public Tian(StochasticProcess1D process, double end, int steps, double strike)
: base(process, end, steps)
{
double q = Math.Exp(process.variance(0.0, x0_, dt_));
double r = Math.Exp(driftPerStep_) * Math.Sqrt(q);
up_ = 0.5 * r * q * (q + 1 + Math.Sqrt(q * q + 2 * q - 3));
down_ = 0.5 * r * q * (q + 1 - Math.Sqrt(q * q + 2 * q - 3));
pu_ = (r - down_) / (up_ - down_);
pd_ = 1.0 - pu_;
// doesn't work
// treeCentering_ = (up_+down_)/2.0;
// up_ = up_-treeCentering_;
if (!(pu_ <= 1.0))
{
throw new ApplicationException("negative probability");
}
if (!(pu_ >= 0.0))
{
throw new ApplicationException("negative probability");
}
}
public Trigeorgis(StochasticProcess1D process, double end, int steps, double strike)
: base(process, end, steps)
{
dx_ = Math.Sqrt(process.variance(0.0, x0_, dt_) + driftPerStep_ * driftPerStep_);
pu_ = 0.5 + 0.5 * driftPerStep_ / dx_;
pd_ = 1.0 - pu_;
Utils.QL_REQUIRE(pu_ <= 1.0, () => "negative probability");
Utils.QL_REQUIRE(pu_ >= 0.0, () => "negative probability");
}
public TrinomialTree(StochasticProcess1D process,
TimeGrid timeGrid,
bool isPositive /*= false*/)
: base(timeGrid.size())
{
branchings_ = new List <Branching>();
dx_ = new InitializedList <double>(1);
timeGrid_ = timeGrid;
x0_ = process.x0();
int nTimeSteps = timeGrid.size() - 1;
int jMin = 0;
int jMax = 0;
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_.Add(v * Math.Sqrt(3.0));
Branching branching = new Branching();
for (int j = jMin; j <= jMax; j++)
{
double x = x0_ + j * dx_[i];
double m = process.expectation(t, x, dt);
int temp = (int)(Math.Floor((m - x0_) / dx_[i + 1] + 0.5));
if (isPositive)
{
while (x0_ + (temp - 1) * dx_[i + 1] <= 0)
{
temp++;
}
}
double e = m - (x0_ + temp * dx_[i + 1]);
double e2 = e * e;
double e3 = e * Math.Sqrt(3.0);
double p1 = (1.0 + e2 / v2 - e3 / v) / 6.0;
double p2 = (2.0 - e2 / v2) / 3.0;
double p3 = (1.0 + e2 / v2 + e3 / v) / 6.0;
branching.add(temp, p1, p2, p3);
}
branchings_.Add(branching);
jMin = branching.jMin();
jMax = branching.jMax();
}
}
public Tian(StochasticProcess1D process, double end, int steps, double strike)
: base(process, end, steps)
{
double q = Math.Exp(process.variance(0.0, x0_, dt_));
double r = Math.Exp(driftPerStep_) * Math.Sqrt(q);
up_ = 0.5 * r * q * (q + 1 + Math.Sqrt(q * q + 2 * q - 3));
down_ = 0.5 * r * q * (q + 1 - Math.Sqrt(q * q + 2 * q - 3));
pu_ = (r - down_) / (up_ - down_);
pd_ = 1.0 - pu_;
Utils.QL_REQUIRE(pu_ <= 1.0, () => "negative probability");
Utils.QL_REQUIRE(pu_ >= 0.0, () => "negative probability");
}
public Trigeorgis(StochasticProcess1D process, double end, int steps, double strike)
: base(process, end, steps)
{
dx_ = Math.Sqrt(process.variance(0.0, x0_, dt_) + driftPerStep_ * driftPerStep_);
pu_ = 0.5 + 0.5 * driftPerStep_ / dx_;;
pd_ = 1.0 - pu_;
if (!(pu_ <= 1.0))
{
throw new ApplicationException("negative probability");
}
if (!(pu_ >= 0.0))
{
throw new ApplicationException("negative probability");
}
}
public LeisenReimer(StochasticProcess1D process, double end, int steps, double strike)
: base(process, end, (steps % 2 != 0 ? steps : steps + 1))
{
Utils.QL_REQUIRE(strike > 0.0, () => "strike must be positive");
int oddSteps = (steps % 2 != 0 ? steps : steps + 1);
double variance = process.variance(0.0, x0_, end);
double ermqdt = Math.Exp(driftPerStep_ + 0.5 * variance / oddSteps);
double d2 = (Math.Log(x0_ / strike) + driftPerStep_ * oddSteps) / Math.Sqrt(variance);
pu_ = Utils.PeizerPrattMethod2Inversion(d2, oddSteps);
pd_ = 1.0 - pu_;
double pdash = Utils.PeizerPrattMethod2Inversion(d2 + Math.Sqrt(variance), oddSteps);
up_ = ermqdt * pdash / pu_;
down_ = (ermqdt - pu_ * up_) / (1.0 - pu_);
}
public Joshi4(StochasticProcess1D process, double end, int steps, double strike)
: base(process, end, (steps % 2 != 0 ? steps : steps + 1))
{
Utils.QL_REQUIRE(strike > 0.0, () => "strike must be positive");
int oddSteps = (steps % 2 != 0 ? steps : steps + 1);
double variance = process.variance(0.0, x0_, end);
double ermqdt = Math.Exp(driftPerStep_ + 0.5 * variance / oddSteps);
double d2 = (Math.Log(x0_ / strike) + driftPerStep_ * oddSteps) / Math.Sqrt(variance);
pu_ = computeUpProb((oddSteps - 1.0) / 2.0, d2);
pd_ = 1.0 - pu_;
double pdash = computeUpProb((oddSteps - 1.0) / 2.0, d2 + Math.Sqrt(variance));
up_ = ermqdt * pdash / pu_;
down_ = (ermqdt - pu_ * up_) / (1.0 - pu_);
}
public AdditiveEQPBinomialTree(StochasticProcess1D process, double end, int steps, double strike)
: base(process, end, steps)
{
up_ = -0.5 * driftPerStep_ + 0.5 * Math.Sqrt(4.0 * process.variance(0.0, x0_, dt_) - 3.0 * driftPerStep_ * driftPerStep_);
}
