private Sample <IPath> next(bool antithetic)
{
Sample <List <double> > sequence_ =
antithetic
? generator_.lastSequence()
: generator_.nextSequence();
if (brownianBridge_)
{
bb_.transform(sequence_.value, temp_);
}
else
{
temp_ = new List <double>(sequence_.value);
}
next_.weight = sequence_.weight;
Path path = (Path)next_.value;
path.setFront(process_.x0());
for (int i = 1; i < path.length(); i++)
{
double t = timeGrid_[i - 1];
double dt = timeGrid_.dt(i - 1);
path[i] = process_.evolve(t, path[i - 1], dt,
antithetic
? -temp_[i - 1]
: temp_[i - 1]);
}
return(next_);
}
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();
}
}
private Sample <IPath> next(bool antithetic)
{
if (brownianBridge_)
{
Utils.QL_FAIL("Brownian bridge not supported");
return(null);
}
Sample <List <double> > sequence_ =
antithetic
? generator_.lastSequence()
: generator_.nextSequence();
int m = process_.size();
int n = process_.factors();
MultiPath path = (MultiPath)next_.value;
Vector asset = process_.initialValues();
for (int j = 0; j < m; j++)
{
path[j].setFront(asset[j]);
}
Vector temp;
next_.weight = sequence_.weight;
TimeGrid timeGrid = path[0].timeGrid();
double t, dt;
for (int i = 1; i < path.pathSize(); i++)
{
int offset = (i - 1) * n;
t = timeGrid[i - 1];
dt = timeGrid.dt(i - 1);
if (antithetic)
{
temp = -1 * new Vector(sequence_.value.GetRange(offset, n));
}
else
{
temp = new Vector(sequence_.value.GetRange(offset, n));
}
asset = process_.evolve(t, asset, dt, temp);
for (int j = 0; j < m; j++)
{
path[j][i] = asset[j];
}
}
return(next_);
}
public double value(IPath path)
{
int n = path.length();
Utils.QL_REQUIRE(n > 1, () => "the path cannot be empty");
bool isOptionActive = false;
int? knockNode = null;
double asset_price = (path as Path).front();
double new_asset_price;
double x, y;
double vol;
TimeGrid timeGrid = (path as Path).timeGrid();
double dt;
List <double> u = sequenceGen_.nextSequence().value;
int i;
switch (barrierType_)
{
case Barrier.Type.DownIn:
isOptionActive = false;
for (i = 0; i < n - 1; i++)
{
new_asset_price = (path as Path)[i + 1];
// terminal or initial vol?
vol = diffProcess_.diffusion(timeGrid[i], asset_price);
dt = timeGrid.dt(i);
x = Math.Log(new_asset_price / asset_price);
y = 0.5 * (x - Math.Sqrt(x * x - 2 * vol * vol * dt * Math.Log(u[i])));
y = asset_price * Math.Exp(y);
if (y <= barrier_)
{
isOptionActive = true;
if (knockNode == null)
{
knockNode = i + 1;
}
}
asset_price = new_asset_price;
}
break;
case Barrier.Type.UpIn:
isOptionActive = false;
for (i = 0; i < n - 1; i++)
{
new_asset_price = (path as Path)[i + 1];
// terminal or initial vol?
vol = diffProcess_.diffusion(timeGrid[i], asset_price);
dt = timeGrid.dt(i);
x = Math.Log(new_asset_price / asset_price);
y = 0.5 * (x + Math.Sqrt(x * x - 2 * vol * vol * dt * Math.Log((1 - u[i]))));
y = asset_price * Math.Exp(y);
if (y >= barrier_)
{
isOptionActive = true;
if (knockNode == null)
{
knockNode = i + 1;
}
}
asset_price = new_asset_price;
}
break;
case Barrier.Type.DownOut:
isOptionActive = true;
for (i = 0; i < n - 1; i++)
{
new_asset_price = (path as Path)[i + 1];
// terminal or initial vol?
vol = diffProcess_.diffusion(timeGrid[i], asset_price);
dt = timeGrid.dt(i);
x = Math.Log(new_asset_price / asset_price);
y = 0.5 * (x - Math.Sqrt(x * x - 2 * vol * vol * dt * Math.Log(u[i])));
y = asset_price * Math.Exp(y);
if (y <= barrier_)
{
isOptionActive = false;
if (knockNode == null)
{
knockNode = i + 1;
}
}
asset_price = new_asset_price;
}
break;
case Barrier.Type.UpOut:
isOptionActive = true;
for (i = 0; i < n - 1; i++)
{
new_asset_price = (path as Path)[i + 1];
// terminal or initial vol?
vol = diffProcess_.diffusion(timeGrid[i], asset_price);
dt = timeGrid.dt(i);
x = Math.Log(new_asset_price / asset_price);
y = 0.5 * (x + Math.Sqrt(x * x - 2 * vol * vol * dt * Math.Log((1 - u[i]))));
y = asset_price * Math.Exp(y);
if (y >= barrier_)
{
isOptionActive = false;
if (knockNode == null)
{
knockNode = i + 1;
}
}
asset_price = new_asset_price;
}
break;
default:
Utils.QL_FAIL("unknown barrier type");
break;
}
if (isOptionActive)
{
return(payoff_.value(asset_price) * discounts_.Last());
}
else
{
switch (barrierType_)
{
case Barrier.Type.UpIn:
case Barrier.Type.DownIn:
return(rebate_.GetValueOrDefault() * discounts_.Last());
case Barrier.Type.UpOut:
case Barrier.Type.DownOut:
return(rebate_.GetValueOrDefault() * discounts_[(int)knockNode]);
default:
Utils.QL_FAIL("unknown barrier type");
return(-1);
}
}
}