public virtual void negativeRates()
{
double shift = 0.05;
Surface surface = ConstantSurface.of("shfit", shift);
SabrInterestRateParameters @params = SabrInterestRateParameters.of(ALPHA_SURFACE, BETA_SURFACE, RHO_SURFACE, NU_SURFACE, surface, FORMULA);
double expiry = 2.0;
double tenor = 3.0;
assertEquals(@params.alpha(expiry, tenor), ALPHA_SURFACE.zValue(expiry, tenor));
assertEquals(@params.beta(expiry, tenor), BETA_SURFACE.zValue(expiry, tenor));
assertEquals(@params.rho(expiry, tenor), RHO_SURFACE.zValue(expiry, tenor));
assertEquals(@params.nu(expiry, tenor), NU_SURFACE.zValue(expiry, tenor));
double strike = -0.02;
double forward = 0.015;
double alpha = ALPHA_SURFACE.zValue(expiry, tenor);
double beta = BETA_SURFACE.zValue(expiry, tenor);
double rho = RHO_SURFACE.zValue(expiry, tenor);
double nu = NU_SURFACE.zValue(expiry, tenor);
assertEquals(@params.volatility(expiry, tenor, strike, forward), FORMULA.volatility(forward + shift, strike + shift, expiry, alpha, beta, rho, nu));
double[] adjCmp = @params.volatilityAdjoint(expiry, tenor, strike, forward).Derivatives.toArray();
double[] adjExp = FORMULA.volatilityAdjoint(forward + shift, strike + shift, expiry, alpha, beta, rho, nu).Derivatives.toArray();
for (int i = 0; i < 4; ++i)
{
assertEquals(adjCmp[i], adjExp[i]);
}
}
public virtual void flatVolTest()
{
double tol = 2.0e-2;
double constantVol = 0.15;
ConstantSurface impliedVolSurface = ConstantSurface.of("impliedVol", constantVol);
System.Func <double, double> zeroRate = (double?x) =>
{
return(0.05d);
};
System.Func <double, double> zeroRate1 = (double?x) =>
{
return(0.02d);
};
ImpliedTrinomialTreeLocalVolatilityCalculator calc = new ImpliedTrinomialTreeLocalVolatilityCalculator(45, 1d, INTERP_TIMESQ_LINEAR);
InterpolatedNodalSurface localVolSurface = calc.localVolatilityFromImpliedVolatility(impliedVolSurface, 100d, zeroRate, zeroRate1);
assertEquals(localVolSurface.ZValues.Where(d => !DoubleMath.fuzzyEquals(d, constantVol, tol)).Count(), 0);
}
public virtual void flatVolPriceTest()
{
double tol = 2.0e-2;
double constantVol = 0.15;
double spot = 100d;
double maxTime = 1d;
int nSteps = 9;
ConstantSurface impliedVolSurface = ConstantSurface.of("impliedVol", constantVol);
System.Func <double, double> zeroRate = (double?x) =>
{
return(0d);
};
System.Func <DoublesPair, ValueDerivatives> func = (DoublesPair x) =>
{
double price = BlackFormulaRepository.price(spot, x.Second, x.First, constantVol, true);
return(ValueDerivatives.of(price, DoubleArray.EMPTY));
};
DeformedSurface priceSurface = DeformedSurface.of(DefaultSurfaceMetadata.of("price"), impliedVolSurface, func);
ImpliedTrinomialTreeLocalVolatilityCalculator calc = new ImpliedTrinomialTreeLocalVolatilityCalculator(nSteps, maxTime, INTERP_TIMESQ_LINEAR);
InterpolatedNodalSurface localVolSurface = calc.localVolatilityFromPrice(priceSurface, spot, zeroRate, zeroRate);
assertEquals(localVolSurface.ZValues.Where(d => !DoubleMath.fuzzyEquals(d, constantVol, tol)).Count(), 0);
}
//-------------------------------------------------------------------------
public virtual void test_presentValueSensitivity()
{
PointSensitivityBuilder pointCaplet = PRICER.presentValueSensitivityRatesStickyModel(CAPLET_LONG, RATES, VOLS);
CurrencyParameterSensitivities computedCaplet = RATES.parameterSensitivity(pointCaplet.build());
PointSensitivityBuilder pointFloorlet = PRICER.presentValueSensitivityRatesStickyModel(FLOORLET_SHORT, RATES, VOLS);
CurrencyParameterSensitivities computedFloorlet = RATES.parameterSensitivity(pointFloorlet.build());
CurrencyParameterSensitivities expectedCaplet = FD_CAL.sensitivity(RATES, p => PRICER_BASE.presentValue(CAPLET_LONG, p, VOLS));
CurrencyParameterSensitivities expectedFloorlet = FD_CAL.sensitivity(RATES, p => PRICER_BASE.presentValue(FLOORLET_SHORT, p, VOLS));
assertTrue(computedCaplet.equalWithTolerance(expectedCaplet, EPS_FD * NOTIONAL * 50d));
assertTrue(computedFloorlet.equalWithTolerance(expectedFloorlet, EPS_FD * NOTIONAL * 50d));
// consistency with shifted Black
PointSensitivityBuilder pointCapletBase = PRICER.presentValueSensitivityRates(CAPLET_LONG, RATES, VOLS);
PointSensitivityBuilder pointFloorletBase = PRICER.presentValueSensitivityRates(FLOORLET_SHORT, RATES, VOLS);
double forward = RATES.iborIndexRates(EUR_EURIBOR_3M).rate(RATE_COMP.Observation);
double expiry = VOLS.relativeTime(CAPLET_LONG.FixingDateTime);
double volatility = VOLS.volatility(expiry, STRIKE, forward);
ShiftedBlackIborCapletFloorletExpiryStrikeVolatilities vols = ShiftedBlackIborCapletFloorletExpiryStrikeVolatilities.of(EUR_EURIBOR_3M, VALUATION, ConstantSurface.of("constVol", volatility).withMetadata(Surfaces.blackVolatilityByExpiryStrike("costVol", DayCounts.ACT_ACT_ISDA)), IborCapletFloorletSabrRateVolatilityDataSet.CURVE_CONST_SHIFT);
PointSensitivityBuilder pointCapletExp = PRICER_BASE.presentValueSensitivityRates(CAPLET_LONG, RATES, vols);
PointSensitivityBuilder pointFloorletExp = PRICER_BASE.presentValueSensitivityRates(FLOORLET_SHORT, RATES, vols);
assertEquals(pointCapletBase, pointCapletExp);
assertEquals(pointFloorletBase, pointFloorletExp);
}
//-------------------------------------------------------------------------
public virtual void test_presentValue_formula()
{
CurrencyAmount computedCaplet = PRICER.presentValue(CAPLET_LONG, RATES, VOLS);
CurrencyAmount computedFloorlet = PRICER.presentValue(FLOORLET_SHORT, RATES, VOLS);
double forward = RATES.iborIndexRates(EUR_EURIBOR_3M).rate(RATE_COMP.Observation);
double expiry = VOLS.relativeTime(CAPLET_LONG.FixingDateTime);
double volatility = VOLS.volatility(expiry, STRIKE, forward);
double df = RATES.discountFactor(EUR, CAPLET_LONG.PaymentDate);
double expectedCaplet = NOTIONAL * df * CAPLET_LONG.YearFraction * BlackFormulaRepository.price(forward + SHIFT, STRIKE + SHIFT, expiry, volatility, CALL.Call);
double expectedFloorlet = -NOTIONAL *df *FLOORLET_SHORT.YearFraction *BlackFormulaRepository.price(forward + SHIFT, STRIKE + SHIFT, expiry, volatility, PUT.Call);
assertEquals(computedCaplet.Currency, EUR);
assertEquals(computedCaplet.Amount, expectedCaplet, NOTIONAL * TOL);
assertEquals(computedFloorlet.Currency, EUR);
assertEquals(computedFloorlet.Amount, expectedFloorlet, NOTIONAL * TOL);
// consistency with shifted Black
ShiftedBlackIborCapletFloorletExpiryStrikeVolatilities vols = ShiftedBlackIborCapletFloorletExpiryStrikeVolatilities.of(EUR_EURIBOR_3M, VALUATION, ConstantSurface.of("constVol", volatility).withMetadata(Surfaces.blackVolatilityByExpiryStrike("costVol", DayCounts.ACT_ACT_ISDA)), IborCapletFloorletSabrRateVolatilityDataSet.CURVE_CONST_SHIFT);
CurrencyAmount computedCapletBlack = PRICER_BASE.presentValue(CAPLET_LONG, RATES, vols);
CurrencyAmount computedFloorletBlack = PRICER_BASE.presentValue(FLOORLET_SHORT, RATES, vols);
assertEquals(computedCaplet.Amount, computedCapletBlack.Amount, NOTIONAL * TOL);
assertEquals(computedFloorlet.Amount, computedFloorletBlack.Amount, NOTIONAL * TOL);
}
