@Test
/** Test the present value using the method with the direct formula with extrapolation. */
public void presentValueAboveCutOff() {
CurrencyAmount methodPrice = METHOD.presentValue(CAP_HIGH_LONG, SABR_BUNDLE);
final double df =
CURVES.getCurve(FUNDING_CURVE_NAME).getDiscountFactor(CAP_HIGH_LONG.getPaymentTime());
final double forward = CAP_HIGH_LONG.accept(PRC, CURVES);
final double maturity =
CAP_HIGH_LONG.getFixingPeriodEndTime() - CAP_LONG.getFixingPeriodStartTime();
final DoublesPair expiryMaturity = new DoublesPair(CAP_HIGH_LONG.getFixingTime(), maturity);
final double alpha = SABR_PARAMETERS.getAlpha(expiryMaturity);
final double beta = SABR_PARAMETERS.getBeta(expiryMaturity);
final double rho = SABR_PARAMETERS.getRho(expiryMaturity);
final double nu = SABR_PARAMETERS.getNu(expiryMaturity);
final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
final SABRExtrapolationRightFunction sabrExtrapolation =
new SABRExtrapolationRightFunction(
forward, sabrParam, CUT_OFF_STRIKE, CAP_HIGH_LONG.getFixingTime(), MU);
final EuropeanVanillaOption option =
new EuropeanVanillaOption(
CAP_HIGH_LONG.getStrike(), CAP_HIGH_LONG.getFixingTime(), CAP_HIGH_LONG.isCap());
final double expectedPrice =
sabrExtrapolation.price(option)
* CAP_HIGH_LONG.getNotional()
* CAP_HIGH_LONG.getPaymentYearFraction()
* df;
assertEquals(
"Cap/floor: SABR with extrapolation pricing", expectedPrice, methodPrice.getAmount(), 1E-2);
methodPrice = METHOD.presentValue(CAP_HIGH_LONG, SABR_BUNDLE);
assertEquals(
"Cap/floor: SABR with extrapolation pricing", expectedPrice, methodPrice.getAmount(), 1E-2);
}
/**
* Computes the present value of an Ibor cap/floor in arrears by replication based on the paper,
* "Swap and Cap/Floors with Fixing in Arrears or Payment Delay," OpenGamma Quantitative
* Documentation
* http://developers.opengamma.com/quantitative-research/In-Arrears-and-Payment-Delay-Swaps-and-Caps-OpenGamma.pdf
*
* @param cap The cap/floor
* @param curves The curves
* @return The present value
*/
public MultipleCurrencyAmount presentValue(
final CapFloorIbor cap, final MulticurveProviderInterface curves) {
ArgumentChecker.notNull(cap, "The cap/floor shoud not be null");
ArgumentChecker.notNull(curves, "curves");
final Currency ccy = cap.getCurrency();
// Construct a "standard" CapFloorIbor whose paymentTime is set to be fixingPeriodEndTime
CapFloorIbor capStandard =
new CapFloorIbor(
cap.getCurrency(),
cap.getFixingPeriodEndTime(),
cap.getPaymentYearFraction(),
cap.getNotional(),
cap.getFixingTime(),
cap.getIndex(),
cap.getFixingPeriodStartTime(),
cap.getFixingPeriodEndTime(),
cap.getFixingAccrualFactor(),
cap.getStrike(),
cap.isCap());
final double forward =
curves.getSimplyCompoundForwardRate(
cap.getIndex(),
cap.getFixingPeriodStartTime(),
cap.getFixingPeriodEndTime(),
cap.getFixingAccrualFactor());
final double beta =
(1.0 + cap.getFixingAccrualFactor() * forward)
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
final double df =
curves.getDiscountFactor(capStandard.getCurrency(), capStandard.getPaymentTime());
final double strikePart =
(1.0 + cap.getFixingAccrualFactor() * capStandard.getStrike())
* presentValueStandard(
forward,
capStandard.getStrike(),
capStandard.getFixingTime(),
capStandard.isCap(),
df,
capStandard.getNotional(),
capStandard.getPaymentYearFraction());
final InArrearsIntegrant integrant = new InArrearsIntegrant(capStandard, curves);
double integralPart;
try {
if (cap.isCap()) {
double atmVol = _smileFunction.getVolatility(forward);
double upper = forward * Math.exp(6.0 * atmVol * Math.sqrt(cap.getFixingTime()));
double strike = cap.getStrike();
integralPart = INTEGRATOR.integrate(integrant, strike, upper);
double reminder = integrant.evaluate(upper) * upper;
double error = reminder / integralPart;
int count = 0;
while (Math.abs(error) > REL_ERROR && count < MAX_COUNT) {
integralPart += INTEGRATOR.integrate(integrant, upper, 2.0 * upper);
upper *= 2.0;
// The increase of integralPart in the next loop is bounded by reminder
reminder = integrant.evaluate(upper) * upper;
error = reminder / integralPart;
++count;
if (count == MAX_COUNT) {
LOGGER.info(
"Maximum iteration count, "
+ MAX_COUNT
+ ", has been reached. Relative error is greater than "
+ REL_ERROR);
}
}
} else {
double strike = cap.getStrike();
integralPart = INTEGRATOR.integrate(integrant, REL_TOL * strike, strike);
}
} catch (final Exception e) {
throw new MathException(e);
}
integralPart *= 2.0 * cap.getFixingAccrualFactor();
final double pv = (strikePart + integralPart) / beta;
return MultipleCurrencyAmount.of(cap.getCurrency(), pv);
}
/**
* Computes the pv sensitivity of an Ibor cap/floor in arrears
*
* @param cap The cap/floor
* @param curves The curves
* @return The sensitivity
*/
public MultipleCurrencyMulticurveSensitivity presentValueCurveSensitivity(
final CapFloorIbor cap, final MulticurveProviderInterface curves) {
ArgumentChecker.notNull(cap, "The cap/floor shoud not be null");
ArgumentChecker.notNull(curves, "curves");
final Currency ccy = cap.getCurrency();
// Construct a "standard" CapFloorIbor whose paymentTime is set to be fixingPeriodEndTime
CapFloorIbor capStandard =
new CapFloorIbor(
cap.getCurrency(),
cap.getFixingPeriodEndTime(),
cap.getPaymentYearFraction(),
cap.getNotional(),
cap.getFixingTime(),
cap.getIndex(),
cap.getFixingPeriodStartTime(),
cap.getFixingPeriodEndTime(),
cap.getFixingAccrualFactor(),
cap.getStrike(),
cap.isCap());
final double forward =
curves.getSimplyCompoundForwardRate(
cap.getIndex(),
cap.getFixingPeriodStartTime(),
cap.getFixingPeriodEndTime(),
cap.getFixingAccrualFactor());
final double beta =
(1.0 + cap.getFixingAccrualFactor() * forward)
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
double df = curves.getDiscountFactor(capStandard.getCurrency(), capStandard.getPaymentTime());
double strikePart =
(1.0 + cap.getFixingAccrualFactor() * capStandard.getStrike())
* presentValueStandard(
forward,
capStandard.getStrike(),
capStandard.getFixingTime(),
capStandard.isCap(),
df,
capStandard.getNotional(),
capStandard.getPaymentYearFraction());
double strikePartDelta =
(1.0 + cap.getFixingAccrualFactor() * capStandard.getStrike())
* presentValueDeltaStandard(
forward,
capStandard.getStrike(),
capStandard.getFixingTime(),
capStandard.isCap(),
df,
capStandard.getNotional(),
capStandard.getPaymentYearFraction());
final InArrearsIntegrant integrant = new InArrearsIntegrant(capStandard, curves);
double integralPart;
double upper = 0.0;
try {
if (cap.isCap()) {
double atmVol = _smileFunction.getVolatility(forward);
upper = forward * Math.exp(6.0 * atmVol * Math.sqrt(cap.getFixingTime()));
double strike = cap.getStrike();
integralPart = INTEGRATOR.integrate(integrant, strike, upper);
double reminder = integrant.evaluate(upper) * upper;
double error = reminder / integralPart;
int count = 0;
while (Math.abs(error) > REL_ERROR && count < MAX_COUNT) {
integralPart += INTEGRATOR.integrate(integrant, upper, 2.0 * upper);
upper *= 2.0;
// The increase of integralPart in the next loop is bounded by reminder
reminder = integrant.evaluate(upper) * upper;
error = reminder / integralPart;
++count;
if (count == MAX_COUNT) {
LOGGER.info(
"Maximum iteration count, "
+ MAX_COUNT
+ ", has been reached. Relative error is greater than "
+ REL_ERROR);
}
}
} else {
double strike = cap.getStrike();
integralPart = INTEGRATOR.integrate(integrant, REL_TOL * strike, strike);
}
} catch (final Exception e) {
throw new MathException(e);
}
integralPart *= 2.0 * cap.getFixingAccrualFactor();
double pv = (strikePart + integralPart) / beta;
double betaFwd =
cap.getFixingAccrualFactor()
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
double betaDscStart =
(1.0 + cap.getFixingAccrualFactor() * forward)
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
* cap.getFixingPeriodStartTime()
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
double betaDscEnd =
-(1.0 + cap.getFixingAccrualFactor() * forward)
* curves.getDiscountFactor(ccy, cap.getFixingPeriodEndTime())
* cap.getFixingPeriodEndTime()
/ curves.getDiscountFactor(ccy, cap.getFixingPeriodStartTime());
List<DoublesPair> listDiscounting = new ArrayList<>();
double strikePartDsc = -capStandard.getPaymentTime() * strikePart;
double integralPartDsc = -capStandard.getPaymentTime() * integralPart;
listDiscounting.add(
DoublesPair.of(capStandard.getPaymentTime(), (strikePartDsc + integralPartDsc) / beta));
listDiscounting.add(DoublesPair.of(cap.getFixingPeriodStartTime(), -pv * betaDscStart / beta));
listDiscounting.add(DoublesPair.of(cap.getFixingPeriodEndTime(), -pv * betaDscEnd / beta));
Map<String, List<DoublesPair>> mapDsc = new HashMap<>();
mapDsc.put(curves.getName(capStandard.getCurrency()), listDiscounting);
final List<ForwardSensitivity> listForward = new ArrayList<>();
double strikePartFwd = strikePartDelta;
double integralPartFwd = 0.0;
final InArrearsDeltaIntegrant integrantFwd = new InArrearsDeltaIntegrant(capStandard, curves);
try {
if (cap.isCap()) {
double strike = cap.getStrike();
integralPartFwd = INTEGRATOR.integrate(integrantFwd, strike, upper);
} else {
double strike = cap.getStrike();
integralPartFwd = INTEGRATOR.integrate(integrantFwd, REL_TOL * strike, strike);
}
} catch (final Exception e) {
throw new MathException(e);
}
integralPartFwd *= 2.0 * cap.getFixingAccrualFactor();
listForward.add(
new SimplyCompoundedForwardSensitivity(
capStandard.getFixingPeriodStartTime(),
capStandard.getFixingPeriodEndTime(),
capStandard.getFixingAccrualFactor(),
(strikePartFwd + integralPartFwd - pv * betaFwd) / beta));
Map<String, List<ForwardSensitivity>> mapFwd = new HashMap<>();
mapFwd.put(curves.getName(capStandard.getIndex()), listForward);
return MultipleCurrencyMulticurveSensitivity.of(
cap.getCurrency(), MulticurveSensitivity.of(mapDsc, mapFwd));
}
