Examples of SABRExtrapolationRightFunction

com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction
Pricing function in the SABR model with Hagan et al. volatility function and controlled extrapolation for large strikes by extrapolation on call prices. The form of the extrapolation as a function of the strike is \begin{equation*} f(K) = K^{-\mu} \exp\left( a + \frac{b}{K} + \frac{c}{K^2} \right). \end{equation*}
Reference: Benaim, S., Dodgson, M., and Kainth, D. (2008). An arbitrage-free method for smile extrapolation. Technical report, Royal Bank of Scotland.
OpenGamma implementation note: Smile extrapolation, version 1.2, May 2011.

Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

      final double alpha = sabr.getSABRParameter().getAlpha(expiryMaturity);
      final double beta = sabr.getSABRParameter().getBeta(expiryMaturity);
      final double rho = sabr.getSABRParameter().getRho(expiryMaturity);
      final double nu = sabr.getSABRParameter().getNu(expiryMaturity);
      final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
      final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, cap.getFixingTime(), _mu);
      sabrExtrapolation.priceAdjointSABR(option, bsDsabr);
    }
    final PresentValueSABRSensitivityDataBundle sensi = new PresentValueSABRSensitivityDataBundle();
    final DoublesPair expiryMaturity = new DoublesPair(cap.getFixingTime(), maturity);
    sensi.addAlpha(expiryMaturity, cap.getNotional() * cap.getPaymentYearFraction() * df * bsDsabr[0]);
    sensi.addBeta(expiryMaturity, cap.getNotional() * cap.getPaymentYearFraction() * df * bsDsabr[1]);

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Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

    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_LONG.getFixingTime(), MU);
    final EuropeanVanillaOption option = new EuropeanVanillaOption(CAP_LONG.getStrike(), CAP_LONG.getFixingTime(), CAP_LONG.isCap());
    final double expectedPrice = sabrExtrapolation.price(option) * CAP_LONG.getNotional() * CAP_LONG.getPaymentYearFraction() * df;
    assertEquals("Cap/floor: SABR with extrapolation pricing", expectedPrice, methodPrice.getAmount(EUR), TOLERANCE_PV);
  }

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Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

    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(EUR), TOLERANCE_PV);
  }

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Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

    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_LONG.getFixingTime(), MU);
    final EuropeanVanillaOption option = new EuropeanVanillaOption(CAP_LONG.getStrike(), CAP_LONG.getFixingTime(), CAP_LONG.isCap());
    final double expectedPrice = sabrExtrapolation.price(option) * CAP_LONG.getNotional() * CAP_LONG.getPaymentYearFraction() * df;
    assertEquals("Cap/floor: SABR with extrapolation pricing", expectedPrice, methodPrice.getAmount(), 1E-2);
  }

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Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

    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);
  }

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Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

      final double alpha = sabrData.getSABRParameter().getAlpha(expiryMaturity);
      final double beta = sabrData.getSABRParameter().getBeta(expiryMaturity);
      final double rho = sabrData.getSABRParameter().getRho(expiryMaturity);
      final double nu = sabrData.getSABRParameter().getNu(expiryMaturity);
      final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
      final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
      price = discountFactorSettle * pvbp * sabrExtrapolation.price(swaption) * (swaption.isLong() ? 1.0 : -1.0);
    }
    return price;
  }

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Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

    final double alpha = sabrData.getSABRParameter().getAlpha(expiryMaturity);
    final double beta = sabrData.getSABRParameter().getBeta(expiryMaturity);
    final double rho = sabrData.getSABRParameter().getRho(expiryMaturity);
    final double nu = sabrData.getSABRParameter().getNu(expiryMaturity);
    final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
    final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
    final double price = sabrExtrapolation.price(swaption);
    result = result.multipliedBy(pvbp * price);
    result = result.plus(forwardDr.multipliedBy(discountFactorSettle * (pvbpDf * price + pvbp * sabrExtrapolation.priceDerivativeForward(swaption))));
    if (!swaption.isLong()) {
      result = result.multipliedBy(-1);
    }
    return result;
  }

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Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

    final double alpha = sabrData.getSABRParameter().getAlpha(expiryMaturity);
    final double beta = sabrData.getSABRParameter().getBeta(expiryMaturity);
    final double rho = sabrData.getSABRParameter().getRho(expiryMaturity);
    final double nu = sabrData.getSABRParameter().getNu(expiryMaturity);
    final SABRFormulaData sabrParam = new SABRFormulaData(alpha, beta, rho, nu);
    final SABRExtrapolationRightFunction sabrExtrapolation = new SABRExtrapolationRightFunction(forward, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
    final double[] priceDSabr = new double[4];
    sabrExtrapolation.priceAdjointSABR(swaption, priceDSabr);
    final double omega = (swaption.isLong() ? 1.0 : -1.0);
    sensi.addAlpha(expiryMaturity, omega * discountFactorSettle * pvbp * priceDSabr[0]);
    sensi.addBeta(expiryMaturity, omega * discountFactorSettle * pvbp * priceDSabr[1]);
    sensi.addRho(expiryMaturity, omega * discountFactorSettle * pvbp * priceDSabr[2]);
    sensi.addNu(expiryMaturity, omega * discountFactorSettle * pvbp * priceDSabr[3]);

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Examples of com.opengamma.analytics.financial.model.option.pricing.analytic.formula.SABRExtrapolationRightFunction

  public static void generateSabrData(PrintStream out) throws IOException {
    double mu;
    double strike;
    double price;
    double impliedVolatilityPct;
    SABRExtrapolationRightFunction sabrExtra;


    BlackImpliedVolatilityFormula implied = new BlackImpliedVolatilityFormula();
    BlackFunctionData blackData = new BlackFunctionData(FORWARD, 1.0, 0.0);


    out.println("Mu\tPrice\tStrike\tImpliedVolPct");


    for (int i = 0; i < MU_VALUES.length; i++) {
      mu = MU_VALUES[i];
      sabrExtra = new SABRExtrapolationRightFunction(FORWARD, SABR_DATA, CUT_OFF_STRIKE, TIME_TO_EXPIRY, mu);


      for (int p = 0; p <= N_PTS; p++) {
        strike = CUT_OFF_STRIKE - RANGE_STRIKE + p * 4.0 * RANGE_STRIKE / N_PTS;
        EuropeanVanillaOption option = new EuropeanVanillaOption(strike, TIME_TO_EXPIRY, true);
        price = sabrExtra.price(option);
        impliedVolatilityPct = implied.getImpliedVolatility(blackData, option, price) * 100;
        out.format("%4.0f\t%1.10f\t%1.10f\t%1.10f%n", mu, price, strike, impliedVolatilityPct);
      }
    }
  }

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