Package com.opengamma.analytics.financial.model.finitedifference

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

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    //TODO the grid involves some magic numbers that should be possible to alter externally by expert users
    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, _nSpaceSteps + 1, 0.001); //0.05
    final MeshingFunction[] timeMeshes = new MeshingFunction[nDivsBeforeExpiry + 1];
    final PDEGrid1D[] grids = new PDEGrid1D[nDivsBeforeExpiry + 1];
    if (nDivsBeforeExpiry == 0) {
      timeMeshes[0] = new ExponentialMeshing(0, expiry, _nTimeSteps, 5.0);
    } else {
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    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);
    final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(pde, initalCond, lower, upper, grid);
    final PDEResults1D res = _solver.solve(db);
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    final int tNodes = 50;
    final int xNodes = 100;
    final BoundaryCondition lower = new DirichletBoundaryCondition(0.0, 0.0);
    final BoundaryCondition upper = new DirichletBoundaryCondition(0.0, 10 * FORWARD_CURVE.getForward(T));
    final MeshingFunction timeMesh = new ExponentialMeshing(0, T, tNodes, 5.0);
    final MeshingFunction spaceMesh = new HyperbolicMeshing(0.0, upper.getLevel(), SPOT, xNodes, 0.01);
    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);

    final ConvectionDiffusionPDE1DFullCoefficients pde1 = PDE_PROVIDER.getFokkerPlank(ConstantDoublesCurve.from(RATE), localVol);
    final ConvectionDiffusionPDE1DStandardCoefficients pde2 = PDE_PROVIDER.getFokkerPlankInStandardCoefficients(ConstantDoublesCurve.from(RATE), localVol);
    final Function1D<Double, Double> initalCondition = INITAL_CONDITION_PROVIDER.getLogNormalDensity(SPOT, 0.01, 0.2);
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      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);
    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
    final Function1D<Double, Double> intCond = (new InitialConditionsProvider()).getForwardCallPut(isCall);
    final PDEFullResults1D res = (PDEFullResults1D) solver.solve(new PDE1DDataBundle<>(pde, intCond, lower, upper, grid));
    return res;
  }
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    }

    // 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)
    final MeshingFunction spaceMesh = new HyperbolicMeshing(0.0, maxFwd, fwdNodeCentre, nFwdNodes, spotMeshBunching);
    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
    final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db = new PDE1DDataBundle<>(pde, payoff, lower, upper, grid);
    final PDEResults1D res = solver.solve(db);
    return res;
  }
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    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 };
    final double[] xb = new double[] {2.0, xH };
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    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);

    final Function1D<DoubleMatrix1D, DoubleMatrix1D> volFunc = new Function1D<DoubleMatrix1D, DoubleMatrix1D>() {
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    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));

    final int fwdIndex = grid.getLowerBoundIndexForSpace(forward);
    final double[] fwd = new double[4];
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    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);
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    final TwoStateMarkovChainPricer mc = new TwoStateMarkovChainPricer(FORWARD_CURVE, MARKOV_CHAIN_DATA);

    final int tNodes = 20;
    final int xNodes = 100;
    final MeshingFunction timeMesh = new ExponentialMeshing(0, 5, tNodes, 5.0);
    final MeshingFunction spaceMesh = new HyperbolicMeshing(0, 6 * SPOT, SPOT, xNodes, 0.01);
    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);

    for (int i = 0; i < warmups; i++) {
      mc.solve(grid, 0.5);
    }
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