Examples of NeumannBoundaryCondition

com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition
Neumann boundary condition, i.e. du/dx(A,t) = f(t), where A is the boundary level, and f(t) is some specified function of time

Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition

    //evaluate the log-payoff on a nominally six sigma range
    final double atmVol = pureLocalVolSurface.getVolatility(expiry, 1.0);
    final double yMin = -Math.sqrt(expiry) * atmVol * SIGMA;
    final double yMax = -yMin;


    final BoundaryCondition lower = new NeumannBoundaryCondition(getLowerBoundaryCondition(divs, expiry), yMin, true);
    final BoundaryCondition upper = new NeumannBoundaryCondition(1.0, yMax, false);


    final MeshingFunction timeMesh = new ExponentialMeshing(0, expiry, _nTimeSteps, LAMBDA_T);
    final MeshingFunction spaceMesh = new ExponentialMeshing(yMin, yMax, _nSpaceSteps, LAMBDA_X);


    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition


    final LocalVolatilitySurfaceMoneyness localVolSurface = new LocalVolatilitySurfaceMoneyness(plv.getSurface(), new ForwardCurve(1.0));
    final ConvectionDiffusionPDE1DStandardCoefficients pde = PDE_PROVIDER.getLogBackwardsLocalVol(tau, localVolSurface);
    final Function1D<Double, Double> initalCond = getCorrectionInitialCondition(ad, curves, index, correctForDividends);


    final BoundaryCondition lower = new NeumannBoundaryCondition(getCorrectionLowerBoundaryCondition(ad, curves, index, correctForDividends, index), yMin, true);
    final BoundaryCondition upper = new NeumannBoundaryCondition(0.0, yMax, false);


    final MeshingFunction timeMesh = new ExponentialMeshing(0, tau, _nTimeSteps, LAMBDA_T);
    final MeshingFunction spaceMesh = new HyperbolicMeshing(yMin, yMax, 0.0, _nSpaceSteps, LAMBDA_X);


    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition

    final double sMax = 5 * S0;
    final MeshingFunction xMesh = new ExponentialMeshing(sMin, sMax, xNodes, 0.0, new double[] {S0 });
    final MeshingFunction tMesh = new ExponentialMeshing(0, T, tNodes, 0.0);
    final PDEGrid1D grid = new PDEGrid1D(tMesh, xMesh);


    final BoundaryCondition lower = new NeumannBoundaryCondition(0.0, sMin, true);
    final BoundaryCondition upper = new NeumannBoundaryCondition(0.0, sMax, true);
    final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, payoff, lower, upper, grid);
    final ThetaMethodFiniteDifference solver = new ThetaMethodFiniteDifference();
    final PDEResults1D res = solver.solve(data);
    final int index = Arrays.binarySearch(grid.getSpaceNodes(), S0);
    final double pdePrice = res.getFunctionValue(index);

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition

      //call option with low strike  is worth the forward - strike, while a put is worthless
      lower = new DirichletBoundaryCondition((1.0 - minMoneyness), minMoneyness);
      upper = new DirichletBoundaryCondition(0.0, maxMoneyness);
    } else {
      lower = new DirichletBoundaryCondition(0.0, minMoneyness);
      upper = new NeumannBoundaryCondition(1.0, maxMoneyness, false);
    }


    final MeshingFunction timeMesh = new ExponentialMeshing(0.0, maxT, nTimeSteps, timeMeshLambda);


    final MeshingFunction spaceMesh = new HyperbolicMeshing(minMoneyness, maxMoneyness, centreMoneyness, nStrikeSteps, strikeMeshBunching);

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition


    BoundaryCondition lower;
    BoundaryCondition upper;
    if (isCall) {
      lower = new DirichletBoundaryCondition(0.0, 0.0); //call option with strike zero is worth 0
      upper = new NeumannBoundaryCondition(1.0, maxFwd, false);
    } else {
      lower = new DirichletBoundaryCondition(strike, 0.0);
      upper = new NeumannBoundaryCondition(0.0, maxFwd, false);
    }


    // MeshingFunction timeMesh = new ExponentialMeshing(0.0, expiry, nTimeNodes, timeMeshLambda);
    final MeshingFunction timeMesh = new DoubleExponentialMeshing(0, expiry, expiry / 2, nTimeNodes, timeMeshLambda, -timeMeshLambda);
    //keep the grid the same regardless of spot (useful for finite-difference)

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition


    final ForwardCurve fwdCurve = new ForwardCurve(1.0);
    final double xL = 0.0;
    final double xH = 4;
    final BoundaryCondition lower = new DirichletBoundaryCondition(1.0, xL);
    final BoundaryCondition upper = new NeumannBoundaryCondition(0.0, xH, false);
    final MeshingFunction spaceMesh = new HyperbolicMeshing(xL, xH, 1.0, 40, 0.05);
    final MeshingFunction timeMesh = new ExponentialMeshing(0, 2.0, 30, 0.2);
    final PDEGrid1D pdeGrid = new PDEGrid1D(timeMesh, spaceMesh);
    final Function1D<Double, Double> initialCond = INITIAL_COND_PROVIDER.getForwardCallPut(true);
    final double[] xa = new double[] {0, 0 };

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition


    final ForwardCurve fwdCurve = new ForwardCurve(1.0);
    final double xL = 0.0;
    final double xH = 6;
    final BoundaryCondition lower = new DirichletBoundaryCondition(1.0, xL);
    final BoundaryCondition upper = new NeumannBoundaryCondition(0.0, xH, false);
    final MeshingFunction spaceMesh = new HyperbolicMeshing(xL, xH, 1.0, 40, 0.05);
    final MeshingFunction timeMesh = new ExponentialMeshing(0, 2.0, 30, 0.2);
    final PDEGrid1D pdeGrid = new PDEGrid1D(timeMesh, spaceMesh);
    final Function1D<Double, Double> initialCond = INITIAL_COND_PROVIDER.getForwardCallPut(true);

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition

    final int nTimeNodes = 50;
    final int nSpotNodes = 100;
    final double upperLevel = 3.5 * forward;


    final BoundaryCondition lower = new DirichletBoundaryCondition(0, 0);
    final BoundaryCondition upper = new NeumannBoundaryCondition(1.0, upperLevel, false);
    final MeshingFunction timeMesh = new ExponentialMeshing(0.0, EXPIRY, nTimeNodes, 6.0);
    final MeshingFunction spaceMesh = new HyperbolicMeshing(0, upperLevel, STRIKE, nSpotNodes, 0.05);
    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
    final PDEResults1D res = solver.solve(new PDE1DDataBundle<>(pde, payoff, lower, upper, grid));

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition

    //TODO shunt this setup into its own class 
    ConvectionDiffusionPDE1DStandardCoefficients pde = pdeProvider.getForwardLocalVol(lvsm);
    Function1D<Double, Double> initialCond = initialConProvider.getForwardCallPut(true);
    double xL = 0.8;
    double xH = 1.2;
    BoundaryCondition lower = new NeumannBoundaryCondition(-1.0, xL, true);
    BoundaryCondition upper = new NeumannBoundaryCondition(0.0, xH, false);
    final MeshingFunction spaceMeshF = new HyperbolicMeshing(xL, xH, 1.0, 200, 0.001);
    final MeshingFunction timeMeshF = new ExponentialMeshing(0, t, 50, 4.0);
    final MeshingFunction timeMeshB = new DoubleExponentialMeshing(0, t, t / 2, 50, 2.0, -4.0);
    final PDEGrid1D grid = new PDEGrid1D(timeMeshF, spaceMeshF);
    PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> dbF = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(pde, initialCond, lower, upper, grid);
    PDETerminalResults1D res = (PDETerminalResults1D) solver.solve(dbF);
    final double minK = Math.exp(-6 * rootT);
    final double maxK = Math.exp(6 * rootT);
    Map<Double, Double> vols = PDEUtilityTools.priceToImpliedVol(fwdCurve, t, res, minK, maxK, true);
    DoubleQuadraticInterpolator1D interpolator = Interpolator1DFactory.DOUBLE_QUADRATIC_INSTANCE;
    Interpolator1DDataBundle idb = interpolator.getDataBundle(vols);


    //set up for solving backwards PDE 
    ConvectionDiffusionPDE1DStandardCoefficients pdeB = pdeProvider.getBackwardsLocalVol(t, lvsm);
    double sL = xL * spot;
    double sH = xH * spot;
    final MeshingFunction spaceMeshB = new HyperbolicMeshing(sL, sH, spot, 200, 0.001);
    final PDEGrid1D gridB = new PDEGrid1D(timeMeshB, spaceMeshB);
    int index = SurfaceArrayUtils.getLowerBoundIndex(gridB.getSpaceNodes(), spot);
    double s1 = gridB.getSpaceNode(index);
    double s2 = gridB.getSpaceNode(index + 1);
    final double w = (s2 - spot) / (s2 - s1);


    //solve a separate backwards PDE for each strike
    for (int i = 0; i < 10; i++) {
      double z = -5 + i;
      double k = spot * Math.exp(0.4 * rootT * z);
      double x = k / fwd;
      double vol = ivs.getVolatility(t, k);
      double volFPDE = interpolator.interpolate(idb, x);


      boolean isCall = (k >= fwd);
      BoundaryCondition lowerB = new NeumannBoundaryCondition(isCall ? 0 : -1, sL, true);
      BoundaryCondition upperB = new NeumannBoundaryCondition(isCall ? 1 : 0, sH, false);


      Function1D<Double, Double> bkdIC = initialConProvider.getEuropeanPayoff(k, isCall);
      PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> dbB = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(pdeB, bkdIC, lowerB, upperB, gridB);
      PDEResults1D resB = solver.solve(dbB);
      double price1 = resB.getFunctionValue(index);

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Examples of com.opengamma.analytics.financial.model.finitedifference.NeumannBoundaryCondition

    final double range = Math.log(5);
    final double yL = lnFT - range;
    final double yH = lnFT + range;
    final ConvectionDiffusionPDESolver solver = new ThetaMethodFiniteDifference(theta, false);


    final BoundaryCondition lower = new NeumannBoundaryCondition(1.0, yL, true);
    final BoundaryCondition upper = new NeumannBoundaryCondition(1.0, yH, false);


    final MeshingFunction timeMesh = new ExponentialMeshing(0, EXPIRY, 100, 0.0);
    final MeshingFunction spaceMesh = new ExponentialMeshing(yL, yH, 101, 0.0);


    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);

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