public void testSqrt()
{
//BOOST_MESSAGE("Testing matricial square root...");
setup();
Matrix m = MatrixUtilitites.pseudoSqrt(M1, MatrixUtilitites.SalvagingAlgorithm.None);
Matrix temp = m * Matrix.transpose(m);
double error = norm(temp - M1);
double tolerance = 1.0e-12;
if (error > tolerance)
{
QAssert.Fail("Matrix square root calculation failed\n"
+ "original matrix:\n" + M1
+ "pseudoSqrt:\n" + m
+ "pseudoSqrt*pseudoSqrt:\n" + temp
+ "\nerror: " + error
+ "\ntolerance: " + tolerance);
}
}
public void testHighamSqrt()
{
//BOOST_MESSAGE("Testing Higham matricial square root...");
setup();
Matrix tempSqrt = MatrixUtilitites.pseudoSqrt(M5, MatrixUtilitites.SalvagingAlgorithm.Higham);
Matrix ansSqrt = MatrixUtilitites.pseudoSqrt(M6, MatrixUtilitites.SalvagingAlgorithm.None);
double error = norm(ansSqrt - tempSqrt);
double tolerance = 1.0e-4;
if (error > tolerance)
{
QAssert.Fail("Higham matrix correction failed\n"
+ "original matrix:\n" + M5
+ "pseudoSqrt:\n" + tempSqrt
+ "should be:\n" + ansSqrt
+ "\nerror: " + error
+ "\ntolerance: " + tolerance);
}
}
protected double mcReferenceValue(CmsCoupon cpn1,
CmsCoupon cpn2,
double cap,
double floor,
Handle <SwaptionVolatilityStructure> vol,
double correlation)
{
List <double> acc = new List <double>();
int samples = 1000000;
Matrix Cov = new Matrix(2, 2);
Cov[0, 0] = vol.currentLink().blackVariance(cpn1.fixingDate(), cpn1.index().tenor(),
cpn1.indexFixing());
Cov[1, 1] = vol.currentLink().blackVariance(cpn2.fixingDate(), cpn2.index().tenor(),
cpn2.indexFixing());
Cov[0, 1] = Cov[1, 0] = Math.Sqrt(Cov[0, 0] * Cov[1, 1]) * correlation;
Matrix C = MatrixUtilitites.pseudoSqrt(Cov, MatrixUtilitites.SalvagingAlgorithm.None);
List <double> atmRate = new InitializedList <double>(2), adjRate = new InitializedList <double>(2),
volShift = new InitializedList <double>(2);
Vector avg = new Vector(2);
atmRate[0] = cpn1.indexFixing();
atmRate[1] = cpn2.indexFixing();
adjRate[0] = cpn1.adjustedFixing;
adjRate[1] = cpn2.adjustedFixing;
if (vol.currentLink().volatilityType() == VolatilityType.ShiftedLognormal)
{
volShift[0] = vol.currentLink().shift(cpn1.fixingDate(), cpn1.index().tenor());
volShift[1] = vol.currentLink().shift(cpn2.fixingDate(), cpn2.index().tenor());
avg[0] =
Math.Log((adjRate[0] + volShift[0]) / (atmRate[0] + volShift[0])) -
0.5 * Cov[0, 0];
avg[1] =
Math.Log((adjRate[1] + volShift[1]) / (atmRate[1] + volShift[1])) -
0.5 * Cov[1, 1];
}
else
{
avg[0] = adjRate[0];
avg[1] = adjRate[1];
}
InverseCumulativeNormal icn = new InverseCumulativeNormal();
SobolRsg sb_ = new SobolRsg(2, 42);
Vector w = new Vector(2), z = new Vector(2);
for (int i = 0; i < samples; ++i)
{
List <double> seq = sb_.nextSequence().value;
w[0] = icn.value(seq[0]);
w[1] = icn.value(seq[1]);
z = C * w + avg;
for (int j = 0; j < 2; ++j)
{
if (vol.currentLink().volatilityType() == VolatilityType.ShiftedLognormal)
{
z[j] =
(atmRate[j] + volShift[j]) * Math.Exp(z[j]) - volShift[j];
}
}
acc.Add(Math.Min(Math.Max(z[0] - z[1], floor), cap));
}
return(acc.Average());
} // mcReferenceValue
