public void testTripleBandMapSolve()
{
int[] dims = new int[] { 100, 400 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
List <Pair <double?, double?> > boundaries = new List <Pair <double?, double?> > ();
boundaries.Add(new Pair <double?, double?>(0, 1.0));
boundaries.Add(new Pair <double?, double?>(0, 1.0));
FdmMesher mesher = new UniformGridMesher(layout, boundaries);
FirstDerivativeOp dy = new FirstDerivativeOp(1, mesher);
dy.axpyb(new Vector(1, 2.0), dy, dy, new Vector(1, 1.0));
// check copy constructor
FirstDerivativeOp copyOfDy = new FirstDerivativeOp(dy);
Vector u = new Vector(layout.size());
for (int i = 0; i < layout.size(); ++i)
{
u[i] = Math.Sin(0.1 * i) + Math.Cos(0.35 * i);
}
Vector t = new Vector(dy.solve_splitting(copyOfDy.apply(u), 1.0, 0.0));
for (int i = 0; i < u.size(); ++i)
{
if (Math.Abs(u[i] - t[i]) > 1e-6)
{
QAssert.Fail("solve and apply are not consistent "
+ "\n expected : " + u[i]
+ "\n calculated : " + t[i]);
}
}
FirstDerivativeOp dx = new FirstDerivativeOp(0, mesher);
dx.axpyb(new Vector(), dx, dx, new Vector(1, 1.0));
FirstDerivativeOp copyOfDx = new FirstDerivativeOp(0, mesher);
// check assignment
copyOfDx = dx;
t = dx.solve_splitting(copyOfDx.apply(u), 1.0, 0.0);
for (int i = 0; i < u.size(); ++i)
{
if (Math.Abs(u[i] - t[i]) > 1e-6)
{
QAssert.Fail("solve and apply are not consistent "
+ "\n expected : " + u[i]
+ "\n calculated : " + t[i]);
}
}
SecondDerivativeOp dxx = new SecondDerivativeOp(0, mesher);
dxx.axpyb(new Vector(1, 0.5), dxx, dx, new Vector(1, 1.0));
// check of copy constructor
SecondDerivativeOp copyOfDxx = new SecondDerivativeOp(dxx);
t = dxx.solve_splitting(copyOfDxx.apply(u), 1.0, 0.0);
for (int i = 0; i < u.size(); ++i)
{
if (Math.Abs(u[i] - t[i]) > 1e-6)
{
QAssert.Fail("solve and apply are not consistent "
+ "\n expected : " + u[i]
+ "\n calculated : " + t[i]);
}
}
//check assignment operator
copyOfDxx.add(new SecondDerivativeOp(1, mesher));
copyOfDxx = dxx;
t = dxx.solve_splitting(copyOfDxx.apply(u), 1.0, 0.0);
for (int i = 0; i < u.size(); ++i)
{
if (Math.Abs(u[i] - t[i]) > 1e-6)
{
QAssert.Fail("solve and apply are not consistent "
+ "\n expected : " + u[i]
+ "\n calculated : " + t[i]);
}
}
}
public void testCrankNicolsonWithDamping()
{
SavedSettings backup = new SavedSettings();
DayCounter dc = new Actual360();
Date today = Date.Today;
SimpleQuote spot = new SimpleQuote(100.0);
YieldTermStructure qTS = Utilities.flatRate(today, 0.06, dc);
YieldTermStructure rTS = Utilities.flatRate(today, 0.06, dc);
BlackVolTermStructure volTS = Utilities.flatVol(today, 0.35, dc);
StrikedTypePayoff payoff =
new CashOrNothingPayoff(Option.Type.Put, 100, 10.0);
double maturity = 0.75;
Date exDate = today + Convert.ToInt32(maturity * 360 + 0.5);
Exercise exercise = new EuropeanExercise(exDate);
BlackScholesMertonProcess process = new
BlackScholesMertonProcess(new Handle <Quote>(spot),
new Handle <YieldTermStructure>(qTS),
new Handle <YieldTermStructure>(rTS),
new Handle <BlackVolTermStructure>(volTS));
IPricingEngine engine =
new AnalyticEuropeanEngine(process);
VanillaOption opt = new VanillaOption(payoff, exercise);
opt.setPricingEngine(engine);
double expectedPV = opt.NPV();
double expectedGamma = opt.gamma();
// fd pricing using implicit damping steps and Crank Nicolson
int csSteps = 25, dampingSteps = 3, xGrid = 400;
List <int> dim = new InitializedList <int>(1, xGrid);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
Fdm1dMesher equityMesher =
new FdmBlackScholesMesher(
dim[0], process, maturity, payoff.strike(),
null, null, 0.0001, 1.5,
new Pair <double?, double?>(payoff.strike(), 0.01));
FdmMesher mesher =
new FdmMesherComposite(equityMesher);
FdmBlackScholesOp map =
new FdmBlackScholesOp(mesher, process, payoff.strike());
FdmInnerValueCalculator calculator =
new FdmLogInnerValue(payoff, mesher, 0);
object rhs = new Vector(layout.size());
Vector x = new Vector(layout.size());
FdmLinearOpIterator endIter = layout.end();
for (FdmLinearOpIterator iter = layout.begin(); iter != endIter;
++iter)
{
(rhs as Vector)[iter.index()] = calculator.avgInnerValue(iter, maturity);
x[iter.index()] = mesher.location(iter, 0);
}
FdmBackwardSolver solver = new FdmBackwardSolver(map, new FdmBoundaryConditionSet(),
new FdmStepConditionComposite(),
new FdmSchemeDesc().Douglas());
solver.rollback(ref rhs, maturity, 0.0, csSteps, dampingSteps);
MonotonicCubicNaturalSpline spline = new MonotonicCubicNaturalSpline(x, x.Count, rhs as Vector);
double s = spot.value();
double calculatedPV = spline.value(Math.Log(s));
double calculatedGamma = (spline.secondDerivative(Math.Log(s))
- spline.derivative(Math.Log(s))) / (s * s);
double relTol = 2e-3;
if (Math.Abs(calculatedPV - expectedPV) > relTol * expectedPV)
{
QAssert.Fail("Error calculating the PV of the digital option" +
"\n rel. tolerance: " + relTol +
"\n expected: " + expectedPV +
"\n calculated: " + calculatedPV);
}
if (Math.Abs(calculatedGamma - expectedGamma) > relTol * expectedGamma)
{
QAssert.Fail("Error calculating the Gamma of the digital option" +
"\n rel. tolerance: " + relTol +
"\n expected: " + expectedGamma +
"\n calculated: " + calculatedGamma);
}
}
public void testFdmLinearOpLayout()
{
int[] dims = new int[] { 5, 7, 8 };
List <int> dim = new List <int>(dims);
FdmLinearOpLayout layout = new FdmLinearOpLayout(dim);
int calculatedDim = layout.dim().Count;
int expectedDim = dim.Count;
if (calculatedDim != expectedDim)
{
QAssert.Fail("index.dimensions() should be " + expectedDim
+ ", but is " + calculatedDim);
}
int calculatedSize = layout.size();
int expectedSize = dim.accumulate(0, 3, 1, (x, y) => (x * y));
if (calculatedSize != expectedSize)
{
QAssert.Fail("index.size() should be "
+ expectedSize + ", but is " + calculatedSize);
}
for (int k = 0; k < dim[0]; ++k)
{
for (int l = 0; l < dim[1]; ++l)
{
for (int m = 0; m < dim[2]; ++m)
{
List <int> tmp = new InitializedList <int>(3);
tmp[0] = k; tmp[1] = l; tmp[2] = m;
int calculatedIndex = layout.index(tmp);
int expectedIndex = k + l * dim[0] + m * dim[0] * dim[1];
if (expectedIndex != layout.index(tmp))
{
QAssert.Fail("index.size() should be " + expectedIndex
+ ", but is " + calculatedIndex);
}
}
}
}
FdmLinearOpIterator iter = layout.begin();
for (int m = 0; m < dim[2]; ++m)
{
for (int l = 0; l < dim[1]; ++l)
{
for (int k = 0; k < dim[0]; ++k, ++iter)
{
for (int n = 1; n < 4; ++n)
{
int nn = layout.neighbourhood(iter, 1, n);
int calculatedIndex = k + m * dim[0] * dim[1]
+ ((l < dim[1] - n)? l + n
: dim[1] - 1 - (l + n - (dim[1] - 1))) * dim[0];
if (nn != calculatedIndex)
{
QAssert.Fail("next neighbourhood index is " + nn
+ " but should be " + calculatedIndex);
}
}
for (int n = 1; n < 7; ++n)
{
int nn = layout.neighbourhood(iter, 2, -n);
int calculatedIndex = k + l * dim[0]
+ ((m < n) ? n - m : m - n) * dim[0] * dim[1];
if (nn != calculatedIndex)
{
QAssert.Fail("next neighbourhood index is " + nn
+ " but should be " + calculatedIndex);
}
}
}
}
}
}