[1], deltaShift);
final YieldCurveBundle curvesBumped = new YieldCurveBundle();
curvesBumped.addAll(curves);
curvesBumped.replaceCurve("Bumped Curve", bumpedCurve);
final double bumpedPvDsc = FRA_METHOD.presentValue(fraBumped, curvesBumped).getAmount();
final double[] resDsc = new double[1];
resDsc[0] = (bumpedPvDsc - pv) / deltaShift;
final double[] nodeTimesFundingMethod = new double[] {FRA.getPaymentTime()};
final double[] sensiFundingMethod =
SensitivityFiniteDifference.curveSensitivity(
fraBumped,
curves,
pv,
FUNDING_CURVE_NAME,
bumpedCurveName,
nodeTimesFundingMethod,
deltaShift,
FRA_METHOD);
assertEquals(
"Sensitivity finite difference method: number of node", 1, sensiFundingMethod.length);
for (int loopnode = 0; loopnode < sensiFundingMethod.length; loopnode++) {
assertEquals(
"Sensitivity finite difference method: node sensitivity",
resDsc[loopnode],
sensiFundingMethod[loopnode]);
}
}
/** Tests finite difference computation of curve sensitivity. */
public class SensitivityFiniteDifferenceTest {
// Index
private static final Period TENOR = Period.ofMonths(3);
private static final int SETTLEMENT_DAYS = 2;
private static final Calendar CALENDAR = new MondayToFridayCalendar("A");
private static final DayCount DAY_COUNT_INDEX =
DayCountFactory.INSTANCE.getDayCount("Actual/360");
private static final BusinessDayConvention BUSINESS_DAY =
BusinessDayConventionFactory.INSTANCE.getBusinessDayConvention("Modified Following");
private static final boolean IS_EOM = true;
private static final Currency CUR = Currency.USD;
private static final IborIndex INDEX =
new IborIndex(CUR, TENOR, SETTLEMENT_DAYS, CALENDAR, DAY_COUNT_INDEX, BUSINESS_DAY, IS_EOM);
// Dates : The above dates are not standard but selected for insure correct testing.
private static final ZonedDateTime FIXING_DATE = DateUtils.getUTCDate(2011, 1, 3);
private static final ZonedDateTime ACCRUAL_START_DATE = DateUtils.getUTCDate(2011, 1, 6);
private static final ZonedDateTime ACCRUAL_END_DATE = DateUtils.getUTCDate(2011, 4, 4);
private static final ZonedDateTime PAYMENT_DATE = DateUtils.getUTCDate(2011, 1, 7);
private static final DayCount DAY_COUNT_PAYMENT =
DayCountFactory.INSTANCE.getDayCount("Actual/365");
private static final double ACCRUAL_FACTOR_PAYMENT =
DAY_COUNT_PAYMENT.getDayCountFraction(ACCRUAL_START_DATE, ACCRUAL_END_DATE);
private static final double FRA_RATE = 0.05;
private static final double NOTIONAL = 1000000; // 1m
// Coupon with specific payment and accrual dates.
private static final ForwardRateAgreementDefinition FRA_DEFINITION =
new ForwardRateAgreementDefinition(
CUR,
PAYMENT_DATE,
ACCRUAL_START_DATE,
ACCRUAL_END_DATE,
ACCRUAL_FACTOR_PAYMENT,
NOTIONAL,
FIXING_DATE,
INDEX,
FRA_RATE);
// To derivatives
private static final ZonedDateTime REFERENCE_DATE = DateUtils.getUTCDate(2009, 8, 18);
private static final String FUNDING_CURVE_NAME = "Funding";
private static final String FORWARD_CURVE_NAME = "Forward";
private static final String[] CURVES = {FUNDING_CURVE_NAME, FORWARD_CURVE_NAME};
private static final ForwardRateAgreement FRA =
(ForwardRateAgreement) FRA_DEFINITION.toDerivative(REFERENCE_DATE, CURVES);
private static final ForwardRateAgreementDiscountingMethod FRA_METHOD =
ForwardRateAgreementDiscountingMethod.getInstance();
@Test
public void curveSensitivityFRA() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final double deltaShift = 1.0E-8;
final double pv = FRA_METHOD.presentValue(FRA, curves).getAmount();
// 1. Forward curve sensitivity
final String bumpedCurveName = "Bumped Curve";
final String[] bumpedCurvesForwardName = {FUNDING_CURVE_NAME, bumpedCurveName};
final ForwardRateAgreement fraBumpedForward =
(ForwardRateAgreement) FRA_DEFINITION.toDerivative(REFERENCE_DATE, bumpedCurvesForwardName);
final YieldAndDiscountCurve curveForward = curves.getCurve(FORWARD_CURVE_NAME);
final double[] timeForward = new double[2];
timeForward[0] = FRA.getFixingPeriodStartTime();
timeForward[1] = FRA.getFixingPeriodEndTime();
final int nbForwardDate = timeForward.length;
final double[] yieldsForward = new double[nbForwardDate + 1];
final double[] nodeTimesForward = new double[nbForwardDate + 1];
yieldsForward[0] = curveForward.getInterestRate(0.0);
for (int i = 0; i < nbForwardDate; i++) {
nodeTimesForward[i + 1] = timeForward[i];
yieldsForward[i + 1] = curveForward.getInterestRate(nodeTimesForward[i + 1]);
}
final YieldAndDiscountCurve tempCurveForward =
YieldCurve.from(
InterpolatedDoublesCurve.fromSorted(
nodeTimesForward, yieldsForward, new LinearInterpolator1D()));
final double[] sensiPvForwardFD = new double[nbForwardDate];
for (int i = 0; i < nbForwardDate; i++) {
final YieldAndDiscountCurve bumpedCurveForward =
tempCurveForward.withSingleShift(nodeTimesForward[i + 1], deltaShift);
final YieldCurveBundle curvesBumpedForward = new YieldCurveBundle();
curvesBumpedForward.addAll(curves);
curvesBumpedForward.setCurve("Bumped Curve", bumpedCurveForward);
final double bumpedPv =
FRA_METHOD.presentValue(fraBumpedForward, curvesBumpedForward).getAmount();
sensiPvForwardFD[i] = (bumpedPv - pv) / deltaShift;
}
final double[] nodeTimesForwardMethod =
new double[] {FRA.getFixingPeriodStartTime(), FRA.getFixingPeriodEndTime()};
final double[] sensiForwardMethod =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardMethod.length);
for (int loopnode = 0; loopnode < sensiForwardMethod.length; loopnode++) {
assertEquals(
"Sensitivity finite difference method: node sensitivity",
sensiPvForwardFD[loopnode],
sensiForwardMethod[loopnode]);
}
// 2. Funding curve sensitivity
final String[] bumpedCurvesFundingName = {bumpedCurveName, FORWARD_CURVE_NAME};
final ForwardRateAgreement fraBumped =
(ForwardRateAgreement) FRA_DEFINITION.toDerivative(REFERENCE_DATE, bumpedCurvesFundingName);
final YieldAndDiscountCurve curveFunding = curves.getCurve(FUNDING_CURVE_NAME);
final double[] yieldsFunding = new double[2];
final double[] nodeTimesFunding = new double[2];
yieldsFunding[0] = curveFunding.getInterestRate(0.0);
nodeTimesFunding[1] = FRA.getPaymentTime();
yieldsFunding[1] = curveFunding.getInterestRate(nodeTimesFunding[1]);
final YieldAndDiscountCurve tempCurveFunding =
YieldCurve.from(
InterpolatedDoublesCurve.fromSorted(
nodeTimesFunding, yieldsFunding, new LinearInterpolator1D()));
final YieldAndDiscountCurve bumpedCurve =
tempCurveFunding.withSingleShift(nodeTimesFunding[1], deltaShift);
final YieldCurveBundle curvesBumped = new YieldCurveBundle();
curvesBumped.addAll(curves);
curvesBumped.replaceCurve("Bumped Curve", bumpedCurve);
final double bumpedPvDsc = FRA_METHOD.presentValue(fraBumped, curvesBumped).getAmount();
final double[] resDsc = new double[1];
resDsc[0] = (bumpedPvDsc - pv) / deltaShift;
final double[] nodeTimesFundingMethod = new double[] {FRA.getPaymentTime()};
final double[] sensiFundingMethod =
SensitivityFiniteDifference.curveSensitivity(
fraBumped,
curves,
pv,
FUNDING_CURVE_NAME,
bumpedCurveName,
nodeTimesFundingMethod,
deltaShift,
FRA_METHOD);
assertEquals(
"Sensitivity finite difference method: number of node", 1, sensiFundingMethod.length);
for (int loopnode = 0; loopnode < sensiFundingMethod.length; loopnode++) {
assertEquals(
"Sensitivity finite difference method: node sensitivity",
resDsc[loopnode],
sensiFundingMethod[loopnode]);
}
}
@Test
public void curveSensitivityCentered() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final double deltaShift = 1.0E-8;
final double pv = FRA_METHOD.presentValue(FRA, curves).getAmount();
// 1. Forward curve sensitivity
final String bumpedCurveName = "Bumped Curve";
final String[] bumpedCurvesForwardName = {FUNDING_CURVE_NAME, bumpedCurveName};
final ForwardRateAgreement fraBumpedForward =
(ForwardRateAgreement) FRA_DEFINITION.toDerivative(REFERENCE_DATE, bumpedCurvesForwardName);
final double[] nodeTimesForwardMethod =
new double[] {FRA.getFixingPeriodStartTime(), FRA.getFixingPeriodEndTime()};
final double[] sensiForward =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD);
final double[] sensiForwardCentered =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD,
FiniteDifferenceType.CENTRAL);
final double[] sensiForwardCentered2 =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD);
final double[] sensiForwardForward =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD,
FiniteDifferenceType.FORWARD);
final double[] sensiForwardBackward =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD,
FiniteDifferenceType.BACKWARD);
assertEquals("Sensitivity finite difference method: number of node", 2, sensiForward.length);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardCentered.length);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardCentered2.length);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardForward.length);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardBackward.length);
for (int loopnode = 0; loopnode < sensiForward.length; loopnode++) {
assertEquals(
"Sensitivity finite difference method: centered vs non-centered",
sensiForward[loopnode],
sensiForwardForward[loopnode],
1.0E-10);
assertEquals(
"Sensitivity finite difference method: centered vs non-centered",
sensiForwardForward[loopnode],
sensiForwardCentered[loopnode],
1.0E-1);
assertEquals(
"Sensitivity finite difference method: centered vs non-centered",
sensiForwardBackward[loopnode],
sensiForwardCentered[loopnode],
1.0E-1);
assertEquals(
"Sensitivity finite difference method: centered vs non-centered",
sensiForwardCentered[loopnode],
sensiForwardCentered2[loopnode],
1.0E-10);
}
}
}
@Test
public void curveSensitivityCentered() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final double deltaShift = 1.0E-8;
final double pv = FRA_METHOD.presentValue(FRA, curves).getAmount();
// 1. Forward curve sensitivity
final String bumpedCurveName = "Bumped Curve";
final String[] bumpedCurvesForwardName = {FUNDING_CURVE_NAME, bumpedCurveName};
final ForwardRateAgreement fraBumpedForward =
(ForwardRateAgreement) FRA_DEFINITION.toDerivative(REFERENCE_DATE, bumpedCurvesForwardName);
final double[] nodeTimesForwardMethod =
new double[] {FRA.getFixingPeriodStartTime(), FRA.getFixingPeriodEndTime()};
final double[] sensiForward =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD);
final double[] sensiForwardCentered =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD,
FiniteDifferenceType.CENTRAL);
final double[] sensiForwardCentered2 =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD);
final double[] sensiForwardForward =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD,
FiniteDifferenceType.FORWARD);
final double[] sensiForwardBackward =
SensitivityFiniteDifference.curveSensitivity(
fraBumpedForward,
curves,
pv,
FORWARD_CURVE_NAME,
bumpedCurveName,
nodeTimesForwardMethod,
deltaShift,
FRA_METHOD,
FiniteDifferenceType.BACKWARD);
assertEquals("Sensitivity finite difference method: number of node", 2, sensiForward.length);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardCentered.length);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardCentered2.length);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardForward.length);
assertEquals(
"Sensitivity finite difference method: number of node", 2, sensiForwardBackward.length);
for (int loopnode = 0; loopnode < sensiForward.length; loopnode++) {
assertEquals(
"Sensitivity finite difference method: centered vs non-centered",
sensiForward[loopnode],
sensiForwardForward[loopnode],
1.0E-10);
assertEquals(
"Sensitivity finite difference method: centered vs non-centered",
sensiForwardForward[loopnode],
sensiForwardCentered[loopnode],
1.0E-1);
assertEquals(
"Sensitivity finite difference method: centered vs non-centered",
sensiForwardBackward[loopnode],
sensiForwardCentered[loopnode],
1.0E-1);
assertEquals(
"Sensitivity finite difference method: centered vs non-centered",
sensiForwardCentered[loopnode],
sensiForwardCentered2[loopnode],
1.0E-10);
}
}