Examples of com.opengamma.analytics.math.rootfinding.BisectionSingleRootFinder

Package com.opengamma.analytics.math.rootfinding

Examples of com.opengamma.analytics.math.rootfinding.BisectionSingleRootFinder

com.opengamma.analytics.math.rootfinding.BisectionSingleRootFinder
Finds a single root of a function using the bisection method.
If a root of a function $f(x)$ is bounded by two values $x_1$ and $x_2$, then $f(x_1)f(x_2) < 0$. The function is evaluated at the midpoint of these values and the bound that gives the same sign in the function evaluation is replaced. The bisection is stopped when the change in the value of $x$ is below the accuracy, or the evaluation of the function at $x$ is zero.

    if (beta == 1) {
      return forward * Math.exp(-alpha * z / nu);
    }


    final BracketRoot bracketer = new BracketRoot();
    final BisectionSingleRootFinder rootFinder = new BisectionSingleRootFinder(1e-5);


    final Function1D<Double, Double> func = new Function1D<Double, Double>() {
      @SuppressWarnings("synthetic-access")
      @Override
      public Double evaluate(final Double strike) {
        return getZ(forward, strike, alpha, beta, nu) - z;
      }
    };


    final double k = forward * Math.exp(-alpha * z / nu * Math.pow(forward, beta - 1));
    double l, h;
    if (z > 0) {
      h = k;
      l = h / 2;
    } else {
      l = k;
      h = 2 * l;
    }


    final double[] brackets = bracketer.getBracketedPoints(func, l, h, forward / 20, 20 * forward);
    return rootFinder.getRoot(func, brackets[0], brackets[1]);
  }

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    return bracketer.getBracketedPoints(func, sigma - Math.abs(change), sigma + Math.abs(change), 0, Double.POSITIVE_INFINITY);
  }


  private static double solveByBisection(final double optionPrice, final Function1D<Double, double[]> pavFunc, final double lowerSigma,
      final double upperSigma) {
    final BisectionSingleRootFinder rootFinder = new BisectionSingleRootFinder(VOL_TOL);
    final Function1D<Double, Double> func = new Function1D<Double, Double>() {


      @Override
      public Double evaluate(final Double volatility) {
        double trialPrice = pavFunc.evaluate(volatility)[0];
        return trialPrice / optionPrice - 1.0;
      }
    };
    return rootFinder.getRoot(func, lowerSigma, upperSigma);
  }

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  }


  private static double solveByBisection(final double forwardPrice, final double forward, final double strike, final double expiry, final boolean isCall, final double lowerSigma,
      final double upperSigma) {


    final BisectionSingleRootFinder rootFinder = new BisectionSingleRootFinder(VOL_TOL);
    final Function1D<Double, Double> func = new Function1D<Double, Double>() {


      @Override
      public Double evaluate(final Double volatility) {
        final double trialPrice = price(forward, strike, expiry, volatility, isCall);
        return trialPrice / forwardPrice - 1.0;
      }
    };
    return rootFinder.getRoot(func, lowerSigma, upperSigma);
  }

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    return rootFinder.getRoot(func, lowerSigma, upperSigma);
  }


  private static double solveByBisection(final SimpleOptionData[] data, final double price, final double sigma, final double change) {
    final BracketRoot bracketer = new BracketRoot();
    final BisectionSingleRootFinder rootFinder = new BisectionSingleRootFinder(EPS);
    final int n = data.length;
    final Function1D<Double, Double> func = new Function1D<Double, Double>() {


      @Override
      public Double evaluate(final Double volatility) {
        double sum = 0.0;
        for (int i = 0; i < n; i++) {
          sum += price(data[i], volatility);
        }
        return sum - price;
      }
    };
    final double[] range = bracketer.getBracketedPoints(func, sigma - Math.abs(change), sigma + Math.abs(change), 0.0, Double.POSITIVE_INFINITY);
    return rootFinder.getRoot(func, range[0], range[1]);
  }

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      if (change > 0 && change > sigma) {
        change = sigma;
      }
      if (count++ > MAX_ITERATIONS) {
        final BracketRoot bracketer = new BracketRoot();
        final BisectionSingleRootFinder rootFinder = new BisectionSingleRootFinder(EPS);
        final Function1D<Double, Double> func = new Function1D<Double, Double>() {
          @SuppressWarnings({"synthetic-access" })
          @Override
          public Double evaluate(final Double volatility) {
            final NormalFunctionData myData = new NormalFunctionData(data.getForward(), data.getNumeraire(), volatility);
            return NORMAL_PRICE_FUNCTION.getPriceFunction(option).evaluate(myData) - optionPrice;
          }
        };
        final double[] range = bracketer.getBracketedPoints(func, 0.0, 10.0);
        return rootFinder.getRoot(func, range[0], range[1]);
      }
    }
    return sigma;
  }

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        return delta;
      }
    };


    final double parSpreadFlat = new BisectionSingleRootFinder().getRoot(function, spreadLowerBound, spreadUpperBound);


    return parSpreadFlat;
  }

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  @SuppressWarnings("unused")
  private Function1D<Double, Double> getStrikeForDeltaFunction(final double forward, final double expiry, final boolean isCall,
      final Function1D<Double, Double> volFunc) {
    final BracketRoot bracketer = new BracketRoot();
    final BisectionSingleRootFinder rootFinder = new BisectionSingleRootFinder(1e-8);


    return new Function1D<Double, Double>() {


      @Override
      public Double evaluate(final Double delta) {


        final Function1D<Double, Double> deltaFunc = new Function1D<Double, Double>() {


          @Override
          public Double evaluate(final Double strike) {
            final double vol = volFunc.evaluate(strike);
            final double deltaTry = BlackFormulaRepository.delta(forward, strike, expiry, vol, isCall);
            return deltaTry - delta;
          }
        };


        final double[] brackets = bracketer.getBracketedPoints(deltaFunc, 0.5, 1.5, 0, 5);
        return rootFinder.getRoot(deltaFunc, brackets[0], brackets[1]);
      }
    };
  }

View Full Code Here

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