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

Examples of com.opengamma.analytics.financial.model.finitedifference.ConvectionDiffusionPDE1DStandardCoefficients

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    //        final NormalDistribution dist = new NormalDistribution(0, _volRootTOffset);
    //        return dist.getPDF(x) / s;
    //      }
    //    };

    return new ConvectionDiffusionPDE1DStandardCoefficients(FunctionalDoublesSurface.from(a), FunctionalDoublesSurface.from(b), FunctionalDoublesSurface.from(c));
  }
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    ArgumentChecker.isTrue(sMax >= k, "strike higher than sMax");

    final int index = Arrays.binarySearch(xNodes, s0);
    ArgumentChecker.isTrue(index >= 0, "cannot find spot on grid");

    final ConvectionDiffusionPDE1DStandardCoefficients coef = PDE.getBackwardsLocalVol(riskFreeRate, costOfCarry, t, localVol);
    final Function1D<Double, Double> payoff = ICP.getEuropeanPayoff(k, option.isCall());

    BoundaryCondition lower;
    BoundaryCondition upper;
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    ArgumentChecker.isTrue(expiry > 0, "expiry > 0");
    ArgumentChecker.notNull(pureLocalVolSurface, "pure local volatility surface");
    //"convert" to a LocalVolatilitySurfaceMoneyness _ DO NOT interpret this as an actual LocalVolatilitySurfaceMoneyness
    final LocalVolatilitySurfaceMoneyness localVolSurface = new LocalVolatilitySurfaceMoneyness(pureLocalVolSurface.getSurface(), new ForwardCurve(1.0));

    final ConvectionDiffusionPDE1DStandardCoefficients pde = PDE_PROVIDER.getForwardLocalVol(localVolSurface);
    final Function1D<Double, Double> initialCond = INITIAL_COND_PROVIDER.getForwardCallPut(true);

    final EquityDividendsCurvesBundle divCurves = new EquityDividendsCurvesBundle(spot, discountCurve, dividends);
    final double terminalFwd = divCurves.getF(expiry);
    final double logNoDivFwd = Math.log(spot) + discountCurve.getInterestRate(expiry) * expiry;
 
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    final EquityDividendsCurvesBundle divs = new EquityDividendsCurvesBundle(spot, discountCurve, dividends);
    final double logNoDivFwd = Math.log(spot) + discountCurve.getInterestRate(expiry) * expiry;
    //"convert" to a LocalVolatilitySurfaceMoneyness _ DO NOT interpret this as an actual LocalVolatilitySurfaceMoneyness
    final LocalVolatilitySurfaceMoneyness localVolSurface = new LocalVolatilitySurfaceMoneyness(pureLocalVolSurface.getSurface(), new ForwardCurve(1.0));

    final ConvectionDiffusionPDE1DStandardCoefficients pde = PDE_PROVIDER.getLogBackwardsLocalVol(expiry, localVolSurface);
    final Function1D<Double, Double> logPayoff = getLogPayoff(divs, expiry);

    //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;
 
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    final double atmVol = plv.getVolatility(tau, 1.0);
    final double yMin = -Math.sqrt(tau) * atmVol * SIGMA;
    final double yMax = -yMin;

    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);

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   * Check a zero coupon bond is priced correctly by the PDE solver. Note, as this is not something one normally prices this way, there
   * is no helper class for the set up
   */
  @Test
  public void zeroCouponBondTest() {
    final ConvectionDiffusionPDE1DStandardCoefficients coef = PDE.getBackwardsLocalVol(RISK_FREE_CURVE, FWD_CURVE.getDriftCurve(), T, LOCAL_VOL_SUR);
    final Function1D<Double, Double> payoff = new Function1D<Double, Double>() {
      @Override
      public Double evaluate(final Double x) {
        return 1.0;
      }
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    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);

    final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db1 = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(pde1, initalCondition, lower, upper, grid);
    final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db2 = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(pde2, initalCondition, lower, upper, grid);
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    return localVolSurface;
  }

  private BlackVolatilitySurfaceMoneyness solveForwardPDE(final ForwardCurve fwdCurve, final BoundaryCondition lower, final BoundaryCondition upper, final PDEGrid1D pdeGrid,
      final Function1D<Double, Double> initialCond, final LocalVolatilitySurfaceMoneyness localVolSurface) {
    final ConvectionDiffusionPDE1DStandardCoefficients pde = PDE_PROVIDER.getForwardLocalVol(localVolSurface);

    final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(pde, initialCond, lower, upper, pdeGrid);
    final PDEFullResults1D res = (PDEFullResults1D) SOLVER.solve(db);
    final Map<DoublesPair, Double> volsurf = PDEUtilityTools.modifiedPriceToImpliedVol(res, 0.1, 2.0, 0.3, 3.0, true);
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    //    PDEUtilityTools.printSurface("local vol (dupire)", dlv.getSurface(), 0, t, 0.99, 1.01);
    //    PDEUtilityTools.printSurface("local vol", lvsm.getSurface(), 0, t, 0.99, 1.01);

    //set up for solving the forward PDE
    //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);
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    final MeshingFunction timeMesh = new ExponentialMeshing(0, EXPIRY, 50, 0.0);
    //  final MeshingFunction spaceMesh = new ExponentialMeshing(fL, fH, 101, 0.0);
    final MeshingFunction spaceMesh = new HyperbolicMeshing(fL, fH, (fL + fH) / 2, 101, 0.4);

    // ZZConvectionDiffusionPDEDataBundle pde_data = PDE_DATA_PROVIDER.getBackwardsLocalVolLogPayoff(EXPIRY, lvm);
    final ConvectionDiffusionPDE1DStandardCoefficients pde = PDE_DATA_PROVIDER.getLogBackwardsLocalVol(EXPIRY, lvm);

    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
    final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(pde, INITIAL_COND, lower, upper, grid);
    final PDEResults1D res = solver.solve(db);
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Related Classes of com.opengamma.analytics.financial.model.finitedifference.ConvectionDiffusionPDE1DStandardCoefficients

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  • com.opengamma.analytics.financial.model.finitedifference.applications.LocalVolPDEPricer
  • com.opengamma.analytics.financial.model.finitedifference.applications.LogPayoffTest
  • com.opengamma.analytics.financial.model.finitedifference.applications.PDE1DCoefficientsProvider
  • com.opengamma.analytics.financial.model.finitedifference.applications.TermStructureRatesTest
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