public LeisenReimerBinomialTree(BlackScholesProcess process, double x0, double strike, double tend, int steps = 200, int peizerPrattMethod = 1)
: base(process, x0, tend, (steps % 2 == 0 ? steps + 1 : steps))
{
_strike = strike;
Dx = process.StdDeviation(0, X0, Dt); // sigma * sqrt(dt)
var drift = process.Drift(0, X0, Dt); // r - q - 0.5 * sigma * sigma
var sigma = process.Diffusion(0, X0); // sigma
var d1 = (Math.Log(X0 / _strike) + (drift + sigma * sigma) * tend) / (sigma * Math.Sqrt(tend)); // d+
var d2 = (Math.Log(X0 / _strike) + drift * tend) / (sigma * Math.Sqrt(tend)); // d-
var p1 = ProbabilityHelper(d1, NumberOfSteps, peizerPrattMethod);
var p2 = ProbabilityHelper(d2, NumberOfSteps, peizerPrattMethod);
var tmp = Math.Exp((drift + 0.5 * sigma * sigma) * Dt);
var u = tmp * p1 / p2;
var d = (tmp - p2 * u) / (1 - p2);
PUp = p2;
PDown = 1 - PUp;
_steps = steps % 2 == 0 ? steps + 1 : steps; // only use odd number
_stateValues = new double[_steps + 1][];
for (int i = 0; i < _steps + 1; ++i)
{
_stateValues[i] = new double[i + 1];
for (int j = 0; j < i + 1; ++j)
{
_stateValues[i][j] = X0 * Math.Pow(u, j) * Math.Pow(d, i - j);
}
}
}
/// <summary>
/// Initializes a new instance of the <see cref="BinomialTree"/> class.
/// The underlying process shall be a Black-Schole process with constant r, sigma
/// </summary>
/// <param name="process">The process.</param>
/// <param name="x0">The x0.</param>
/// <param name="tend">The end time in years.</param>
/// <param name="steps">The number of time steps.</param>
//protected BinomialTree(BlackScholesProcess process, double x0, double tend, int steps = 200)
protected BinomialTree(BlackScholesProcess process, double x0, double tend, int steps)
{
Process = process;
X0 = x0;
Dt = tend / steps;
NumberOfSteps = steps;
DriftPerStep = process.Drift(0, x0, Dt) * Dt;
AllBranchDirections = new List <BranchDirection> {
BranchDirection.Down, BranchDirection.Up
};
}
