///<summary>
///</summary>
///<param name="process"></param>
///<param name="timeGrid"></param>
///<param name="isPositive"></param>
public TrinomialTree(IDiffusionProcess process,
ITimeGrid timeGrid, bool isPositive) : base(timeGrid.Count)
{
TimeGrid = timeGrid;
_x0 = process.X0;
_dx = new double[timeGrid.Count];
// dx[0] = 0.0;
int nTimeSteps = timeGrid.Count - 1;
int jMin = 0;
int jMax = 0;
_branchings = new TrinomialBranching[nTimeSteps];
for (int i = 0; i < nTimeSteps; i++)
{
double t = timeGrid[i];
double dt = timeGrid.Dt(i);
//Variance must be independent of x
double v2 = process.Variance(t, 0.0, dt);
double v = Math.Sqrt(v2);
_dx[i + 1] = v * Math.Sqrt(3.0); // Add dx
var branching =
new TrinomialBranching(jMax - jMin + 1);
int jNewMin = int.MaxValue;
int jNewMax = int.MinValue;
for (int j = jMin; j <= jMax; j++)
{
double x = _x0 + j * _dx[i];
double m = process.Expectation(t, x, dt);
var temp = (int)Math.Floor((m - _x0) / _dx[i + 1] + 0.5);
if (isPositive)
{
while (_x0 + (temp - 1) * _dx[i + 1] <= 0)
{
temp++;
}
}
if (temp < jNewMin)
{
jNewMin = temp;
}
if (temp > jNewMax)
{
jNewMax = temp;
}
double e = m - (_x0 + temp * _dx[i + 1]);
double e2 = e * e;
double e3 = e * Math.Sqrt(3.0);
int j0 = j - jMin;
branching.K[j0] = temp;
branching.Probs[0, j0] = (1.0 + e2 / v2 - e3 / v) / 6.0;
branching.Probs[1, j0] = (2.0 - e2 / v2) / 3.0;
branching.Probs[2, j0] = (1.0 + e2 / v2 + e3 / v) / 6.0;
}
branching.JMin = jNewMin - 1;
branching.JMax = jNewMax + 1;
_branchings[i] = branching; // Add branching
jMin = branching.JMin;
jMax = branching.JMax;
}
}
///<summary>
///</summary>
///<param name="process"></param>
///<param name="endTime"></param>
///<param name="steps"></param>
public StandardBinomialTree(IDiffusionProcess process,
double endTime, int steps) : base(steps + 1)
{
double dt = endTime / steps;
_x0 = process.X0;
_dx = Math.Sqrt(process.Variance(0.0, 0.0, dt));
}