/**
* Computes the interest rate sensitivity of future price.
*
* @param future The future security.
* @param curves The curves.
* @return The curve sensitivity.
*/
@Override
public InterestRateCurveSensitivity priceCurveSensitivity(
final FederalFundsFutureSecurity future, final YieldCurveBundle curves) {
Validate.notNull(future, "Future");
Validate.notNull(curves, "Curves");
int nbFixing = future.getFixingPeriodAccrualFactor().length;
YieldAndDiscountCurve ois = curves.getCurve(future.getOISCurveName());
double[] df = new double[nbFixing + 1];
for (int loopfix = 0; loopfix < nbFixing + 1; loopfix++) {
df[loopfix] = ois.getDiscountFactor(future.getFixingPeriodTime()[loopfix]);
}
// Backward sweep
double priceBar = 1.0;
double interestBar = -1.0 / future.getFixingTotalAccrualFactor() * priceBar;
double[] dfBar = new double[nbFixing + 1];
for (int loopfix = 0; loopfix < nbFixing; loopfix++) {
dfBar[loopfix] += 1.0 / df[loopfix + 1] * interestBar;
dfBar[loopfix + 1] += -df[loopfix] / (df[loopfix + 1] * df[loopfix + 1]) * interestBar;
}
Map<String, List<DoublesPair>> resultMap = new HashMap<String, List<DoublesPair>>();
List<DoublesPair> listOIS = new ArrayList<DoublesPair>();
for (int loopfix = 0; loopfix < nbFixing + 1; loopfix++) {
listOIS.add(
new DoublesPair(
future.getFixingPeriodTime()[loopfix],
-future.getFixingPeriodTime()[loopfix] * df[loopfix] * dfBar[loopfix]));
}
resultMap.put(future.getOISCurveName(), listOIS);
InterestRateCurveSensitivity result = new InterestRateCurveSensitivity(resultMap);
return result;
}
@Test
/** Test the price computed from the curves */
public void price() {
final YieldCurveBundle curves = TestsDataSets.createCurves1();
final double price = METHOD.price(ERU2, curves);
final YieldAndDiscountCurve forwardCurve = curves.getCurve(FORWARD_CURVE_NAME);
final double forward =
(forwardCurve.getDiscountFactor(FIXING_START_TIME)
/ forwardCurve.getDiscountFactor(FIXING_END_TIME)
- 1)
/ FIXING_ACCRUAL;
final double factor = MODEL.futureConvexityFactor(ERU2, MODEL_PARAMETERS);
final double expectedPrice = 1.0 - factor * forward + (1 - factor) / FIXING_ACCRUAL;
assertEquals("Future price from curves in Hull-White one factor model", expectedPrice, price);
}
public void test() {
final ConvectionDiffusionPDESolver solver = new ThetaMethodFiniteDifference(0.5, false);
final int tNodes = 20;
final int xNodes = 101;
final PDEGrid1D grid = new PDEGrid1D(tNodes, xNodes, T, LOWER.getLevel(), UPPER.getLevel());
final PDEResults1D res = solver.solve(DATA, grid, LOWER, UPPER);
final int i = (int) (xNodes * SPOT / UPPER.getLevel());
final double spot = res.getSpaceValue(i);
final double price = res.getFunctionValue(i);
final double df = YIELD_CURVE.getDiscountFactor(T);
assertEquals(SPOT, spot, 1e-9);
assertEquals(SABR_PRICE_SURFACE.getPrice(T, STRIKE), price, price * 2e-3);
final BlackFunctionData data = new BlackFunctionData(spot / df, df, 0.0);
double impVol;
try {
impVol = BLACK_IMPLIED_VOL.getImpliedVolatility(data, OPTION, price);
} catch (final Exception e) {
impVol = 0.0;
}
assertEquals(SABR_VOL_SURFACE.getVolatility(T, STRIKE), impVol, 1e-3);
}
static {
ALPHA = ATM_VOL * Math.pow(SPOT, 1 - BETA);
final Function<Double, Double> sabrSurface =
new Function<Double, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final Double... x) {
final double t = x[0];
final double k = x[1];
final SABRFormulaData sabrdata =
new SABRFormulaData(SPOT * Math.exp(RATE * t), ALPHA, BETA, NU, RHO);
final EuropeanVanillaOption option = new EuropeanVanillaOption(k, t, true);
final Function1D<SABRFormulaData, Double> func = SABR.getVolatilityFunction(option);
return func.evaluate(sabrdata);
}
};
SABR_VOL_SURFACE = new BlackVolatilitySurface(FunctionalDoublesSurface.from(sabrSurface));
final Function<Double, Double> priceSurface =
new Function<Double, Double>() {
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final Double... x) {
final double t = x[0];
final double k = x[1];
final double sigma = sabrSurface.evaluate(x);
final double df = YIELD_CURVE.getDiscountFactor(t);
final BlackFunctionData data = new BlackFunctionData(SPOT / df, df, sigma);
final EuropeanVanillaOption option = new EuropeanVanillaOption(k, t, true);
final Function1D<BlackFunctionData, Double> pfunc =
BLACK_PRICE_FUNCTION.getPriceFunction(option);
final double price = pfunc.evaluate(data);
return price;
}
};
SABR_PRICE_SURFACE = new PriceSurface(FunctionalDoublesSurface.from(priceSurface));
final DupireLocalVolatilityCalculator cal = new DupireLocalVolatilityCalculator();
SABR_LOCAL_VOL = cal.getAbsoluteLocalVolatilitySurface(SABR_VOL_SURFACE, SPOT, RATE);
STRIKE = SPOT / YIELD_CURVE.getDiscountFactor(T);
OPTION = new EuropeanVanillaOption(STRIKE, T, true);
LOWER = new DirichletBoundaryCondition(0, 0.0);
UPPER = new FixedSecondDerivativeBoundaryCondition(0.0, 5.0 * SPOT, false);
DATA = PDE_DATA_PROVIDER.getBackwardsLocalVol(FORWARD, STRIKE, T, 0.0, true, SABR_LOCAL_VOL);
}
/**
* Computes the price of a future from the curves using an estimation of the future rate without
* convexity adjustment.
*
* @param future The future.
* @param curves The Hull-White parameters and the curves.
* @return The price.
*/
public double price(
final InterestRateFuture future, final HullWhiteOneFactorPiecewiseConstantDataBundle curves) {
Validate.notNull(future, "Future");
Validate.notNull(curves, "Curves");
final YieldAndDiscountCurve forwardCurve = curves.getCurve(future.getForwardCurveName());
double dfForwardStart = forwardCurve.getDiscountFactor(future.getFixingPeriodStartTime());
double dfForwardEnd = forwardCurve.getDiscountFactor(future.getFixingPeriodEndTime());
double forward = (dfForwardStart / dfForwardEnd - 1) / future.getFixingPeriodAccrualFactor();
double futureConvexityFactor =
MODEL.futureConvexityFactor(
future.getLastTradingTime(),
future.getFixingPeriodStartTime(),
future.getFixingPeriodEndTime(),
curves.getHullWhiteParameter());
double price =
1.0
- futureConvexityFactor * forward
+ (1 - futureConvexityFactor) / future.getFixingPeriodAccrualFactor();
return price;
}
@Override
public Set<ComputedValue> execute(
FunctionExecutionContext executionContext,
FunctionInputs inputs,
ComputationTarget target,
Set<ValueRequirement> desiredValues) {
// 1. Get the expiry _time_ from the trade
SimpleTrade trade =
(SimpleTrade) target.getTrade(); // confirms that the ComputationTargetType == TRADE
EquityVarianceSwapSecurity security = (EquityVarianceSwapSecurity) trade.getSecurity();
double expiry =
TimeCalculator.getTimeBetween(
executionContext.getValuationClock().zonedDateTime(),
security.getLastObservationDate());
// ExternalId id = security.getSpotUnderlyingIdentifier();
// 2. Get the discount curve and spot value
Object discountObject = inputs.getValue(getDiscountRequirement(security));
if (discountObject == null) {
throw new OpenGammaRuntimeException("Could not get Discount Curve");
}
YieldAndDiscountCurve discountCurve = (YieldAndDiscountCurve) discountObject;
Object spotObject = inputs.getValue(getSpotRequirement(security));
if (spotObject == null) {
throw new OpenGammaRuntimeException("Could not get Underlying's Spot value");
}
double spot = (Double) spotObject;
// 3. Compute the forward
final double discountFactor = discountCurve.getDiscountFactor(expiry);
Validate.isTrue(
discountFactor != 0,
"The discount curve has returned a zero value for a discount bond. Check rates.");
final double forward = spot / discountFactor;
ValueSpecification valueSpec = getValueSpecification(security);
return Collections.singleton(new ComputedValue(valueSpec, forward));
}
/**
* Compute the price sensitivity to rates of a interest rate future by discounting.
*
* @param future The future.
* @param curves The Hull-White parameters and the curves.
* @return The price rate sensitivity.
*/
public InterestRateCurveSensitivity priceCurveSensitivity(
final InterestRateFuture future, final HullWhiteOneFactorPiecewiseConstantDataBundle curves) {
Validate.notNull(future, "Future");
Validate.notNull(curves, "Curves");
final YieldAndDiscountCurve forwardCurve = curves.getCurve(future.getForwardCurveName());
double dfForwardStart = forwardCurve.getDiscountFactor(future.getFixingPeriodStartTime());
double dfForwardEnd = forwardCurve.getDiscountFactor(future.getFixingPeriodEndTime());
double futureConvexityFactor =
MODEL.futureConvexityFactor(
future.getLastTradingTime(),
future.getFixingPeriodStartTime(),
future.getFixingPeriodEndTime(),
curves.getHullWhiteParameter());
// Backward sweep
double priceBar = 1.0;
double forwardBar = -futureConvexityFactor * priceBar;
double dfForwardEndBar =
-dfForwardStart
/ (dfForwardEnd * dfForwardEnd)
/ future.getFixingPeriodAccrualFactor()
* forwardBar;
double dfForwardStartBar =
1.0 / (future.getFixingPeriodAccrualFactor() * dfForwardEnd) * forwardBar;
Map<String, List<DoublesPair>> resultMap = new HashMap<String, List<DoublesPair>>();
List<DoublesPair> listForward = new ArrayList<DoublesPair>();
listForward.add(
new DoublesPair(
future.getFixingPeriodStartTime(),
-future.getFixingPeriodStartTime() * dfForwardStart * dfForwardStartBar));
listForward.add(
new DoublesPair(
future.getFixingPeriodEndTime(),
-future.getFixingPeriodEndTime() * dfForwardEnd * dfForwardEndBar));
resultMap.put(future.getForwardCurveName(), listForward);
InterestRateCurveSensitivity result = new InterestRateCurveSensitivity(resultMap);
return result;
}
@Override
/**
* Computes the Federal Funds future price using average of forward rates (not convexity
* adjustment).
*
* @param future The future security.
* @param curves The curves.
* @return The price.
*/
public double price(final FederalFundsFutureSecurity future, final YieldCurveBundle curves) {
Validate.notNull(future, "Future");
Validate.notNull(curves, "Curves");
int nbFixing = future.getFixingPeriodAccrualFactor().length;
YieldAndDiscountCurve ois = curves.getCurve(future.getOISCurveName());
double[] df = new double[nbFixing + 1];
for (int loopfix = 0; loopfix < nbFixing + 1; loopfix++) {
df[loopfix] = ois.getDiscountFactor(future.getFixingPeriodTime()[loopfix]);
}
double interest = future.getAccruedInterest();
for (int loopfix = 0; loopfix < nbFixing; loopfix++) {
interest += df[loopfix] / df[loopfix + 1] - 1.0;
}
return 1.0 - interest / future.getFixingTotalAccrualFactor();
}
@Test
/**
* Test the present value sensitivity to rate for a swaption with strike above the cut-off strike.
*/
public void testPresentValueSensitivityExtra() {
final YieldCurveBundle curves = TestsDataSetsSABR.createCurves1();
final SABRInterestRateParameters sabrParameter = TestsDataSetsSABR.createSABR1();
final SABRInterestRateDataBundle sabrBundle =
new SABRInterestRateDataBundle(sabrParameter, curves);
final double highStrike = 0.10;
final SwapFixedIborDefinition swapDefinitionPayerHighStrike =
SwapFixedIborDefinition.from(
SETTLEMENT_DATE, CMS_INDEX, NOTIONAL, highStrike, FIXED_IS_PAYER);
final SwaptionCashFixedIborDefinition swaptionDefinitionLongPayerHighStrike =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, swapDefinitionPayerHighStrike, IS_LONG);
final SwaptionCashFixedIborDefinition swaptionDefinitionShortPayerHighStrike =
SwaptionCashFixedIborDefinition.from(EXPIRY_DATE, swapDefinitionPayerHighStrike, !IS_LONG);
final SwaptionCashFixedIbor swaptionLongPayerHighStrike =
swaptionDefinitionLongPayerHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
final SwaptionCashFixedIbor swaptionShortPayerHighStrike =
swaptionDefinitionShortPayerHighStrike.toDerivative(REFERENCE_DATE, CURVES_NAME);
final SwaptionCashFixedIborSABRExtrapolationRightMethod methodExtra =
new SwaptionCashFixedIborSABRExtrapolationRightMethod(CUT_OFF_STRIKE, MU);
// Swaption sensitivity
InterestRateCurveSensitivity pvsLongPayerExtra =
methodExtra.presentValueSensitivity(swaptionLongPayerHighStrike, sabrBundle);
final InterestRateCurveSensitivity pvsShortPayerExtra =
methodExtra.presentValueSensitivity(swaptionShortPayerHighStrike, sabrBundle);
// Long/short parity
final InterestRateCurveSensitivity pvsShortPayer_1 = pvsShortPayerExtra.multiply(-1);
assertEquals(pvsLongPayerExtra.getSensitivities(), pvsShortPayer_1.getSensitivities());
// Present value sensitivity comparison with finite difference.
final double deltaTolerance = 5.0E+4;
// Testing note: Sensitivity is for a movement of 1. 1E+2 = 1 cent for a 1 bp move. Tolerance
// increased to cope with numerical imprecision of finite difference.
final double deltaShift = 1.0E-5;
pvsLongPayerExtra = pvsLongPayerExtra.clean();
final double pv = methodExtra.presentValue(swaptionLongPayerHighStrike, sabrBundle);
// 1. Forward curve sensitivity
final String bumpedCurveName = "Bumped Curve";
final String[] bumpedCurvesForwardName = {FUNDING_CURVE_NAME, bumpedCurveName};
final SwaptionCashFixedIbor swaptionBumpedForward =
swaptionDefinitionLongPayerHighStrike.toDerivative(REFERENCE_DATE, bumpedCurvesForwardName);
final YieldAndDiscountCurve curveForward = curves.getCurve(FORWARD_CURVE_NAME);
final Set<Double> timeForwardSet = new TreeSet<Double>();
for (final Payment pay :
swaptionLongPayerHighStrike.getUnderlyingSwap().getSecondLeg().getPayments()) {
final CouponIbor coupon = (CouponIbor) pay;
timeForwardSet.add(coupon.getFixingPeriodStartTime());
timeForwardSet.add(coupon.getFixingPeriodEndTime());
}
final int nbForwardDate = timeForwardSet.size();
final List<Double> timeForwardList = new ArrayList<Double>(timeForwardSet);
Double[] timeForwardArray = new Double[nbForwardDate];
timeForwardArray = timeForwardList.toArray(timeForwardArray);
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] = timeForwardArray[i];
yieldsForward[i + 1] = curveForward.getInterestRate(nodeTimesForward[i + 1]);
}
final YieldAndDiscountCurve tempCurveForward =
new YieldCurve(
InterpolatedDoublesCurve.fromSorted(
nodeTimesForward, yieldsForward, new LinearInterpolator1D()));
final List<DoublesPair> tempForward =
pvsLongPayerExtra.getSensitivities().get(FORWARD_CURVE_NAME);
final double[] resFwd = 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 SABRInterestRateDataBundle sabrBundleBumped =
new SABRInterestRateDataBundle(sabrParameter, curvesBumpedForward);
final double bumpedpv = methodExtra.presentValue(swaptionBumpedForward, sabrBundleBumped);
resFwd[i] = (bumpedpv - pv) / deltaShift;
final DoublesPair pair = tempForward.get(i);
assertEquals(
"Sensitivity to forward curve: Node " + i,
nodeTimesForward[i + 1],
pair.getFirst(),
1E-8);
assertEquals(
"Sensitivity to forward curve: Node " + i, resFwd[i], pair.getSecond(), deltaTolerance);
}
// 2. Funding curve sensitivity
final String[] bumpedCurvesFundingName = {bumpedCurveName, FORWARD_CURVE_NAME};
final SwaptionCashFixedIbor swaptionBumpedFunding =
swaptionDefinitionLongPayerHighStrike.toDerivative(REFERENCE_DATE, bumpedCurvesFundingName);
final int nbPayDate =
swaptionDefinitionLongPayerHighStrike.getUnderlyingSwap().getIborLeg().getPayments().length;
final YieldAndDiscountCurve curveFunding = curves.getCurve(FUNDING_CURVE_NAME);
final double[] yieldsFunding = new double[nbPayDate + 2];
final double[] nodeTimesFunding = new double[nbPayDate + 2];
yieldsFunding[0] = curveFunding.getInterestRate(0.0);
nodeTimesFunding[1] = swaptionLongPayerHighStrike.getSettlementTime();
yieldsFunding[1] = curveFunding.getInterestRate(nodeTimesFunding[1]);
for (int i = 0; i < nbPayDate; i++) {
nodeTimesFunding[i + 2] =
swaptionLongPayerHighStrike
.getUnderlyingSwap()
.getSecondLeg()
.getNthPayment(i)
.getPaymentTime();
yieldsFunding[i + 2] = curveFunding.getInterestRate(nodeTimesFunding[i + 2]);
}
final YieldAndDiscountCurve tempCurveFunding =
new YieldCurve(
InterpolatedDoublesCurve.fromSorted(
nodeTimesFunding, yieldsFunding, new LinearInterpolator1D()));
final List<DoublesPair> tempFunding =
pvsLongPayerExtra.getSensitivities().get(FUNDING_CURVE_NAME);
final double[] resDsc = new double[nbPayDate];
for (int i = 0; i < nbPayDate; i++) {
final YieldAndDiscountCurve bumpedCurve =
tempCurveFunding.withSingleShift(nodeTimesFunding[i + 1], deltaShift);
final YieldCurveBundle curvesBumped = new YieldCurveBundle();
curvesBumped.addAll(curves);
curvesBumped.setCurve("Bumped Curve", bumpedCurve);
final SABRInterestRateDataBundle sabrBundleBumped =
new SABRInterestRateDataBundle(sabrParameter, curvesBumped);
final double bumpedpv = methodExtra.presentValue(swaptionBumpedFunding, sabrBundleBumped);
resDsc[i] = (bumpedpv - pv) / deltaShift;
final DoublesPair pair = tempFunding.get(i);
assertEquals(
"Sensitivity to discounting curve: Node " + i,
nodeTimesFunding[i + 1],
pair.getFirst(),
1E-8);
assertEquals(
"Sensitivity to discounting curve: Node " + i,
resDsc[i],
pair.getSecond(),
deltaTolerance);
}
}
