Examples of ThetaMethodFiniteDifference

com.opengamma.analytics.financial.model.finitedifference.ThetaMethodFiniteDifference
A theta (i.e. weighted between explicit and implicit time stepping) scheme using SOR algorithm to solve the matrix system at each time step This uses the exponentially fitted scheme of duffy

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

  private final ThetaMethodFiniteDifference _solver;


  public LocalVolatilityPDECalculator(final double theta) {
    _pdeProvider = new PDE1DCoefficientsProvider();
    _initialCondProvider = new InitialConditionsProvider();
    _solver = new ThetaMethodFiniteDifference(theta, false);
  }

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

    } else if (localVolatility instanceof LocalVolatilitySurfaceMoneyness) {
      pde = provider.getForwardLocalVol((LocalVolatilitySurfaceMoneyness) localVolatility);
    } else {
      throw new IllegalArgumentException();
    }
    final ConvectionDiffusionPDESolver solver = new ThetaMethodFiniteDifference(theta, true);


    final double minMoneyness = Math.exp(-maxAbsProxyDelta * Math.sqrt(maxT));
    final double maxMoneyness = 1.0 / minMoneyness;
    ArgumentChecker.isTrue(minMoneyness < centreMoneyness, "min moneyness of {} greater than centreMoneyness of {}. Increase maxAbsProxydelta", minMoneyness, centreMoneyness);
    ArgumentChecker.isTrue(maxMoneyness > centreMoneyness, "max moneyness of {} less than centreMoneyness of {}. Increase maxAbsProxydelta", maxMoneyness, centreMoneyness);


    BoundaryCondition lower;
    BoundaryCondition upper;
    if (isCall) {
      //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);
    final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
    final Function1D<Double, Double> initialCond = (new InitialConditionsProvider()).getForwardCallPut(isCall);
    final PDEFullResults1D res = (PDEFullResults1D) solver.solve(new PDE1DDataBundle<>(pde, initialCond, lower, upper, grid));
    return res;
  }

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

      };


      final FunctionalDoublesSurface free = new FunctionalDoublesSurface(func);


      PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, payoff, lower, upper, free, grid[0]);
      ThetaMethodFiniteDifference solver = new ThetaMethodFiniteDifference(theta[0], false);
      res = solver.solve(data);
      for (int ii = 1; ii < n; ii++) {
        data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, res.getTerminalResults(), lower, upper, free, grid[ii]);
        solver = new ThetaMethodFiniteDifference(theta[ii], false);
        res = solver.solve(data);
      }
      // European
    } else {
      if (isCall) {
        lower = new NeumannBoundaryCondition(0.0, sMin, true);
        final Function1D<Double, Double> upFunc = new Function1D<Double, Double>() {
          @Override
          public Double evaluate(final Double time) {
            return Math.exp(-q * time);
          }
        };
        upper = new NeumannBoundaryCondition(upFunc, sMax, false);
      } else {
        final Function1D<Double, Double> downFunc = new Function1D<Double, Double>() {
          @Override
          public Double evaluate(final Double time) {
            return -Math.exp(-q * time);
          }
        };
        lower = new NeumannBoundaryCondition(downFunc, sMin, true);
        upper = new NeumannBoundaryCondition(0.0, sMax, false);
      }
      PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, payoff, lower, upper, grid[0]);
      ThetaMethodFiniteDifference solver = new ThetaMethodFiniteDifference(theta[0], false);
      res = solver.solve(data);
      for (int ii = 1; ii < n; ii++) {
        data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, res.getTerminalResults(), lower, upper, grid[ii]);
        solver = new ThetaMethodFiniteDifference(theta[ii], false);
        res = solver.solve(data);
      }
    }


    return res.getFunctionValue(index);
  }

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

      };


      final FunctionalDoublesSurface free = new FunctionalDoublesSurface(func);


      PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, payoff, lower, upper, free, grid[0]);
      ThetaMethodFiniteDifference solver = new ThetaMethodFiniteDifference(theta[0], false);
      res = solver.solve(data);
      for (int ii = 1; ii < n; ii++) {
        data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, res.getTerminalResults(), lower, upper, free, grid[ii]);
        solver = new ThetaMethodFiniteDifference(theta[ii], false);
        res = solver.solve(data);
      }
      // European
    } else {
      if (option.isCall()) {
        lower = new NeumannBoundaryCondition(0.0, sMin, true);
        final Function1D<Double, Double> upFunc = new Function1D<Double, Double>() {
          @Override
          public Double evaluate(final Double tau) {
            return Math.exp((costOfCarry.getYValue(tau) - riskFreeRate.getYValue(tau)) * tau);
          }
        };
        upper = new NeumannBoundaryCondition(upFunc, sMax, false);
      } else {
        final Function1D<Double, Double> downFunc = new Function1D<Double, Double>() {
          @Override
          public Double evaluate(final Double tau) {
            return -Math.exp((costOfCarry.getYValue(tau) - riskFreeRate.getYValue(tau)) * tau);
          }
        };
        lower = new NeumannBoundaryCondition(downFunc, sMin, true);
        upper = new NeumannBoundaryCondition(0.0, sMax, false);
      }
      PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, payoff, lower, upper, grid[0]);
      ThetaMethodFiniteDifference solver = new ThetaMethodFiniteDifference(theta[0], false);
      res = solver.solve(data);
      for (int ii = 1; ii < n; ii++) {
        data = new PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(coef, res.getTerminalResults(), lower, upper, grid[ii]);
        solver = new ThetaMethodFiniteDifference(theta[ii], false);
        res = solver.solve(data);
      }
    }


    return res.getFunctionValue(index);
  }

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

   */
  public EquityVarianceSwapForwardPurePDE() {
    _nTimeSteps = 100;
    _nSpaceSteps = 100;
    _minStepsBetweenDividends = 5;
    _solver = new ThetaMethodFiniteDifference(DEFAULT_THETA, false);
  }

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

    ArgumentChecker.notNegativeOrZero(minStepsBetweenDividends, "minimum number of steps between dividends");
    ArgumentChecker.isInRangeInclusive(0, 1, theta);
    _nTimeSteps = nTimeSteps;
    _nSpaceSteps = nSpaceSteps;
    _minStepsBetweenDividends = minStepsBetweenDividends;
    _solver = new ThetaMethodFiniteDifference(theta, false);
  }

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

   * Sets up the PDE
   */
  public EquityVarianceSwapBackwardsPurePDE() {
    _nTimeSteps = 100;
    _nSpaceSteps = 100;
    _solver = new ThetaMethodFiniteDifference(DEFAULT_THETA, false);
  }

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

    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);


    //System.out.println(DF+"\t"+pdePrice);
    assertEquals(DF, pdePrice, DF * 5e-5);

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

    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);


    final ThetaMethodFiniteDifference thetaMethod = new ThetaMethodFiniteDifference(0.5, true);


    final PDEFullResults1D res1 = (PDEFullResults1D) thetaMethod.solve(db1);
    final PDEFullResults1D res2 = (PDEFullResults1D) thetaMethod.solve(db2);


    PDEUtilityTools.printSurface("State 1 density", res1);
    PDEUtilityTools.printSurface("State 2 density", res2);
  }

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

      final double theta, final double maxT, final double maxAbsProxyDelta, final int nTimeSteps, final int nStrikeSteps,
      final double timeMeshLambda, final double strikeMeshBunching, final double centreMoneyness) {


    final PDE1DCoefficientsProvider provider = new PDE1DCoefficientsProvider();
    final ConvectionDiffusionPDE1DCoefficients pde = provider.getForwardLocalVol(localVolatility);
    final ConvectionDiffusionPDESolver solver = new ThetaMethodFiniteDifference(theta, true);


    final double minMoneyness = Math.exp(-maxAbsProxyDelta * Math.sqrt(maxT));
    final double maxMoneyness = 1.0 / minMoneyness;
    ArgumentChecker.isTrue(minMoneyness < centreMoneyness, "min moneyness of {} greater than centreMoneyness of {}. Increase maxAbsProxydelta", minMoneyness, centreMoneyness);
    ArgumentChecker.isTrue(maxMoneyness > centreMoneyness, "max moneyness of {} less than centreMoneyness of {}. Increase maxAbsProxydelta", maxMoneyness, centreMoneyness);


    BoundaryCondition lower;
    BoundaryCondition upper;
    if (isCall) {
      //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);
    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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