Package com.opengamma.analytics.financial.model.volatility

Examples of com.opengamma.analytics.financial.model.volatility.NormalImpliedVolatilityFormula

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  @Test
  /**
   * Approximation analysis.
   */
  public void presentValueApproximationAnalysis() {
    final NormalImpliedVolatilityFormula implied = new NormalImpliedVolatilityFormula();
    final int nbStrike = 20;
    final double[] pvExplicit = new double[nbStrike + 1];
    final double[] pvApproximation = new double[nbStrike + 1];
    final double[] strike = new double[nbStrike + 1];
    final double[] volExplicit = new double[nbStrike + 1];
    final double[] volApprox = new double[nbStrike + 1];
    final double strikeRange = 0.010;
    final SwapFixedCoupon<Coupon> swap = SWAP_PAYER_DEFINITION.toDerivative(REFERENCE_DATE);
    final double forward = swap.accept(PRDC, MULTICURVES);
    final double pvbp = METHOD_SWAP.presentValueBasisPoint(swap, MULTICURVES);
    for (int loopstrike = 0; loopstrike <= nbStrike; loopstrike++) {
      strike[loopstrike] = forward - strikeRange + 3 * strikeRange * loopstrike / nbStrike; // From forward-strikeRange to forward+2*strikeRange
      final SwapFixedIborDefinition swapDefinition = SwapFixedIborDefinition.from(SETTLEMENT_DATE, SWAP_TENOR, EUR1YEURIBOR6M, NOTIONAL, strike[loopstrike], FIXED_IS_PAYER);
      final SwaptionPhysicalFixedIborDefinition swaptionDefinition = SwaptionPhysicalFixedIborDefinition.from(EXPIRY_DATE, swapDefinition, IS_LONG);
      final SwaptionPhysicalFixedIbor swaption = swaptionDefinition.toDerivative(REFERENCE_DATE);
      pvExplicit[loopstrike] = METHOD_HW.presentValue(swaption, HW_MULTICURVES).getAmount(EUR);
      pvApproximation[loopstrike] = METHOD_HW_APPROXIMATION.presentValue(swaption, HW_MULTICURVES).getAmount(EUR);
      final NormalFunctionData data = new NormalFunctionData(forward, pvbp, 0.01);
      volExplicit[loopstrike] = implied.getImpliedVolatility(data, swaption, pvExplicit[loopstrike]);
      volApprox[loopstrike] = implied.getImpliedVolatility(data, swaption, pvApproximation[loopstrike]);
      assertEquals("Swaption physical - Hull-White - implied volatility - explicit/approximation", volExplicit[loopstrike], volApprox[loopstrike], 1.0E-3); // 0.10%
    }
  }
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    final CapFloorCMSSpreadSABRBinormalMethod method = new CapFloorCMSSpreadSABRBinormalMethod(correlationFunction, METHOD_CMS_CAP, METHOD_CMS_COUPON);
    final double cmsSpreadPrice = method.presentValue(CMS_CAP_SPREAD, SABR_BUNDLE).getAmount();
    final double discountFactorPayment = CURVES.getCurve(FUNDING_CURVE_NAME).getDiscountFactor(PAYMENT_TIME);
    final CouponCMSSABRReplicationMethod methodCms = CouponCMSSABRReplicationMethod.getInstance();
    final CapFloorCMSSABRReplicationMethod methodCmsCap = CapFloorCMSSABRReplicationMethod.getDefaultInstance();
    final NormalImpliedVolatilityFormula impliedVolatility = new NormalImpliedVolatilityFormula();
    final NormalPriceFunction normalPrice = new NormalPriceFunction();
    final ParRateCalculator parRate = ParRateCalculator.getInstance();
    final CouponCMS cmsCoupon1 = CouponCMS.from(CMS_CAP_SPREAD, SWAP_1, SETTLEMENT_TIME);
    final CouponCMS cmsCoupon2 = CouponCMS.from(CMS_CAP_SPREAD, SWAP_2, SETTLEMENT_TIME);
    final double cmsCoupon1Price = methodCms.presentValue(cmsCoupon1, SABR_BUNDLE).getAmount();
    final double cmsCoupon2Price = methodCms.presentValue(cmsCoupon2, SABR_BUNDLE).getAmount();
    final double expectedRate1 = cmsCoupon1Price / discountFactorPayment / cmsCoupon1.getNotional() / cmsCoupon1.getPaymentYearFraction();
    final double expectedRate2 = cmsCoupon2Price / discountFactorPayment / cmsCoupon2.getNotional() / cmsCoupon2.getPaymentYearFraction();
    final double forward1 = SWAP_1.accept(parRate, CURVES);
    final double forward2 = SWAP_2.accept(parRate, CURVES);
    final CapFloorCMS cmsCap1 = CapFloorCMS.from(cmsCoupon1, forward1, true);
    final CapFloorCMS cmsCap2 = CapFloorCMS.from(cmsCoupon2, forward2, true);
    final double cmsCap1Price = methodCmsCap.presentValue(cmsCap1, SABR_BUNDLE).getAmount();
    final double cmsCap2Price = methodCmsCap.presentValue(cmsCap2, SABR_BUNDLE).getAmount();
    final EuropeanVanillaOption optionCap1 = new EuropeanVanillaOption(forward1, FIXING_TIME, true);
    final NormalFunctionData dataCap1 = new NormalFunctionData(expectedRate1, 1.0, 0.0);
    final double cmsCap1IV = impliedVolatility.getImpliedVolatility(dataCap1, optionCap1, cmsCap1Price / discountFactorPayment / cmsCoupon1.getNotional() / cmsCoupon1.getPaymentYearFraction());
    final EuropeanVanillaOption optionCap2 = new EuropeanVanillaOption(forward2, FIXING_TIME, true);
    final NormalFunctionData dataCap2 = new NormalFunctionData(expectedRate2, 1.0, 0.0);
    final double cmsCap2IV = impliedVolatility.getImpliedVolatility(dataCap2, optionCap2, cmsCap2Price / discountFactorPayment / cmsCoupon2.getNotional() / cmsCoupon2.getPaymentYearFraction());
    double spreadVol = cmsCap1IV * cmsCap1IV - 2 * correlation * cmsCap1IV * cmsCap2IV + cmsCap2IV * cmsCap2IV;
    spreadVol = Math.sqrt(spreadVol);
    final EuropeanVanillaOption optionSpread = new EuropeanVanillaOption(STRIKE, FIXING_TIME, IS_CAP);
    final NormalFunctionData dataSpread = new NormalFunctionData(expectedRate1 - expectedRate2, 1.0, spreadVol);
    final Function1D<NormalFunctionData, Double> priceFunction = normalPrice.getPriceFunction(optionSpread);
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    final double[][][] volApprox = new double[nbExpiry][nbTenor][nbStrike];
    final double[][][] pvNI = new double[nbExpiry][nbTenor][nbStrike];
    final double[][][] volNI = new double[nbExpiry][nbTenor][nbStrike];
    final double[][][] pvDiff = new double[nbExpiry][nbTenor][nbStrike];
    final double[][][] volDiff = new double[nbExpiry][nbTenor][nbStrike];
    final NormalImpliedVolatilityFormula implied = new NormalImpliedVolatilityFormula(); // Normal vol: LogNormal vol not always well defined with G2++ prices
    for (int loopexp = 0; loopexp < nbExpiry; loopexp++) {
      for (int loopten = 0; loopten < nbTenor; loopten++) {
        for (int loopstrike = 0; loopstrike < nbStrike; loopstrike++) {
          pvApprox[loopexp][loopten][loopstrike] = METHOD_G2PP_APPROXIMATION.presentValue(swaption[loopexp][loopten][loopstrike], bundleG2pp).getAmount(CUR);
          pvNI[loopexp][loopten][loopstrike] = METHOD_G2PP_NI.presentValue(swaption[loopexp][loopten][loopstrike], bundleG2pp).getAmount(CUR);
          pvDiff[loopexp][loopten][loopstrike] = pvApprox[loopexp][loopten][loopstrike] - pvNI[loopexp][loopten][loopstrike];
          final double pvbp = METHOD_SWAP.presentValueBasisPoint(swaption[loopexp][loopten][loopstrike].getUnderlyingSwap(), MULTICURVES);
          final double forward = swaption[loopexp][loopten][loopstrike].getUnderlyingSwap().accept(PRDC, MULTICURVES);
          final NormalFunctionData data = new NormalFunctionData(forward, pvbp, 0.01);
          volApprox[loopexp][loopten][loopstrike] = implied.getImpliedVolatility(data, swaption[loopexp][loopten][loopstrike], pvApprox[loopexp][loopten][loopstrike]);
          volNI[loopexp][loopten][loopstrike] = implied.getImpliedVolatility(data, swaption[loopexp][loopten][loopstrike], pvNI[loopexp][loopten][loopstrike]);
          volDiff[loopexp][loopten][loopstrike] = (volApprox[loopexp][loopten][loopstrike] - volNI[loopexp][loopten][loopstrike]) / BP1; // In bp
        }
      }
    }
    for (int loopexp = 0; loopexp < nbExpiry; loopexp++) {
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    final CapFloorCMSSpreadSABRBinormalMethod method = new CapFloorCMSSpreadSABRBinormalMethod(correlationFunction, METHOD_CMS_CAP, METHOD_CMS_COUPON);
    final double cmsSpreadPrice = method.presentValue(CMS_CAP_SPREAD, SABR_MULTICURVES).getAmount(EUR);
    final double discountFactorPayment = MULTICURVES.getDiscountFactor(EUR, PAYMENT_TIME);
    final CouponCMSSABRReplicationMethod methodCms = CouponCMSSABRReplicationMethod.getInstance();
    final CapFloorCMSSABRReplicationMethod methodCmsCap = CapFloorCMSSABRReplicationMethod.getDefaultInstance();
    final NormalImpliedVolatilityFormula impliedVolatility = new NormalImpliedVolatilityFormula();
    final NormalPriceFunction normalPrice = new NormalPriceFunction();
    final CouponCMS cmsCoupon1 = CouponCMS.from(CMS_CAP_SPREAD, SWAP_1, SETTLEMENT_TIME);
    final CouponCMS cmsCoupon2 = CouponCMS.from(CMS_CAP_SPREAD, SWAP_2, SETTLEMENT_TIME);
    final double cmsCoupon1Price = methodCms.presentValue(cmsCoupon1, SABR_MULTICURVES).getAmount(EUR);
    final double cmsCoupon2Price = methodCms.presentValue(cmsCoupon2, SABR_MULTICURVES).getAmount(EUR);
    final double expectedRate1 = cmsCoupon1Price / discountFactorPayment / cmsCoupon1.getNotional() / cmsCoupon1.getPaymentYearFraction();
    final double expectedRate2 = cmsCoupon2Price / discountFactorPayment / cmsCoupon2.getNotional() / cmsCoupon2.getPaymentYearFraction();
    final double forward1 = SWAP_1.accept(PRDC, MULTICURVES);
    final double forward2 = SWAP_2.accept(PRDC, MULTICURVES);
    final CapFloorCMS cmsCap1 = CapFloorCMS.from(cmsCoupon1, forward1, true);
    final CapFloorCMS cmsCap2 = CapFloorCMS.from(cmsCoupon2, forward2, true);
    final double cmsCap1Price = methodCmsCap.presentValue(cmsCap1, SABR_MULTICURVES).getAmount(EUR);
    final double cmsCap2Price = methodCmsCap.presentValue(cmsCap2, SABR_MULTICURVES).getAmount(EUR);
    final EuropeanVanillaOption optionCap1 = new EuropeanVanillaOption(forward1, FIXING_TIME, true);
    final NormalFunctionData dataCap1 = new NormalFunctionData(expectedRate1, 1.0, 0.0);
    final double cmsCap1IV = impliedVolatility.getImpliedVolatility(dataCap1, optionCap1, cmsCap1Price / discountFactorPayment / cmsCoupon1.getNotional() / cmsCoupon1.getPaymentYearFraction());
    final EuropeanVanillaOption optionCap2 = new EuropeanVanillaOption(forward2, FIXING_TIME, true);
    final NormalFunctionData dataCap2 = new NormalFunctionData(expectedRate2, 1.0, 0.0);
    final double cmsCap2IV = impliedVolatility.getImpliedVolatility(dataCap2, optionCap2, cmsCap2Price / discountFactorPayment / cmsCoupon2.getNotional() / cmsCoupon2.getPaymentYearFraction());
    double spreadVol = cmsCap1IV * cmsCap1IV - 2 * correlation * cmsCap1IV * cmsCap2IV + cmsCap2IV * cmsCap2IV;
    spreadVol = Math.sqrt(spreadVol);
    final EuropeanVanillaOption optionSpread = new EuropeanVanillaOption(STRIKE, FIXING_TIME, IS_CAP);
    final NormalFunctionData dataSpread = new NormalFunctionData(expectedRate1 - expectedRate2, 1.0, spreadVol);
    final Function1D<NormalFunctionData, Double> priceFunction = normalPrice.getPriceFunction(optionSpread);
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