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 = 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(forwardModified, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
    return pvbpModified * sabrExtrapolation.price(option) * (swaption.isLong() ? 1.0 : -1.0);
  }

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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(forwardModified, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
    InterestRateCurveSensitivity result = pvbpModifiedDr.multipliedBy(sabrExtrapolation.price(option));
    final double priceDF = sabrExtrapolation.priceDerivativeForward(option);
    result = result.plus(forwardModifiedDr.multipliedBy(pvbpModified * priceDF));
    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(forwardModified, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
    final double[] priceDSabr = new double[4];
    sabrExtrapolation.priceAdjointSABR(option, priceDSabr);
    final double omega = (swaption.isLong() ? 1.0 : -1.0);
    sensi.addAlpha(expiryMaturity, omega * pvbpModified * priceDSabr[0]);
    sensi.addBeta(expiryMaturity, omega * pvbpModified * priceDSabr[1]);
    sensi.addRho(expiryMaturity, omega * pvbpModified * priceDSabr[2]);
    sensi.addNu(expiryMaturity, omega * pvbpModified * priceDSabr[3]);

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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(forwardModified, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
    return MultipleCurrencyAmount.of(ccy, pvbpModified * sabrExtrapolation.price(option) * (swaption.isLong() ? 1.0 : -1.0));
  }

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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(forwardModified, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
    MulticurveSensitivity result = pvbpModifiedDr.multipliedBy(sabrExtrapolation.price(option));
    final double priceDF = sabrExtrapolation.priceDerivativeForward(option);
    result = result.plus(forwardModifiedDr.multipliedBy(pvbpModified * priceDF));
    if (!swaption.isLong()) {
      result = result.multipliedBy(-1);
    }
    return MultipleCurrencyMulticurveSensitivity.of(ccy, 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(forwardModified, sabrParam, _cutOffStrike, swaption.getTimeToExpiry(), _mu);
    final double[] priceDSabr = new double[4];
    sabrExtrapolation.priceAdjointSABR(option, priceDSabr);
    final double omega = (swaption.isLong() ? 1.0 : -1.0);
    sensi.addAlpha(expiryMaturity, omega * pvbpModified * priceDSabr[0]);
    sensi.addBeta(expiryMaturity, omega * pvbpModified * priceDSabr[1]);
    sensi.addRho(expiryMaturity, omega * pvbpModified * priceDSabr[2]);
    sensi.addNu(expiryMaturity, omega * pvbpModified * priceDSabr[3]);

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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);
      pv = discountFactorSettle * pvbp * sabrExtrapolation.price(swaption) * (swaption.isLong() ? 1.0 : -1.0);
    }
    return MultipleCurrencyAmount.of(ccy, pv);
  }

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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 MultipleCurrencyMulticurveSensitivity.of(ccy, 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

    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;

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