/**
* Class used to compute the price of a CMS cap/floor by swaption replication on a SABR formula with
* extrapolation. Reference: Hagan, P. S. (2003). Convexity conundrums: Pricing CMS swaps, caps, and
* floors. Wilmott Magazine, March, pages 38--44. OpenGamma implementation note: Replication pricing
* for linear and TEC format CMS, Version 1.2, March 2011. OpenGamma implementation note for the
* extrapolation: Smile extrapolation, version 1.2, May 2011.
*
* @deprecated Use classes descended from {@link CapFloorCMSSABRReplicationAbstractMethod}
*/
@Deprecated
public class CapFloorCMSSABRExtrapolationRightReplicationMethod
extends CapFloorCMSSABRReplicationAbstractMethod {
/** The cut-off strike. The smile is extrapolated above that level. */
private final double _cutOffStrike;
/** The tail thickness parameter. */
private final double _mu;
/** The par rate calculator. */
private static final ParRateCalculator PRC = ParRateCalculator.getInstance();
/** The par rate sensitivity calculator. */
private static final ParRateCurveSensitivityCalculator PRSC =
ParRateCurveSensitivityCalculator.getInstance();
/**
* Default constructor of the CMS cap/floor replication method. The default integration interval
* is 1.00 (100%).
*
* @param cutOffStrike The cut-off strike.
* @param mu The tail thickness parameter.
*/
public CapFloorCMSSABRExtrapolationRightReplicationMethod(
final double cutOffStrike, final double mu) {
super(1.0);
_mu = mu;
_cutOffStrike = cutOffStrike;
}
/**
* Default constructor of the CMS cap/floor replication method. The default integration interval
* is 1.00 (100%).
*
* @param cutOffStrike The cut-off strike.
* @param mu The tail thickness parameter.
* @param integrationInterval Integration range.
*/
public CapFloorCMSSABRExtrapolationRightReplicationMethod(
final double cutOffStrike, final double mu, final double integrationInterval) {
super(integrationInterval);
_mu = mu;
_cutOffStrike = cutOffStrike;
}
/**
* Compute the present value of a CMS cap/floor by replication in SABR framework with
* extrapolation on the right.
*
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle.
* @return The present value.
*/
@Override
public CurrencyAmount presentValue(
final CapFloorCMS cmsCapFloor, final SABRInterestRateDataBundle sabrData) {
Validate.notNull(cmsCapFloor);
Validate.notNull(sabrData);
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRC, sabrData);
final double discountFactorTp =
sabrData
.getCurve(underlyingSwap.getFixedLeg().getNthPayment(0).getFundingCurveName())
.getDiscountFactor(cmsCapFloor.getPaymentTime());
final double maturity =
underlyingSwap
.getFixedLeg()
.getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(cmsCapFloor.getFixingTime(), maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
final SABRFormulaData sabrPoint = new SABRFormulaData(alpha, beta, rho, nu);
final CMSIntegrant integrant =
new CMSIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final double strike = cmsCapFloor.getStrike();
final double factor = discountFactorTp / integrant.h(forward) * integrant.g(forward);
final double strikePart = factor * integrant.k(strike) * integrant.bs(strike);
final double absoluteTolerance =
1.0 / (factor * Math.abs(cmsCapFloor.getNotional()) * cmsCapFloor.getPaymentYearFraction());
final double relativeTolerance = 1E-10;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
double integralPart;
try {
if (cmsCapFloor.isCap()) {
integralPart =
discountFactorTp
* integrator.integrate(integrant, strike, strike + getIntegrationInterval());
} else {
integralPart = discountFactorTp * integrator.integrate(integrant, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
final double priceCMS =
(strikePart + integralPart)
* cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction();
return CurrencyAmount.of(cmsCapFloor.getCurrency(), priceCMS);
}
@Override
public CurrencyAmount presentValue(
final InstrumentDerivative instrument, final YieldCurveBundle curves) {
Validate.isTrue(instrument instanceof CapFloorCMS, "CMS cap/floor");
Validate.isTrue(
curves instanceof SABRInterestRateDataBundle, "Bundle should contain SABR data");
return presentValue((CapFloorCMS) instrument, (SABRInterestRateDataBundle) curves);
}
/**
* Computes the present value sensitivity to the yield curves of a CMS cap/floor by replication in
* the SABR framework with extrapolation on the right.
*
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle. The SABR function need to be the Hagan function.
* @return The present value sensitivity to curves.
*/
@Override
public InterestRateCurveSensitivity presentValueCurveSensitivity(
final CapFloorCMS cmsCapFloor, final SABRInterestRateDataBundle sabrData) {
Validate.notNull(cmsCapFloor);
Validate.notNull(sabrData);
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRC, sabrData);
final double discountFactor =
sabrData
.getCurve(underlyingSwap.getFixedLeg().getNthPayment(0).getFundingCurveName())
.getDiscountFactor(cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
final double maturity =
underlyingSwap
.getFixedLeg()
.getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(cmsCapFloor.getFixingTime(), maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
final SABRFormulaData sabrPoint = new SABRFormulaData(alpha, beta, rho, nu);
// Common
final CMSIntegrant integrantPrice =
new CMSIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final CMSDeltaIntegrant integrantDelta =
new CMSDeltaIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final double factor = discountFactor / integrantDelta.h(forward) * integrantDelta.g(forward);
final double absoluteTolerance =
1.0 / (factor * Math.abs(cmsCapFloor.getNotional()) * cmsCapFloor.getPaymentYearFraction());
final double relativeTolerance = 1E-10;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
// Price
final double[] bs = integrantDelta.bsbsp(strike);
@SuppressWarnings("synthetic-access")
final double[] n = integrantDelta.nnp(forward);
final double strikePartPrice = discountFactor * integrantDelta.k(strike) * n[0] * bs[0];
double integralPartPrice;
try {
if (cmsCapFloor.isCap()) {
integralPartPrice =
discountFactor
* integrator.integrate(integrantPrice, strike, strike + getIntegrationInterval());
} else {
integralPartPrice = discountFactor * integrator.integrate(integrantPrice, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
final double price =
(strikePartPrice + integralPartPrice)
* cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction();
// Delta
final double strikePart =
discountFactor * integrantDelta.k(strike) * (n[1] * bs[0] + n[0] * bs[1]);
double integralPart;
try {
if (cmsCapFloor.isCap()) {
integralPart =
discountFactor
* integrator.integrate(integrantDelta, strike, strike + getIntegrationInterval());
} else {
integralPart = discountFactor * integrator.integrate(integrantDelta, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
final double deltaS0 =
(strikePart + integralPart)
* cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction();
final double deltaPD = price / discountFactor;
final double sensiDF = -cmsCapFloor.getPaymentTime() * discountFactor * deltaPD;
final List<DoublesPair> list = new ArrayList<>();
list.add(new DoublesPair(cmsCapFloor.getPaymentTime(), sensiDF));
final Map<String, List<DoublesPair>> resultMap = new HashMap<>();
resultMap.put(
cmsCapFloor.getUnderlyingSwap().getFixedLeg().getNthPayment(0).getFundingCurveName(), list);
InterestRateCurveSensitivity result = new InterestRateCurveSensitivity(resultMap);
final InterestRateCurveSensitivity forwardDr =
new InterestRateCurveSensitivity(cmsCapFloor.getUnderlyingSwap().accept(PRSC, sabrData));
result = result.plus(forwardDr.multipliedBy(deltaS0));
return result;
}
/**
* Computes the present value sensitivity to the SABR parameters of a CMS cap/floor by replication
* in SABR framework with extrapolation on the right.
*
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle. The SABR function need to be the Hagan function.
* @return The present value sensitivity to SABR parameters.
*/
@Override
public PresentValueSABRSensitivityDataBundle presentValueSABRSensitivity(
final CapFloorCMS cmsCapFloor, final SABRInterestRateDataBundle sabrData) {
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRC, sabrData);
final double discountFactorTp =
sabrData
.getCurve(underlyingSwap.getFixedLeg().getNthPayment(0).getFundingCurveName())
.getDiscountFactor(cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
final double maturity =
underlyingSwap
.getFixedLeg()
.getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(cmsCapFloor.getFixingTime(), maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
final SABRFormulaData sabrPoint = new SABRFormulaData(alpha, beta, rho, nu);
final CMSVegaIntegrant integrantVega =
new CMSVegaIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final double factor = discountFactorTp / integrantVega.h(forward) * integrantVega.g(forward);
final SABRExtrapolationRightFunction sabrExtrapolation =
new SABRExtrapolationRightFunction(
forward, sabrPoint, _cutOffStrike, cmsCapFloor.getFixingTime(), _mu);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(strike, cmsCapFloor.getFixingTime(), cmsCapFloor.isCap());
final double factor2 = factor * integrantVega.k(strike);
final double[] strikePartPrice = new double[4];
sabrExtrapolation.priceAdjointSABR(option, strikePartPrice);
for (int loopvega = 0; loopvega < 4; loopvega++) {
strikePartPrice[loopvega] *= factor2;
}
final double absoluteTolerance =
1.0 / (factor * Math.abs(cmsCapFloor.getNotional()) * cmsCapFloor.getPaymentYearFraction());
final double relativeTolerance = 1E-3;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
final double[] integralPart = new double[4];
final double[] totalSensi = new double[4];
for (int loopparameter = 0; loopparameter < 4; loopparameter++) {
integrantVega.setParameterIndex(loopparameter);
try {
if (cmsCapFloor.isCap()) {
integralPart[loopparameter] =
discountFactorTp
* integrator.integrate(integrantVega, strike, strike + getIntegrationInterval());
} else {
integralPart[loopparameter] =
discountFactorTp * integrator.integrate(integrantVega, 0.0, strike);
}
} catch (final Exception e) {
throw new RuntimeException(e);
}
totalSensi[loopparameter] =
(strikePartPrice[loopparameter] + integralPart[loopparameter])
* cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction();
}
final PresentValueSABRSensitivityDataBundle sensi = new PresentValueSABRSensitivityDataBundle();
sensi.addAlpha(expiryMaturity, totalSensi[0]);
sensi.addBeta(expiryMaturity, totalSensi[1]);
sensi.addRho(expiryMaturity, totalSensi[2]);
sensi.addNu(expiryMaturity, totalSensi[3]);
return sensi;
}
/**
* Computes the present value sensitivity to the strike of a CMS cap/floor by replication in SABR
* framework with extrapolation on the right.
*
* @param cmsCapFloor The CMS cap/floor.
* @param sabrData The SABR data bundle. The SABR function need to be the Hagan function.
* @return The present value sensitivity to strike.
*/
@Override
public double presentValueStrikeSensitivity(
final CapFloorCMS cmsCapFloor, final SABRInterestRateDataBundle sabrData) {
final SABRInterestRateParameters sabrParameter = sabrData.getSABRParameter();
final SwapFixedCoupon<? extends Payment> underlyingSwap = cmsCapFloor.getUnderlyingSwap();
final double forward = underlyingSwap.accept(PRC, sabrData);
final double discountFactor =
sabrData
.getCurve(underlyingSwap.getFixedLeg().getNthPayment(0).getFundingCurveName())
.getDiscountFactor(cmsCapFloor.getPaymentTime());
final double strike = cmsCapFloor.getStrike();
final double maturity =
underlyingSwap
.getFixedLeg()
.getNthPayment(underlyingSwap.getFixedLeg().getNumberOfPayments() - 1)
.getPaymentTime()
- cmsCapFloor.getSettlementTime();
final DoublesPair expiryMaturity = new DoublesPair(cmsCapFloor.getFixingTime(), maturity);
final double alpha = sabrParameter.getAlpha(expiryMaturity);
final double beta = sabrParameter.getBeta(expiryMaturity);
final double rho = sabrParameter.getRho(expiryMaturity);
final double nu = sabrParameter.getNu(expiryMaturity);
final SABRFormulaData sabrPoint = new SABRFormulaData(alpha, beta, rho, nu);
final CMSStrikeIntegrant integrant =
new CMSStrikeIntegrant(cmsCapFloor, sabrPoint, forward, _cutOffStrike, _mu);
final double factor = discountFactor * integrant.g(forward) / integrant.h(forward);
final double absoluteTolerance = 1.0E-9;
final double relativeTolerance = 1.0E-5;
final RungeKuttaIntegrator1D integrator =
new RungeKuttaIntegrator1D(absoluteTolerance, relativeTolerance, getNbIteration());
final SABRExtrapolationRightFunction sabrExtrapolation =
new SABRExtrapolationRightFunction(
forward, sabrPoint, _cutOffStrike, cmsCapFloor.getFixingTime(), _mu);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(strike, cmsCapFloor.getFixingTime(), cmsCapFloor.isCap());
final double[] kpkpp = integrant.kpkpp(strike);
double firstPart;
double thirdPart;
if (cmsCapFloor.isCap()) {
firstPart = -kpkpp[0] * integrant.bs(strike);
thirdPart = integrator.integrate(integrant, strike, strike + getIntegrationInterval());
} else {
firstPart = 3 * kpkpp[0] * integrant.bs(strike);
thirdPart = integrator.integrate(integrant, 0.0, strike);
}
final double secondPart = integrant.k(strike) * sabrExtrapolation.priceDerivativeStrike(option);
return cmsCapFloor.getNotional()
* cmsCapFloor.getPaymentYearFraction()
* factor
* (firstPart + secondPart + thirdPart);
}
/** Inner class to implement the integration used in price replication. */
private class CMSIntegrant extends Function1D<Double, Double> {
protected static final double EPS = 1E-10;
private final int _nbFixedPeriod;
private final int _nbFixedPaymentYear;
private final double _tau;
private final double _delta;
private final double _eta;
private final double _timeToExpiry;
private final double _strike;
private final double _forward;
private final double _factor;
private final SABRExtrapolationRightFunction _sabrExtrapolation;
private final boolean _isCall;
/**
* Gets the _nbFixedPeriod field.
*
* @return the _nbFixedPeriod
*/
public int getNbFixedPeriod() {
return _nbFixedPeriod;
}
/**
* Gets the _nbFixedPaymentYear field.
*
* @return the _nbFixedPaymentYear
*/
public int getNbFixedPaymentYear() {
return _nbFixedPaymentYear;
}
/**
* Gets the _tau field.
*
* @return the _tau
*/
public double getTau() {
return _tau;
}
/**
* Gets the _eta field.
*
* @return the _eta
*/
public double getEta() {
return _eta;
}
/**
* Gets the _timeToExpiry field.
*
* @return the _timeToExpiry
*/
public double getTimeToExpiry() {
return _timeToExpiry;
}
/**
* Gets the _sabrExtrapolation field.
*
* @return the _sabrExtrapolation
*/
public SABRExtrapolationRightFunction getSabrExtrapolation() {
return _sabrExtrapolation;
}
/**
* Gets the _isCall field.
*
* @return the _isCall
*/
public boolean isCall() {
return _isCall;
}
/**
* Gets the _strike field.
*
* @return the _strike
*/
public double getStrike() {
return _strike;
}
/**
* Constructor.
*
* @param cmsCap The CMS cap/floor.
* @param sabrParameter The SABR parameters.
* @param forward The forward.
* @param cutOffStrike The cut-off strike.
* @param mu The tail thickness parameter.
*/
public CMSIntegrant(
final CapFloorCMS cmsCap,
final SABRFormulaData sabrPoint,
final double forward,
final double cutOffStrike,
final double mu) {
_nbFixedPeriod = cmsCap.getUnderlyingSwap().getFixedLeg().getPayments().length;
_nbFixedPaymentYear =
(int)
Math.round(
1.0
/ cmsCap
.getUnderlyingSwap()
.getFixedLeg()
.getNthPayment(0)
.getPaymentYearFraction());
_tau = 1.0 / _nbFixedPaymentYear;
_delta = cmsCap.getPaymentTime() - cmsCap.getSettlementTime();
_eta = -_delta;
_timeToExpiry = cmsCap.getFixingTime();
_forward = forward;
_sabrExtrapolation =
new SABRExtrapolationRightFunction(forward, sabrPoint, cutOffStrike, _timeToExpiry, mu);
_isCall = cmsCap.isCap();
_strike = cmsCap.getStrike();
_factor = g(_forward) / h(_forward);
}
@Override
public Double evaluate(final Double x) {
final double[] kD = kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative
// of k.
return _factor * (kD[1] * (x - _strike) + 2.0 * kD[0]) * bs(x);
}
/**
* The approximation of the discount factor as function of the swap rate.
*
* @param x The swap rate.
* @return The discount factor.
*/
double h(final double x) {
return Math.pow(1.0 + _tau * x, _eta);
}
/**
* The cash annuity.
*
* @param x The swap rate.
* @return The annuity.
*/
double g(final double x) {
if (x >= EPS) {
final double periodFactor = 1 + x / _nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -_nbFixedPeriod);
return 1.0 / x * (1.0 - nPeriodDiscount);
}
return ((double) _nbFixedPeriod) / _nbFixedPaymentYear;
}
/**
* The factor used in the strike part and in the integration of the replication.
*
* @param x The swap rate.
* @return The factor.
*/
double k(final double x) {
double g;
double h;
if (x >= EPS) {
final double periodFactor = 1 + x / _nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -_nbFixedPeriod);
g = 1.0 / x * (1.0 - nPeriodDiscount);
h = Math.pow(1.0 + _tau * x, _eta);
} else {
g = ((double) _nbFixedPeriod) / _nbFixedPaymentYear;
h = 1.0;
}
return h / g;
}
/**
* The first and second derivative of the function k.
*
* @param x The swap rate.
* @return The derivative (first element is the first derivative, second element is second
* derivative.
*/
protected double[] kpkpp(final double x) {
final double periodFactor = 1 + x / _nbFixedPaymentYear;
final double nPeriodDiscount = Math.pow(periodFactor, -_nbFixedPeriod);
/** The value of the annuity and its first and second derivative. */
double g, gp, gpp;
if (x >= EPS) {
g = 1.0 / x * (1.0 - nPeriodDiscount);
gp = -g / x + _nbFixedPeriod / x / _nbFixedPaymentYear * nPeriodDiscount / periodFactor;
gpp =
2.0 / (x * x) * g
- 2.0
* _nbFixedPeriod
/ (x * x)
/ _nbFixedPaymentYear
* nPeriodDiscount
/ periodFactor
- (_nbFixedPeriod + 1.0)
* _nbFixedPeriod
/ x
/ (_nbFixedPaymentYear * _nbFixedPaymentYear)
* nPeriodDiscount
/ (periodFactor * periodFactor);
} else {
// Implementation comment: When x is (almost) 0, useful for CMS swaps which are priced as
// CMS cap of strike 0.
g = ((double) _nbFixedPeriod) / _nbFixedPaymentYear;
gp =
-_nbFixedPeriod
/ 2.0
* (_nbFixedPeriod + 1.0)
/ (_nbFixedPaymentYear * _nbFixedPaymentYear);
gpp =
_nbFixedPeriod
/ 2.0
* (_nbFixedPeriod + 1.0)
* (1.0 + (_nbFixedPeriod + 2.0) / 3.0)
/ (_nbFixedPaymentYear * _nbFixedPaymentYear * _nbFixedPaymentYear);
}
final double h = Math.pow(1.0 + _tau * x, _eta);
final double hp = _eta * _tau * h / periodFactor;
final double hpp = (_eta - 1.0) * _tau * hp / periodFactor;
final double kp = hp / g - h * gp / (g * g);
final double kpp =
hpp / g - 2 * hp * gp / (g * g) - h * (gpp / (g * g) - 2 * (gp * gp) / (g * g * g));
return new double[] {kp, kpp};
}
/**
* The Black-Scholes formula with numeraire 1 as function of the strike.
*
* @param strike The strike.
* @return The Black-Scholes formula.
*/
double bs(final double strike) {
final EuropeanVanillaOption option =
new EuropeanVanillaOption(strike, _timeToExpiry, _isCall);
return _sabrExtrapolation.price(option);
}
}
private class CMSDeltaIntegrant extends CMSIntegrant {
private final double[] _nnp;
public CMSDeltaIntegrant(
final CapFloorCMS cmsCap,
final SABRFormulaData sabrPoint,
final double forward,
final double cutOffStrike,
final double mu) {
super(cmsCap, sabrPoint, forward, cutOffStrike, mu);
_nnp = nnp(forward);
}
@Override
public Double evaluate(final Double x) {
final double[] kD = kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative
// of k.
final double[] bs = bsbsp(x);
return (kD[1] * (x - getStrike()) + 2.0 * kD[0]) * (_nnp[1] * bs[0] + _nnp[0] * bs[1]);
}
/**
* The Black-Scholes formula and its derivative with respect to the forward.
*
* @param strike The strike.
* @return The Black-Scholes formula and its derivative.
*/
double[] bsbsp(final double strike) {
final double[] result = new double[2];
final EuropeanVanillaOption option =
new EuropeanVanillaOption(strike, getTimeToExpiry(), isCall());
result[0] = getSabrExtrapolation().price(option);
result[1] = getSabrExtrapolation().priceDerivativeForward(option);
return result;
}
private double[] nnp(final double x) {
final double[] result = new double[2];
final double[] ggp = ggp(x);
final double[] hhp = hhp(x);
result[0] = ggp[0] / hhp[0];
result[1] = ggp[1] / hhp[0] - ggp[0] * hhp[1] / (hhp[0] * hhp[0]);
return result;
}
private double[] ggp(final double x) {
final double[] result = new double[2];
if (x >= EPS) {
final double periodFactor = 1 + x / getNbFixedPaymentYear();
final double nPeriodDiscount = Math.pow(periodFactor, -getNbFixedPeriod());
result[0] = 1.0 / x * (1.0 - nPeriodDiscount);
result[1] =
-result[0] / x + getTau() * getNbFixedPeriod() / x * nPeriodDiscount / periodFactor;
} else {
result[0] = getNbFixedPeriod() * getTau();
result[1] = -getNbFixedPeriod() * (getNbFixedPeriod() + 1.0) * getTau() * getTau() / 2.0;
}
return result;
}
private double[] hhp(final double x) {
final double[] result = new double[2];
result[0] = Math.pow(1.0 + getTau() * x, getEta());
result[1] = getEta() * getTau() * result[0] / (1 + x * getTau());
return result;
}
}
private class CMSVegaIntegrant extends CMSIntegrant {
/** The index of the sensitivity computed. */
private int _parameterIndex;
/**
* Constructor.
*
* @param cmsCap The CMS cap/floor.
* @param sabrParameter The SABR parameters.
* @param forward The forward.
* @param cutOffStrike The cut-off strike.
* @param mu The tail thickness parameter.
*/
public CMSVegaIntegrant(
final CapFloorCMS cmsCap,
final SABRFormulaData sabrPoint,
final double forward,
final double cutOffStrike,
final double mu) {
super(cmsCap, sabrPoint, forward, cutOffStrike, mu);
}
/**
* Sets the index of the sensitivity computed.
*
* @param parameterIndex The index.
*/
public void setParameterIndex(final int parameterIndex) {
this._parameterIndex = parameterIndex;
}
@SuppressWarnings("synthetic-access")
@Override
public Double evaluate(final Double x) {
final double[] kD = super.kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative
// of k.
final EuropeanVanillaOption option =
new EuropeanVanillaOption(x, super._timeToExpiry, super._isCall);
final double[] priceDerivativeSABR = new double[4];
getSabrExtrapolation().priceAdjointSABR(option, priceDerivativeSABR);
return super._factor
* (kD[1] * (x - super._strike) + 2.0 * kD[0])
* priceDerivativeSABR[_parameterIndex];
}
}
private class CMSStrikeIntegrant extends CMSIntegrant {
/**
* @param cmsCap
* @param sabrParameter
* @param forward
*/
public CMSStrikeIntegrant(
final CapFloorCMS cmsCap,
final SABRFormulaData sabrPoint,
final double forward,
final double cutOffStrike,
final double mu) {
super(cmsCap, sabrPoint, forward, cutOffStrike, mu);
}
@Override
public Double evaluate(final Double x) {
final double[] kD = super.kpkpp(x);
// Implementation note: kD[0] contains the first derivative of k; kD[1] the second derivative
// of k.
return -kD[1] * bs(x);
}
} // End CMSStrikeIntegrant
}
/**
* Constructs a single yield curve and its Jacobian from an FX-implied yield curve calculation
* configuration and a yield curve definition that contains <b>only</b> {@link
* StripInstrumentType#CASH} strips. The transformation of the yield curve allows risk to be
* displayed with respect to implied deposit rates, not FX forwards.
*/
public class ImpliedDepositCurveFunction extends AbstractFunction {
/** The calculation method property value */
public static final String IMPLIED_DEPOSIT = "ImpliedDeposit";
/** The Cash instrument method */
private static final CashDiscountingMethod METHOD_CASH = CashDiscountingMethod.getInstance();
/** Calculates the par rate */
private static final ParRateCalculator PAR_RATE_CALCULATOR = ParRateCalculator.getInstance();
/** Calculates the sensitivity of the par rate to the curves */
private static final ParRateCurveSensitivityCalculator PAR_RATE_SENSITIVITY_CALCULATOR =
ParRateCurveSensitivityCalculator.getInstance();
/** The business day convention used for FX forward dates computation * */
private static final BusinessDayConvention MOD_FOL = BusinessDayConventions.MODIFIED_FOLLOWING;
/** The logger */
private static final Logger s_logger = LoggerFactory.getLogger(ImpliedDepositCurveFunction.class);
/** The curve name */
private final String _curveCalculationConfig;
private ConfigSourceQuery<MultiCurveCalculationConfig> _multiCurveCalculationConfig;
private ConfigSourceQuery<YieldCurveDefinition> _yieldCurveDefinition;
/** @param curveCalculationConfig The curve name, not null */
public ImpliedDepositCurveFunction(final String curveCalculationConfig) {
ArgumentChecker.notNull(curveCalculationConfig, "curve name");
_curveCalculationConfig = curveCalculationConfig;
}
@Override
public void init(final FunctionCompilationContext context) {
_multiCurveCalculationConfig =
ConfigSourceQuery.init(context, this, MultiCurveCalculationConfig.class);
_yieldCurveDefinition = ConfigSourceQuery.init(context, this, YieldCurveDefinition.class);
}
@Override
public CompiledFunctionDefinition compile(
final FunctionCompilationContext context, final Instant atInstant) {
final MultiCurveCalculationConfig impliedConfiguration =
_multiCurveCalculationConfig.get(_curveCalculationConfig);
if (impliedConfiguration == null) {
throw new OpenGammaRuntimeException(
"Multi-curve calculation called " + _curveCalculationConfig + " was null");
}
ComputationTarget target =
context.getComputationTargetResolver().resolve(impliedConfiguration.getTarget());
if (!(target.getValue() instanceof Currency)) {
throw new OpenGammaRuntimeException(
"Target of curve calculation configuration was not a currency");
}
final Currency impliedCurrency = (Currency) target.getValue();
if (!IMPLIED_DEPOSIT.equals(impliedConfiguration.getCalculationMethod())) {
throw new OpenGammaRuntimeException(
"Curve calculation method was not "
+ IMPLIED_DEPOSIT
+ " for configuration called "
+ _curveCalculationConfig);
}
final String[] impliedCurveNames = impliedConfiguration.getYieldCurveNames();
if (impliedCurveNames.length != 1) {
throw new OpenGammaRuntimeException(
"Can only handle configurations with a single implied curve");
}
final LinkedHashMap<String, String[]> originalConfigurationName =
impliedConfiguration.getExogenousConfigData();
if (originalConfigurationName == null || originalConfigurationName.size() != 1) {
throw new OpenGammaRuntimeException("Need a configuration with one exogenous configuration");
}
final Map.Entry<String, String[]> entry =
Iterables.getOnlyElement(originalConfigurationName.entrySet());
final String[] originalCurveNames = entry.getValue();
if (originalCurveNames.length != 1) {
s_logger.warn("Found more than one exogenous configuration name; using only the first");
}
final MultiCurveCalculationConfig originalConfiguration =
_multiCurveCalculationConfig.get(entry.getKey());
if (originalConfiguration == null) {
throw new OpenGammaRuntimeException(
"Multi-curve calculation called " + entry.getKey() + " was null");
}
target = context.getComputationTargetResolver().resolve(originalConfiguration.getTarget());
if (!(target.getValue() instanceof Currency)) {
throw new OpenGammaRuntimeException(
"Target of curve calculation configuration was not a currency");
}
final Currency originalCurrency = (Currency) target.getValue();
if (!originalCurrency.equals(impliedCurrency)) {
throw new OpenGammaRuntimeException(
"Currency targets for configurations "
+ _curveCalculationConfig
+ " and "
+ entry.getKey()
+ " did not match");
}
final YieldCurveDefinition impliedDefinition =
_yieldCurveDefinition.get(impliedCurveNames[0] + "_" + impliedCurrency.getCode());
if (impliedDefinition == null) {
throw new OpenGammaRuntimeException(
"Could not get implied definition called "
+ impliedCurveNames[0]
+ "_"
+ impliedCurrency.getCode());
}
final Set<FixedIncomeStrip> strips = impliedDefinition.getStrips();
for (final FixedIncomeStrip strip : strips) {
if (strip.getInstrumentType() != StripInstrumentType.CASH) {
throw new OpenGammaRuntimeException(
"Can only handle yield curve definitions with CASH strips");
}
}
final ZonedDateTime atZDT = ZonedDateTime.ofInstant(atInstant, ZoneOffset.UTC);
return new MyCompiledFunction(
atZDT.with(LocalTime.MIDNIGHT),
atZDT.plusDays(1).with(LocalTime.MIDNIGHT).minusNanos(1000000),
impliedConfiguration,
impliedDefinition,
originalConfiguration,
originalCurveNames[0]);
};
private class MyCompiledFunction extends AbstractInvokingCompiledFunction {
/** The definition of the implied curve */
private final YieldCurveDefinition _impliedDefinition;
/** The implied curve calculation configuration */
private final MultiCurveCalculationConfig _impliedConfiguration;
/** The original curve calculation configuration */
private final MultiCurveCalculationConfig _originalConfiguration;
/** The implied curve name */
private final String _impliedCurveName;
/** The original curve name */
private final String _originalCurveName;
/** The currency */
private final Currency _currency;
/** The interpolator */
private final String _interpolatorName;
/** The left extrapolator */
private final String _leftExtrapolatorName;
/** The right extrapolator */
private final String _rightExtrapolatorName;
public MyCompiledFunction(
final ZonedDateTime earliestInvokation,
final ZonedDateTime latestInvokation,
final MultiCurveCalculationConfig impliedConfiguration,
final YieldCurveDefinition impliedDefinition,
final MultiCurveCalculationConfig originalConfiguration,
final String originalCurveName) {
super(earliestInvokation, latestInvokation);
_impliedConfiguration = impliedConfiguration;
_impliedDefinition = impliedDefinition;
_originalConfiguration = originalConfiguration;
_impliedCurveName = impliedDefinition.getName();
_originalCurveName = originalCurveName;
_currency = impliedDefinition.getCurrency();
_interpolatorName = impliedDefinition.getInterpolatorName();
_leftExtrapolatorName = impliedDefinition.getLeftExtrapolatorName();
_rightExtrapolatorName = impliedDefinition.getRightExtrapolatorName();
}
@Override
public Set<ComputedValue> execute(
final FunctionExecutionContext executionContext,
final FunctionInputs inputs,
final ComputationTarget target,
final Set<ValueRequirement> desiredValues)
throws AsynchronousExecution {
final Object originalCurveObject = inputs.getValue(YIELD_CURVE);
if (originalCurveObject == null) {
throw new OpenGammaRuntimeException("Could not get original curve");
}
ValueProperties resultCurveProperties = null;
String absoluteToleranceName = null;
String relativeToleranceName = null;
String iterationsName = null;
String decompositionName = null;
String useFiniteDifferenceName = null;
for (final ValueRequirement desiredValue : desiredValues) {
if (desiredValue.getValueName().equals(YIELD_CURVE)) {
absoluteToleranceName =
desiredValue.getConstraint(
MultiYieldCurvePropertiesAndDefaults.PROPERTY_ROOT_FINDER_ABSOLUTE_TOLERANCE);
relativeToleranceName =
desiredValue.getConstraint(
MultiYieldCurvePropertiesAndDefaults.PROPERTY_ROOT_FINDER_RELATIVE_TOLERANCE);
iterationsName =
desiredValue.getConstraint(
MultiYieldCurvePropertiesAndDefaults.PROPERTY_ROOT_FINDER_MAX_ITERATIONS);
decompositionName =
desiredValue.getConstraint(
MultiYieldCurvePropertiesAndDefaults.PROPERTY_DECOMPOSITION);
useFiniteDifferenceName =
desiredValue.getConstraint(
MultiYieldCurvePropertiesAndDefaults.PROPERTY_USE_FINITE_DIFFERENCE);
resultCurveProperties = desiredValue.getConstraints().copy().get();
break;
}
}
if (resultCurveProperties == null) {
throw new OpenGammaRuntimeException("Could not get result curve properties");
}
final ValueProperties resultJacobianProperties = resultCurveProperties.withoutAny(CURVE);
ZonedDateTime valuationDateTime =
executionContext
.getValuationTime()
.atZone(executionContext.getValuationClock().getZone());
final HolidaySource holidaySource =
OpenGammaExecutionContext.getHolidaySource(executionContext);
final ConventionSource conventionSource =
OpenGammaExecutionContext.getConventionSource(executionContext);
final Calendar calendar = CalendarUtils.getCalendar(holidaySource, _currency);
final DepositConvention convention =
conventionSource.getSingle(
ExternalId.of(SCHEME_NAME, getConventionName(_currency, DEPOSIT)),
DepositConvention.class);
final int spotLag = convention.getSettlementDays();
final ExternalId conventionSettlementRegion = convention.getRegionCalendar();
ZonedDateTime spotDate;
if (spotLag == 0 && conventionSettlementRegion == null) {
spotDate = valuationDateTime;
} else {
spotDate = ScheduleCalculator.getAdjustedDate(valuationDateTime, spotLag, calendar);
;
}
final YieldCurveBundle curves = new YieldCurveBundle();
final String fullYieldCurveName = _originalCurveName + "_" + _currency;
curves.setCurve(fullYieldCurveName, (YieldAndDiscountCurve) originalCurveObject);
final int n = _impliedDefinition.getStrips().size();
final double[] t = new double[n];
final double[] r = new double[n];
int i = 0;
final DayCount dayCount =
DayCountFactory.INSTANCE.getDayCount(
"Act/360"); // TODO: Get the convention from the curve.
final String impliedDepositCurveName = _curveCalculationConfig + "_" + _currency.getCode();
final List<InstrumentDerivative> derivatives = new ArrayList<>();
for (final FixedIncomeStrip strip : _impliedDefinition.getStrips()) {
final Tenor tenor = strip.getCurveNodePointTime();
final ZonedDateTime paymentDate =
ScheduleCalculator.getAdjustedDate(
spotDate, tenor.getPeriod(), MOD_FOL, calendar, true);
final double startTime = TimeCalculator.getTimeBetween(valuationDateTime, spotDate);
final double endTime = TimeCalculator.getTimeBetween(valuationDateTime, paymentDate);
final double accrualFactor = dayCount.getDayCountFraction(spotDate, paymentDate, calendar);
final Cash cashFXCurve =
new Cash(_currency, startTime, endTime, 1, 0, accrualFactor, fullYieldCurveName);
final double parRate = METHOD_CASH.parRate(cashFXCurve, curves);
final Cash cashDepositCurve =
new Cash(_currency, startTime, endTime, 1, 0, accrualFactor, impliedDepositCurveName);
derivatives.add(cashDepositCurve);
t[i] = endTime;
r[i++] = parRate;
}
final CombinedInterpolatorExtrapolator interpolator =
CombinedInterpolatorExtrapolatorFactory.getInterpolator(
_interpolatorName, _leftExtrapolatorName, _rightExtrapolatorName);
final double absoluteTolerance = Double.parseDouble(absoluteToleranceName);
final double relativeTolerance = Double.parseDouble(relativeToleranceName);
final int iterations = Integer.parseInt(iterationsName);
final Decomposition<?> decomposition =
DecompositionFactory.getDecomposition(decompositionName);
final boolean useFiniteDifference = Boolean.parseBoolean(useFiniteDifferenceName);
final LinkedHashMap<String, double[]> curveNodes = new LinkedHashMap<>();
final LinkedHashMap<String, Interpolator1D> interpolators = new LinkedHashMap<>();
curveNodes.put(impliedDepositCurveName, t);
interpolators.put(impliedDepositCurveName, interpolator);
final FXMatrix fxMatrix = new FXMatrix();
final YieldCurveBundle knownCurve = new YieldCurveBundle();
final MultipleYieldCurveFinderDataBundle data =
new MultipleYieldCurveFinderDataBundle(
derivatives, r, knownCurve, curveNodes, interpolators, useFiniteDifference, fxMatrix);
final NewtonVectorRootFinder rootFinder =
new BroydenVectorRootFinder(
absoluteTolerance, relativeTolerance, iterations, decomposition);
final Function1D<DoubleMatrix1D, DoubleMatrix1D> curveCalculator =
new MultipleYieldCurveFinderFunction(data, PAR_RATE_CALCULATOR);
final Function1D<DoubleMatrix1D, DoubleMatrix2D> jacobianCalculator =
new MultipleYieldCurveFinderJacobian(data, PAR_RATE_SENSITIVITY_CALCULATOR);
final double[] fittedYields =
rootFinder.getRoot(curveCalculator, jacobianCalculator, new DoubleMatrix1D(r)).getData();
final DoubleMatrix2D jacobianMatrix =
jacobianCalculator.evaluate(new DoubleMatrix1D(fittedYields));
final YieldCurve impliedDepositCurve =
new YieldCurve(
impliedDepositCurveName,
InterpolatedDoublesCurve.from(t, fittedYields, interpolator));
final ValueSpecification curveSpec =
new ValueSpecification(YIELD_CURVE, target.toSpecification(), resultCurveProperties);
final ValueSpecification jacobianSpec =
new ValueSpecification(
YIELD_CURVE_JACOBIAN, target.toSpecification(), resultJacobianProperties);
return Sets.newHashSet(
new ComputedValue(curveSpec, impliedDepositCurve),
new ComputedValue(jacobianSpec, jacobianMatrix));
}
@Override
public ComputationTargetType getTargetType() {
return ComputationTargetType.CURRENCY;
}
@Override
public Set<ValueSpecification> getResults(
final FunctionCompilationContext compilationContext, final ComputationTarget target) {
final ValueProperties curveProperties =
getCurveProperties(_impliedCurveName, _impliedConfiguration.getCalculationConfigName());
final ValueProperties jacobianProperties =
getJacobianProperties(_impliedConfiguration.getCalculationConfigName());
final ComputationTargetSpecification targetSpec = target.toSpecification();
final ValueSpecification curve =
new ValueSpecification(YIELD_CURVE, targetSpec, curveProperties);
final ValueSpecification jacobian =
new ValueSpecification(YIELD_CURVE_JACOBIAN, targetSpec, jacobianProperties);
return Sets.newHashSet(curve, jacobian);
}
@Override
public Set<ValueRequirement> getRequirements(
final FunctionCompilationContext compilationContext,
final ComputationTarget target,
final ValueRequirement desiredValue) {
final ValueProperties constraints = desiredValue.getConstraints();
final Set<String> rootFinderAbsoluteTolerance =
constraints.getValues(PROPERTY_ROOT_FINDER_ABSOLUTE_TOLERANCE);
if (rootFinderAbsoluteTolerance == null || rootFinderAbsoluteTolerance.size() != 1) {
return null;
}
final Set<String> rootFinderRelativeTolerance =
constraints.getValues(PROPERTY_ROOT_FINDER_RELATIVE_TOLERANCE);
if (rootFinderRelativeTolerance == null || rootFinderRelativeTolerance.size() != 1) {
return null;
}
final Set<String> maxIterations = constraints.getValues(PROPERTY_ROOT_FINDER_MAX_ITERATIONS);
if (maxIterations == null || maxIterations.size() != 1) {
return null;
}
final Set<String> decomposition = constraints.getValues(PROPERTY_DECOMPOSITION);
if (decomposition == null || decomposition.size() != 1) {
return null;
}
final Set<String> useFiniteDifference = constraints.getValues(PROPERTY_USE_FINITE_DIFFERENCE);
if (useFiniteDifference == null || useFiniteDifference.size() != 1) {
return null;
}
if (!_originalConfiguration.getTarget().equals(target.toSpecification())) {
s_logger.info(
"Invalid target, was {} - expected {}", target, _originalConfiguration.getTarget());
return null;
}
final ValueProperties properties =
ValueProperties.builder()
.with(CURVE_CALCULATION_METHOD, _originalConfiguration.getCalculationMethod())
.with(CURVE_CALCULATION_CONFIG, _originalConfiguration.getCalculationConfigName())
.with(CURVE, _originalCurveName)
.get();
return Collections.singleton(
new ValueRequirement(YIELD_CURVE, target.toSpecification(), properties));
}
/**
* Gets the properties of the implied yield curve.
*
* @param curveName The implied curve name
* @return The properties
*/
private ValueProperties getCurveProperties(
final String curveName, final String curveCalculationConfig) {
return createValueProperties()
.with(CURVE_CALCULATION_METHOD, IMPLIED_DEPOSIT)
.with(CURVE, curveName)
.with(CURVE_CALCULATION_CONFIG, curveCalculationConfig)
.withAny(PROPERTY_ROOT_FINDER_ABSOLUTE_TOLERANCE)
.withAny(PROPERTY_ROOT_FINDER_RELATIVE_TOLERANCE)
.withAny(PROPERTY_ROOT_FINDER_MAX_ITERATIONS)
.withAny(PROPERTY_DECOMPOSITION)
.withAny(PROPERTY_USE_FINITE_DIFFERENCE)
.with(InterpolatedDataProperties.X_INTERPOLATOR_NAME, _interpolatorName)
.with(InterpolatedDataProperties.LEFT_X_EXTRAPOLATOR_NAME, _leftExtrapolatorName)
.with(InterpolatedDataProperties.RIGHT_X_EXTRAPOLATOR_NAME, _rightExtrapolatorName)
.get();
}
/**
* Gets the properties of the Jacobian with no values set.
*
* @return The properties.
*/
private ValueProperties getJacobianProperties(final String curveCalculationConfig) {
return createValueProperties()
.with(CURVE_CALCULATION_METHOD, IMPLIED_DEPOSIT)
.with(CURVE_CALCULATION_CONFIG, curveCalculationConfig)
.withAny(PROPERTY_ROOT_FINDER_ABSOLUTE_TOLERANCE)
.withAny(PROPERTY_ROOT_FINDER_RELATIVE_TOLERANCE)
.withAny(PROPERTY_ROOT_FINDER_MAX_ITERATIONS)
.withAny(PROPERTY_DECOMPOSITION)
.withAny(PROPERTY_USE_FINITE_DIFFERENCE)
.with(InterpolatedDataProperties.X_INTERPOLATOR_NAME, _interpolatorName)
.with(InterpolatedDataProperties.LEFT_X_EXTRAPOLATOR_NAME, _leftExtrapolatorName)
.with(InterpolatedDataProperties.RIGHT_X_EXTRAPOLATOR_NAME, _rightExtrapolatorName)
.get();
}
}
}