/**
* Prices a log-contract for a given local volatility surface by backwards solving the PDE
* expressed in terms of (the log of) the real stock price - this requires having jumps conditions
* in the PDE
*
* @param lv Local volatility
* @return Forward (non-discounted) price of log-contact
*/
private double logContractPriceFromSpotPDE(final LocalVolatilitySurfaceStrike lv) {
// Set up the PDE to give the forward (non-discounted) option price
final ConvectionDiffusionPDE1DCoefficients pde =
PDE_PROVIDER.getLogBackwardsLocalVol(0.0, -DRIFT, EXPIRY, lv);
final Function1D<Double, Double> initialCon =
INITIAL_COND_PROVIDER.getLogContractPayoffInLogCoordinate();
final double theta = 0.5;
final double yL = Math.log(SPOT / 6);
final double yH = Math.log(6 * SPOT);
final ConvectionDiffusionPDESolver solver = new ThetaMethodFiniteDifference(theta, false);
final BoundaryCondition lower1 = new NeumannBoundaryCondition(1.0, yL, true);
final BoundaryCondition upper1 = new NeumannBoundaryCondition(1.0, yH, false);
final MeshingFunction timeMesh1 =
new ExponentialMeshing(0, EXPIRY - DIVIDEND_DATE - 1e-6, 50, 0.0);
final MeshingFunction timeMesh2 =
new ExponentialMeshing(EXPIRY - DIVIDEND_DATE + 1e-6, EXPIRY, 50, 0.0);
final MeshingFunction spaceMesh = new ExponentialMeshing(yL, yH, 101, 0.0);
final PDEGrid1D grid1 = new PDEGrid1D(timeMesh1, spaceMesh);
final double[] sNodes1 = grid1.getSpaceNodes();
// run the PDE solver backward to the dividend date
final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db1 =
new PDE1DDataBundle<>(pde, initialCon, lower1, upper1, grid1);
final PDETerminalResults1D res1 = (PDETerminalResults1D) solver.solve(db1);
// Map the spot nodes after (in calendar time) the dividend payment to nodes before
final int nSNodes = sNodes1.length;
final double[] sNodes2 = new double[nSNodes];
final double lnBeta = Math.log(1 - BETA);
for (int i = 0; i < nSNodes; i++) {
final double temp = sNodes1[i];
if (temp < 0) {
sNodes2[i] = Math.log(Math.exp(temp) + ALPHA) - lnBeta;
} else {
sNodes2[i] = temp + Math.log(1 + ALPHA * Math.exp(-temp)) - lnBeta;
}
}
final PDEGrid1D grid2 = new PDEGrid1D(timeMesh2.getPoints(), sNodes2);
final BoundaryCondition lower2 = new NeumannBoundaryCondition(1.0, sNodes2[0], true);
final BoundaryCondition upper2 = new NeumannBoundaryCondition(1.0, sNodes2[nSNodes - 1], false);
// run the PDE solver backward from the dividend date to zero
final PDE1DDataBundle<ConvectionDiffusionPDE1DCoefficients> db2 =
new PDE1DDataBundle<>(pde, res1.getTerminalResults(), lower2, upper2, grid2);
final PDETerminalResults1D res2 = (PDETerminalResults1D) solver.solve(db2);
final Interpolator1DDataBundle interpolDB2 =
INTEPOLATOR1D.getDataBundle(sNodes2, res2.getTerminalResults());
final double val2 = INTEPOLATOR1D.interpolate(interpolDB2, Math.log(SPOT));
return val2;
}
/**
* 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));
}
