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;
}
/**
* Check the the log-contract is correctly prices using a backwards PDE expressed in terms of (the
* log of) the real stock price - this requires having jumps conditions in the PDE. The local
* volatility surface is derived from the flat pure local volatility surface.
*/
@Test
public void backwardsLogSpotPDEtest() {
final double fT = DIV_CURVES.getF(EXPIRY);
final double lnFT = Math.log(fT);
final double val = logContractPriceFromSpotPDE(LOCAL_VOL);
assertEquals(PURE_VOL, Math.sqrt(-2 * (val - lnFT) / EXPIRY), 1e-4);
// System.out.println(val + "\t" + Math.sqrt(-2 * (val - lnFT) / EXPIRY));
}
/**
* Price the log-contact using the PDE in spot (with the jump conditions) with a flat local
* volatility surface, and the PDE in pure spot using the pure local volatility surface derived
* from the flat surface. They MUST give the same answer
*/
@Test
public void backwardsPDETest() {
final double fT = DIV_CURVES.getF(EXPIRY);
final double lnFT = Math.log(fT);
final double val1 = logContractPriceFromSpotPDE(LOCAL_VOL_FLAT);
final double val2 = logContactPriceFromPureSpot(PURE_LOCAL_VOL);
// convert to realised vol
final double vol1 = Math.sqrt(-2 * (val1 - lnFT) / EXPIRY);
final double vol2 = Math.sqrt(-2 * (val2 - lnFT) / EXPIRY);
assertEquals(vol1, vol2, 1e-3);
// System.out.println(vol1 + "\t" + vol2);
}
/**
* Check the the log-contract is correctly prices using a backwards PDE expressed in terms of (the
* log of) the forward F(t,T) - this requires NO jumps conditions in the PDE
*/
@Test
public void backwardsDebugPDEtest() {
final double fT = DIV_CURVES.getF(EXPIRY);
final double lnFT = Math.log(fT);
final Function1D<Double, Double> payoff =
new Function1D<Double, Double>() {
@Override
public Double evaluate(final Double y) {
return y - lnFT;
}
};
// ZZConvectionDiffusionPDEDataBundle pdeBundle1 = getBackwardsPDEDataBundle(EXPIRY, LOCAL_VOL,
// payoff);
// ConvectionDiffusionPDE1DCoefficients pde =
// PDE_PROVIDER.getLogBackwardsLocalVol(FORWARD_CURVE, EXPIRY, LOCAL_VOL);
final ConvectionDiffusionPDE1DCoefficients pde =
PDE_PROVIDER.getLogBackwardsLocalVol(0.0, 0.0, EXPIRY, LOCAL_VOL_SPECIAL);
final double theta = 0.5;
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);
final double[] sNodes = grid.getSpaceNodes();
// run the PDE solver backward to the dividend date
// PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db1 = new
// PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients>(pde, initialCon, lower1, upper1,
// grid1);
final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db1 =
new PDE1DDataBundle<>(pde, payoff, lower, upper, grid);
final PDETerminalResults1D res = (PDETerminalResults1D) solver.solve(db1);
final Interpolator1DDataBundle interpolDB =
INTEPOLATOR1D.getDataBundle(sNodes, res.getTerminalResults());
final double val = INTEPOLATOR1D.interpolate(interpolDB, lnFT);
assertEquals(0.41491529, Math.sqrt(-2 * (val) / EXPIRY), 5e-4); // Number from backwardsPDETest
// System.out.println(val + "\t" + Math.sqrt(-2 * val / EXPIRY));
}
