private double logContactPriceFromPureSpot(final LocalVolatilitySurfaceMoneyness lv) {
final double fT = DIV_CURVES.getF(EXPIRY);
final double dT = DIV_CURVES.getD(EXPIRY);
final double dStar = dT / (fT - dT);
final ConvectionDiffusionPDE1DCoefficients pde =
PDE_PROVIDER.getLogBackwardsLocalVol(EXPIRY, lv);
final double theta = 0.5;
final double yL = -0.5;
final double yH = 0.5;
final ConvectionDiffusionPDESolver solver = new ThetaMethodFiniteDifference(theta, false);
final BoundaryCondition lower =
new NeumannBoundaryCondition(1 / (1 + dStar * Math.exp(-yL)), yL, true);
final BoundaryCondition upper = new NeumannBoundaryCondition(1.0, yH, false);
final MeshingFunction timeMesh = new ExponentialMeshing(0.0, EXPIRY, 100, 0.0);
final MeshingFunction spaceMesh = new ExponentialMeshing(yL, yH, 101, 0.0);
final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db =
new PDE1DDataBundle<>(pde, PURE_LOG_PAY_OFF, lower, upper, grid);
final PDEResults1D res = solver.solve(db);
final int n = res.getNumberSpaceNodes();
final double val = res.getFunctionValue(n / 2);
return val;
}
public void testMixedLogNormalVolSurface() {
final double[] weights = new double[] {0.9, 0.1};
final double[] sigmas = new double[] {0.2, 0.8};
final MultiHorizonMixedLogNormalModelData data =
new MultiHorizonMixedLogNormalModelData(weights, sigmas);
final LocalVolatilitySurfaceStrike lv =
MixedLogNormalVolatilitySurface.getLocalVolatilitySurface(FORWARD_CURVE, data);
final LocalVolatilitySurfaceMoneyness lvm =
LocalVolatilitySurfaceConverter.toMoneynessSurface(lv, FORWARD_CURVE);
final double expected =
Math.sqrt(weights[0] * sigmas[0] * sigmas[0] + weights[1] * sigmas[1] * sigmas[1]);
final double ft = FORWARD_CURVE.getForward(EXPIRY);
final double theta = 0.5;
// Review the accuracy is very dependent on these numbers
final double fL = Math.log(ft / 30);
final double fH = Math.log(30 * ft);
final ConvectionDiffusionPDESolver solver = new ThetaMethodFiniteDifference(theta, false);
final BoundaryCondition lower = new NeumannBoundaryCondition(1.0, fL, true);
final BoundaryCondition upper = new NeumannBoundaryCondition(1.0, fH, false);
final MeshingFunction timeMesh = new ExponentialMeshing(0, EXPIRY, 50, 0.0);
final MeshingFunction spaceMesh = new HyperbolicMeshing(fL, fH, (fL + fH) / 2, 101, 0.4);
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);
final int n = res.getNumberSpaceNodes();
final double[] values = new double[n];
for (int i = 0; i < n; i++) {
values[i] = res.getFunctionValue(i);
}
final Interpolator1DDataBundle idb = INTERPOLATOR.getDataBundle(grid.getSpaceNodes(), values);
final double elogS = INTERPOLATOR.interpolate(idb, Math.log(ft));
final double kVol = Math.sqrt(-2 * (elogS - Math.log(ft)) / EXPIRY);
assertEquals(
expected, kVol,
1e-3); // TODO Improve on 10bps error - local surface is (by construction) very smooth.
// NOTE: this has got worse since we improved the T -> 0
// behaviour of the mixed log-normal local volatility surface
}
public void testFlatSurface() {
final double theta = 0.5;
final double ft = FORWARD_CURVE.getForward(EXPIRY);
final double fL = Math.log(ft / 5.0);
final double fH = Math.log(5.0 * ft);
final ConvectionDiffusionPDESolver solver = new ThetaMethodFiniteDifference(theta, false);
final BoundaryCondition lower = new NeumannBoundaryCondition(1.0, fL, true);
final BoundaryCondition upper = new NeumannBoundaryCondition(1.0, fH, false);
final MeshingFunction timeMesh = new ExponentialMeshing(0, EXPIRY, 100, 0.0);
final MeshingFunction spaceMesh = new ExponentialMeshing(fL, fH, 101, 0.0);
final PDEGrid1D grid = new PDEGrid1D(timeMesh, spaceMesh);
final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db =
new PDE1DDataBundle<>(PDE, INITIAL_COND, lower, upper, grid);
final PDEResults1D res = solver.solve(db);
final int n = res.getNumberSpaceNodes();
final double kVol = Math.sqrt(-2 * (res.getFunctionValue(n / 2) - Math.log(ft)) / EXPIRY);
assertEquals(FLAT_VOL, kVol, 1e-6);
final YieldAndDiscountCurve yieldCurve =
new YieldCurve("test", ConstantDoublesCurve.from(DRIFT));
final AffineDividends ad = AffineDividends.noDividends();
final EquityVarianceSwapBackwardsPurePDE backSolver = new EquityVarianceSwapBackwardsPurePDE();
final PureLocalVolatilitySurface plv =
new PureLocalVolatilitySurface(ConstantDoublesSurface.from(FLAT_VOL));
final double[] res2 = backSolver.expectedVariance(SPOT, yieldCurve, ad, EXPIRY, plv);
final double kVol2 = Math.sqrt(res2[0] / EXPIRY);
assertEquals(FLAT_VOL, kVol2, 1e-6);
}
