public LongstaffSchwartzPathPricer(TimeGrid times, IEarlyExercisePathPricer <PathType, double> pathPricer,
YieldTermStructure termStructure)
{
calibrationPhase_ = true;
pathPricer_ = pathPricer;
coeff_ = new InitializedList <Vector>(times.size() - 1);
dF_ = new InitializedList <double>(times.size() - 1);
v_ = pathPricer_.basisSystem();
for (int i = 0; i < times.size() - 1; ++i)
{
dF_[i] = termStructure.discount(times[i + 1])
/ termStructure.discount(times[i]);
}
}
public MultiPathGenerator(StochasticProcess process, TimeGrid times, GSG generator, bool brownianBridge)
{
brownianBridge_ = brownianBridge;
process_ = process;
generator_ = generator;
next_ = new Sample <IPath>(new MultiPath(process.size(), times), 1.0);
Utils.QL_REQUIRE(generator_.dimension() == process.factors() * (times.size() - 1), () =>
"dimension (" + generator_.dimension()
+ ") is not equal to ("
+ process.factors() + " * " + (times.size() - 1)
+ ") the number of factors "
+ "times the number of time steps");
Utils.QL_REQUIRE(times.size() > 1, () => "no times given");
}
public override Lattice tree(TimeGrid grid)
{
TermStructureFittingParameter phi = new TermStructureFittingParameter(termStructure());
ShortRateDynamics numericDynamics =
new Dynamics(phi, a(), sigma());
TrinomialTree trinomial =
new TrinomialTree(numericDynamics.process(), grid);
ShortRateTree numericTree =
new ShortRateTree(trinomial, numericDynamics, grid);
TermStructureFittingParameter.NumericalImpl impl =
(TermStructureFittingParameter.NumericalImpl)phi.implementation();
impl.reset();
double value = 1.0;
double vMin = -50.0;
double vMax = 50.0;
for (int i = 0; i < (grid.size() - 1); i++)
{
double discountBond = termStructure().link.discount(grid[i + 1]);
double xMin = trinomial.underlying(i, 0);
double dx = trinomial.dx(i);
Helper finder = new Helper(i, xMin, dx, discountBond, numericTree);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
impl.setvalue(grid[i], value);
}
return(numericTree);
}
public override Lattice tree(TimeGrid grid)
{
TermStructureFittingParameter phi = new TermStructureFittingParameter(termStructure());
ShortRateDynamics numericDynamics = new Dynamics(phi, a(), sigma());
TrinomialTree trinomial = new TrinomialTree(numericDynamics.process(), grid);
ShortRateTree numericTree = new ShortRateTree(trinomial, numericDynamics, grid);
TermStructureFittingParameter.NumericalImpl impl =
(TermStructureFittingParameter.NumericalImpl)phi.implementation();
impl.reset();
for (int i = 0; i < (grid.size() - 1); i++)
{
double discountBond = termStructure().link.discount(grid[i + 1]);
Vector statePrices = numericTree.statePrices(i);
int size = numericTree.size(i);
double dt = numericTree.timeGrid().dt(i);
double dx = trinomial.dx(i);
double x = trinomial.underlying(i, 0);
double value = 0.0;
for (int j = 0; j < size; j++)
{
value += statePrices[j] * Math.Exp(-x * dt);
x += dx;
}
value = Math.Log(value / discountBond) / dt;
impl.setvalue(grid[i], value);
}
return(numericTree);
}
protected override IPathGenerator <IRNG> pathGenerator()
{
TimeGrid grid = timeGrid();
IRNG gen = new RNG().make_sequence_generator(grid.size() - 1, seed_);
return(new PathGenerator <IRNG>(process_, grid, gen, brownianBridge_));
}
public LatticeShortRateModelEngine(ShortRateModel model,
TimeGrid timeGrid)
: base(model)
{
timeGrid_ = new TimeGrid(timeGrid.Last(), timeGrid.size() - 1 /*timeGrid.dt(1) - timeGrid.dt(0)*/);
timeGrid_ = timeGrid;
timeSteps_ = 0;
lattice_ = this.model_.link.tree(timeGrid);
}
public PathGenerator(StochasticProcess process, TimeGrid timeGrid, GSG generator, bool brownianBridge)
{
brownianBridge_ = brownianBridge;
generator_ = generator;
dimension_ = generator_.dimension();
timeGrid_ = timeGrid;
process_ = process as StochasticProcess1D;
next_ = new Sample <IPath>(new Path(timeGrid_), 1.0);
temp_ = new InitializedList <double>(dimension_);
bb_ = new BrownianBridge(timeGrid_);
Utils.QL_REQUIRE(dimension_ == timeGrid_.size() - 1, () =>
"sequence generator dimensionality (" + dimension_ + ") != timeSteps (" + (timeGrid_.size() - 1) + ")");
}
protected override PathPricer <IPath> pathPricer()
{
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-plain payoff given");
TimeGrid grid = timeGrid();
List <double> discounts = new InitializedList <double>(grid.size());
for (int i = 0; i < grid.size(); i++)
{
discounts[i] = process_.riskFreeRate().currentLink().discount(grid[i]);
}
// do this with template parameters?
if (isBiased_)
{
return(new BiasedBarrierPathPricer(arguments_.barrierType,
arguments_.barrier,
arguments_.rebate,
payoff.optionType(),
payoff.strike(),
discounts));
}
else
{
IRNG sequenceGen = new RandomSequenceGenerator <MersenneTwisterUniformRng>(grid.size() - 1, 5);
return(new BarrierPathPricer(arguments_.barrierType,
arguments_.barrier,
arguments_.rebate,
payoff.optionType(),
payoff.strike(),
discounts,
process_,
sequenceGen));
}
}
//! generic times
public BrownianBridge(TimeGrid timeGrid)
{
size_ = timeGrid.size() - 1;
t_ = new InitializedList <double>(size_);
sqrtdt_ = new InitializedList <double>(size_);
sqrtdt_ = new InitializedList <double>(size_);
bridgeIndex_ = new InitializedList <int>(size_);
leftIndex_ = new InitializedList <int>(size_);
rightIndex_ = new InitializedList <int>(size_);
leftWeight_ = new InitializedList <double>(size_);
rightWeight_ = new InitializedList <double>(size_);
stdDev_ = new InitializedList <double>(size_);
for (int i = 0; i < size_; ++i)
{
t_[i] = timeGrid[i + 1];
}
initialize();
}
//! Tree build-up + numerical fitting to term-structure
public ShortRateTree(TrinomialTree tree, ShortRateDynamics dynamics, TermStructureFittingParameter.NumericalImpl theta,
TimeGrid timeGrid)
: base(timeGrid, tree.size(1))
{
tree_ = tree;
dynamics_ = dynamics;
theta.reset();
double value = 1.0;
double vMin = -100.0;
double vMax = 100.0;
for (int i = 0; i < (timeGrid.size() - 1); i++)
{
double discountBond = theta.termStructure().link.discount(t_[i + 1]);
Helper finder = new Helper(i, discountBond, theta, this);
Brent s1d = new Brent();
s1d.setMaxEvaluations(1000);
value = s1d.solve(finder, 1e-7, value, vMin, vMax);
theta.change(value);
}
}
protected override IPathGenerator <IRNG> pathGenerator()
{
int dimensions = process_.factors();
TimeGrid grid = timeGrid();
IRNG generator = (IRNG)FastActivator <RNG> .Create().make_sequence_generator(dimensions * (grid.size() - 1), seed_);
return(new PathGenerator <IRNG>(process_, grid, generator, brownianBridge_));
}
protected override IPathGenerator <IRNG> controlPathGenerator()
{
int dimensions = process_.factors();
TimeGrid grid = this.timeGrid();
IRNG generator = (IRNG) new RNG().make_sequence_generator(dimensions * (grid.size() - 1), this.seed_);
HybridHestonHullWhiteProcess process = process_ as HybridHestonHullWhiteProcess;
Utils.QL_REQUIRE(process != null, () => "invalid process");
HybridHestonHullWhiteProcess cvProcess = new HybridHestonHullWhiteProcess(process.hestonProcess(),
process.hullWhiteProcess(), 0.0, process.discretization());
return(new MultiPathGenerator <IRNG>(cvProcess, grid, generator, false));
}
public override void calculate()
{
// this is an european option pricer
Utils.QL_REQUIRE(arguments_.exercise.type() == Exercise.Type.European, () => "not an European option");
// plain vanilla
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-striked payoff given");
double v0 = model_.link.v0();
double spotPrice = model_.link.s0();
Utils.QL_REQUIRE(spotPrice > 0.0, () => "negative or null underlying given");
double strike = payoff.strike();
double term = model_.link.riskFreeRate().link.dayCounter().yearFraction(
model_.link.riskFreeRate().link.referenceDate(), arguments_.exercise.lastDate());
double riskFreeDiscount = model_.link.riskFreeRate().link.discount(arguments_.exercise.lastDate());
double dividendDiscount = model_.link.dividendYield().link.discount(arguments_.exercise.lastDate());
//average values
TimeGrid timeGrid = model_.link.timeGrid();
int n = timeGrid.size() - 1;
double kappaAvg = 0.0, thetaAvg = 0.0, sigmaAvg = 0.0, rhoAvg = 0.0;
for (int i = 1; i <= n; ++i)
{
double t = 0.5 * (timeGrid[i - 1] + timeGrid[i]);
kappaAvg += model_.link.kappa(t);
thetaAvg += model_.link.theta(t);
sigmaAvg += model_.link.sigma(t);
rhoAvg += model_.link.rho(t);
}
kappaAvg /= n;
thetaAvg /= n;
sigmaAvg /= n;
rhoAvg /= n;
double c_inf = Math.Min(10.0, Math.Max(0.0001,
Math.Sqrt(1.0 - Math.Pow(rhoAvg, 2)) / sigmaAvg)) * (v0 + kappaAvg * thetaAvg * term);
double p1 = integration_.calculate(c_inf,
new Fj_Helper(model_, term, strike, 1).value) / Const.M_PI;
double p2 = integration_.calculate(c_inf,
new Fj_Helper(model_, term, strike, 2).value) / Const.M_PI;
switch (payoff.optionType())
{
case Option.Type.Call:
results_.value = spotPrice * dividendDiscount * (p1 + 0.5)
- strike * riskFreeDiscount * (p2 + 0.5);
break;
case Option.Type.Put:
results_.value = spotPrice * dividendDiscount * (p1 - 0.5)
- strike * riskFreeDiscount * (p2 - 0.5);
break;
default:
Utils.QL_FAIL("unknown option type");
break;
}
}
public int length()
{
return(timeGrid_.size());
}
