public void pdf()
{
double mu = 0.0;
double sigma = 1;
double x = 1;
double y = 1;
double t = 1.0;
double s = 0.0;
double actual = new LogNormalDensity(
mu, sigma).density(s, t, x, y);
double expected = Normal.PDF(
0, 1, (Math.Log(y / x) - (mu - 0.5 * sigma * sigma) * (t - s)) / (sigma * Math.Sqrt(t - s)));
Assert.AreEqual(expected, actual, 1e-8);
mu = 0.1;
sigma = 0.43;
x = 1;
y = 2;
t = 4.0;
s = 2.0;
actual = new LogNormalDensity(
mu, sigma).density(s, t, x, y);
expected = Normal.PDF(
0, 1, (Math.Log(y / x) - (mu - 0.5 * sigma * sigma) * (t - s)) / (sigma * Math.Sqrt(t - s)))
/ (y * sigma * Math.Sqrt(t - s));
Assert.AreEqual(expected, actual, 1e-8);
}
public void meshTest()
{
Func <double, double> f = (double x) => { return(x * x); };
var random = new GaussianRandomNumber(seed: 1);
int numOfPath = 100;
int numOfMesh = 100;
double dt = 0.1;
int maturityYear = 1;
double mu = 0.1;
double sigma = 0.3;
var und = new BsUnderlying(initialValue: 100, sigma: sigma, mu: mu,
dt: dt, maturityInYear: maturityYear, numOfPath: numOfPath, random: random);
LogNormalDensity density = new LogNormalDensity(mu, sigma);
var stochasticMesh = new StochasticMeshOperator(numOfMesh,
und, density);
int startGrid = 3;
int endGrid = 10;
double state = 0.1;
double actual = stochasticMesh.Get(f, startGrid, endGrid)(state);
double expected = 0.0;
for (int i = 0; i < numOfPath; ++i)
{
double xEnd = und.GetLastState(i);
IEnumerable <double> mesh
= from index in Enumerable.Range(0, numOfMesh)
select und.GetState(index, startGrid);
double denominator = mesh.Select(
x => density.density(dt * startGrid,
maturityYear, x, xEnd)).Average();
expected += f(xEnd) * density.density(startGrid * dt, endGrid * dt,
state, xEnd);
}
Assert.AreEqual(expected, actual, 1e-10);
}
