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 PiecewiseTimeDependentHestonModel(Handle <YieldTermStructure> riskFreeRate,
Handle <YieldTermStructure> dividendYield,
Handle <Quote> s0,
double v0,
Parameter theta,
Parameter kappa,
Parameter sigma,
Parameter rho,
TimeGrid timeGrid)
: base(5)
{
s0_ = s0;
riskFreeRate_ = riskFreeRate;
dividendYield_ = dividendYield;
timeGrid_ = timeGrid;
arguments_[0] = theta;
arguments_[1] = kappa;
arguments_[2] = sigma;
arguments_[3] = rho;
arguments_[4] = new ConstantParameter(v0, new PositiveConstraint());
s0.registerWith(update);
riskFreeRate.registerWith(update);
dividendYield.registerWith(update);
}
public TreeLattice(TimeGrid timeGrid, int n) : base(timeGrid)
{
n_ = n;
Utils.QL_REQUIRE(n > 0, () => "there is no zeronomial lattice!");
statePrices_ = new InitializedList <Vector>(1, new Vector(1, 1.0));
statePricesLimit_ = 0;
}
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);
}
//! 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);
// vMin = value - 1.0;
// vMax = value + 1.0;
theta.change(value);
}
}
public TreeCallableFixedRateBondEngine(ShortRateModel model, TimeGrid timeGrid,
Handle <YieldTermStructure> termStructure)
: base(model, timeGrid)
{
termStructure_ = termStructure;
termStructure_.registerWith(update);
}
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 MultiPath(int nAsset, TimeGrid timeGrid)
{
multiPath_ = new List<Path>(nAsset);
for (int i = 0; i < nAsset; i++)
multiPath_.Add(new Path(timeGrid));
if (!(nAsset > 0)) throw new ApplicationException("number of asset must be positive");
}
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;
}
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);
// vMin = value - 10.0;
// vMax = value + 10.0;
}
return numericTree;
}
//! Return by default a trinomial recombining tree
public override Lattice tree(TimeGrid grid)
{
//throw new NotImplementedException();
TrinomialTree trinomial = new TrinomialTree(dynamics().process(), grid);
return(new ShortRateTree(trinomial, dynamics(), grid));
}
//! Plain tree build-up from short-rate dynamics
public ShortRateTree(TrinomialTree tree,
ShortRateDynamics dynamics,
TimeGrid timeGrid)
: base(timeGrid, tree.size(1))
{
tree_ = tree;
dynamics_ = dynamics;
}
public TreeVanillaSwapEngine(ShortRateModel model,
TimeGrid timeGrid,
Handle <YieldTermStructure> termStructure)
: base(model, timeGrid)
{
termStructure_ = termStructure;
termStructure_.registerWith(update);
}
public override Lattice tree(TimeGrid grid)
{
ShortRateDynamics dyn = dynamics();
TrinomialTree tree1 = new TrinomialTree(dyn.xProcess(), grid);
TrinomialTree tree2 = new TrinomialTree(dyn.yProcess(), grid);
return((Lattice)(new ShortRateTree(tree1, tree2, dyn)));
}
public MultiPath(int nAsset, TimeGrid timeGrid)
{
multiPath_ = new List <Path>(nAsset);
for (int i = 0; i < nAsset; i++)
{
multiPath_.Add(new Path(timeGrid));
}
Utils.QL_REQUIRE(nAsset > 0, () => "number of asset must be positive");
}
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 Path(TimeGrid timeGrid, Vector values) {
timeGrid_ = timeGrid;
values_ = (Vector)values.Clone();
if (values_.empty())
values_ = new Vector(timeGrid_.size());
if (values_.size() != timeGrid_.size())
throw new ApplicationException("different number of times and asset values");
}
public TreeLattice(TimeGrid timeGrid, int n) : base(timeGrid)
{
n_ = n;
if (!(n > 0))
{
throw new Exception("there is no zeronomial lattice!");
}
statePrices_ = new InitializedList <Vector>(1, new Vector(1, 1.0));
statePricesLimit_ = 0;
}
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 Path(TimeGrid timeGrid, Vector values)
{
timeGrid_ = timeGrid;
values_ = (Vector)values.Clone();
if (values_.empty())
{
values_ = new Vector(timeGrid_.size());
}
Utils.QL_REQUIRE(values_.size() == timeGrid_.size(), () => "different number of times and asset values");
}
public MultiPath(int nAsset, TimeGrid timeGrid)
{
multiPath_ = new List <Path>(nAsset);
for (int i = 0; i < nAsset; i++)
{
multiPath_.Add(new Path(timeGrid));
}
if (!(nAsset > 0))
{
throw new Exception("number of asset must be positive");
}
}
public DiscretizedVanillaOption(VanillaOption.Arguments args, StochasticProcess process, TimeGrid grid) {
arguments_ = args;
stoppingTimes_ = new InitializedList<double>(args.exercise.dates().Count);
for (int i=0; i<stoppingTimes_.Count; ++i) {
stoppingTimes_[i] = process.time(args.exercise.date(i));
if (!grid.empty()) {
// adjust to the given grid
stoppingTimes_[i] = grid.closestTime(stoppingTimes_[i]);
}
}
}
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));
}
// constructors
public PathGenerator(StochasticProcess process, double length, int timeSteps, GSG generator, bool brownianBridge)
{
brownianBridge_ = brownianBridge;
generator_ = generator;
dimension_ = generator_.dimension();
timeGrid_ = new TimeGrid(length, timeSteps);
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_ == timeSteps, () =>
"sequence generator dimensionality (" + dimension_ + ") != timeSteps (" + timeSteps + ")");
}
public override void calculate()
{
if (base.model_ == null)
{
throw new ArgumentException("no model specified");
}
Date referenceDate;
DayCounter dayCounter;
ITermStructureConsistentModel tsmodel =
(ITermStructureConsistentModel)base.model_.link;
try
{
if (tsmodel != null)
{
referenceDate = tsmodel.termStructure().link.referenceDate();
dayCounter = tsmodel.termStructure().link.dayCounter();
}
else
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
}
catch
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
DiscretizedSwap swap = new DiscretizedSwap(arguments_, referenceDate, dayCounter);
List <double> times = swap.mandatoryTimes();
Lattice lattice;
if (lattice_ != null)
{
lattice = lattice_;
}
else
{
TimeGrid timeGrid = new TimeGrid(times, times.Count, timeSteps_);
lattice = model_.link.tree(timeGrid);
}
swap.initialize(lattice, times.Last());
swap.rollback(0.0);
results_.value = swap.presentValue();
}
public Path(TimeGrid timeGrid, Vector values)
{
timeGrid_ = timeGrid;
values_ = (Vector)values.Clone();
if (values_.empty())
{
values_ = new Vector(timeGrid_.size());
}
if (values_.size() != timeGrid_.size())
{
throw new ApplicationException("different number of times and asset values");
}
}
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");
}
//! 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();
}
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]);
}
}
private void pathGenerator(UnderlyingInfo under)
{
ulong seed = 1;
int timeSteps = 365;
//
int dimensions = this.processArr_.factors();
double t = processArr_.time(maturity);
TimeGrid grid = new TimeGrid(t, timeSteps);
IRNG rndGenerator = (IRNG)new PseudoRandom().make_sequence_generator(dimensions * (grid.size() - 1), seed);
this.pathGenerator_ = new MultiPathGenerator<IRNG>(this.processArr_, grid, rndGenerator, false);
}
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_);
if (dimension_ != timeGrid_.size() - 1)
{
throw new Exception("sequence generator dimensionality (" + dimension_
+ ") != timeSteps (" + (timeGrid_.size() - 1) + ")");
}
}
//! 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();
}
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);
if (generator_.dimension() != process.factors() * (times.size() - 1))
{
throw new Exception("dimension (" + generator_.dimension()
+ ") is not equal to ("
+ process.factors() + " * " + (times.size() - 1)
+ ") the number of factors "
+ "times the number of time steps");
}
if (!(times.size() > 1))
{
throw new Exception("no times given");
}
}
//@}
public override void calculate()
{
Utils.QL_REQUIRE(model_ != null, () => "no model specified");
Date referenceDate;
DayCounter dayCounter;
ITermStructureConsistentModel tsmodel = (ITermStructureConsistentModel)base.model_.link;
if (tsmodel != null)
{
referenceDate = tsmodel.termStructure().link.referenceDate();
dayCounter = tsmodel.termStructure().link.dayCounter();
}
else
{
referenceDate = termStructure_.link.referenceDate();
dayCounter = termStructure_.link.dayCounter();
}
DiscretizedCallableFixedRateBond callableBond = new DiscretizedCallableFixedRateBond(arguments_, referenceDate, dayCounter);
Lattice lattice;
if (lattice_ != null)
{
lattice = lattice_;
}
else
{
List <double> times = callableBond.mandatoryTimes();
TimeGrid timeGrid = new TimeGrid(times, times.Count, timeSteps_);
lattice = model_.link.tree(timeGrid);
}
double redemptionTime = dayCounter.yearFraction(referenceDate, arguments_.redemptionDate);
callableBond.initialize(lattice, redemptionTime);
callableBond.rollback(0.0);
results_.value = results_.settlementValue = callableBond.presentValue();
}
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));
}
}
public override void calculate()
{
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
Calendar volcal = process_.blackVolatility().link.calendar();
double s0 = process_.stateVariable().link.value();
if (!(s0 > 0.0))
{
throw new ApplicationException("negative or null underlying given");
}
double v = process_.blackVolatility().link.blackVol(arguments_.exercise.lastDate(), s0);
Date maturityDate = arguments_.exercise.lastDate();
double r = process_.riskFreeRate().link.zeroRate(maturityDate, rfdc, Compounding.Continuous, Frequency.NoFrequency).rate();
double q = process_.dividendYield().link.zeroRate(maturityDate, divdc, Compounding.Continuous, Frequency.NoFrequency).rate();
Date referenceDate = process_.riskFreeRate().link.referenceDate();
// binomial trees with constant coefficient
var flatRiskFree = new Handle <YieldTermStructure>(new FlatForward(referenceDate, r, rfdc));
var flatDividends = new Handle <YieldTermStructure>(new FlatForward(referenceDate, q, divdc));
var flatVol = new Handle <BlackVolTermStructure>(new BlackConstantVol(referenceDate, volcal, v, voldc));
PlainVanillaPayoff payoff = arguments_.payoff as PlainVanillaPayoff;
if (payoff == null)
{
throw new ApplicationException("non-plain payoff given");
}
double maturity = rfdc.yearFraction(referenceDate, maturityDate);
StochasticProcess1D bs =
new GeneralizedBlackScholesProcess(process_.stateVariable(), flatDividends, flatRiskFree, flatVol);
TimeGrid grid = new TimeGrid(maturity, timeSteps_);
T tree = new T().factory(bs, maturity, timeSteps_, payoff.strike());
BlackScholesLattice <T> lattice = new BlackScholesLattice <T>(tree, r, maturity, timeSteps_);
DiscretizedVanillaOption option = new DiscretizedVanillaOption(arguments_, process_, grid);
option.initialize(lattice, maturity);
// Partial derivatives calculated from various points in the
// binomial tree (Odegaard)
// Rollback to third-last step, and get underlying price (s2) &
// option values (p2) at this point
option.rollback(grid[2]);
Vector va2 = new Vector(option.values());
if (!(va2.size() == 3))
{
throw new ApplicationException("Expect 3 nodes in grid at second step");
}
double p2h = va2[2]; // high-price
double s2 = lattice.underlying(2, 2); // high price
// Rollback to second-last step, and get option value (p1) at
// this point
option.rollback(grid[1]);
Vector va = new Vector(option.values());
if (!(va.size() == 2))
{
throw new ApplicationException("Expect 2 nodes in grid at first step");
}
double p1 = va[1];
// Finally, rollback to t=0
option.rollback(0.0);
double p0 = option.presentValue();
double s1 = lattice.underlying(1, 1);
// Calculate partial derivatives
double delta0 = (p1 - p0) / (s1 - s0); // dp/ds
double delta1 = (p2h - p1) / (s2 - s1); // dp/ds
// Store results
results_.value = p0;
results_.delta = delta0;
results_.gamma = 2.0 * (delta1 - delta0) / (s2 - s0); //d(delta)/ds
results_.theta = Utils.blackScholesTheta(process_,
results_.value.GetValueOrDefault(),
results_.delta.GetValueOrDefault(),
results_.gamma.GetValueOrDefault());
}
override public void setPosition(TimeGrid timeGrid,
DayCounter dayCounter,
Calendar calendar)
{
}
public override Lattice tree(TimeGrid grid){
TrinomialTree trinomial = new TrinomialTree(dynamics().process(), grid, true);
return new ShortRateTree(trinomial, dynamics(), grid);
}
public void testLambdaBootstrapping()
{
//"Testing caplet LMM lambda bootstrapping..."
//SavedSettings backup;
double tolerance = 1e-10;
double[] lambdaExpected = {14.3010297550, 19.3821411939, 15.9816590141,
15.9953118303, 14.0570815635, 13.5687599894,
12.7477197786, 13.7056638165, 11.6191989567};
LiborForwardModelProcess process = makeProcess();
Matrix covar = process.covariance(0.0, null, 1.0);
for (int i=0; i<9; ++i) {
double calculated = Math.Sqrt(covar[i+1,i+1]);
double expected = lambdaExpected[i]/100;
if (Math.Abs(calculated - expected) > tolerance)
Assert.Fail("Failed to reproduce expected lambda values"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
}
LfmCovarianceParameterization param = process.covarParam();
List<double> tmp = process.fixingTimes();
TimeGrid grid= new TimeGrid(tmp.Last(), 14);
for (int t=0; t<grid.size(); ++t) {
//verifier la presence du null
Matrix diff = param.integratedCovariance(grid[t],null)
- param.integratedCovariance(grid[t], null);
for (int i=0; i<diff.rows(); ++i)
{
for (int j=0; j<diff.columns(); ++j)
{
if (Math.Abs(diff[i,j]) > tolerance)
{
Assert.Fail("Failed to reproduce integrated covariance"
+ "\n calculated: " + diff[i,j]
+ "\n expected: " + 0);
}
}
}
}
}
public void testMonteCarloCapletPricing()
{
//"Testing caplet LMM Monte-Carlo caplet pricing..."
//SavedSettings backup;
/* factor loadings are taken from Hull & White article
plus extra normalisation to get orthogonal eigenvectors
http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf */
double[] compValues = {0.85549771, 0.46707264, 0.22353259,
0.91915359, 0.37716089, 0.11360610,
0.96438280, 0.26413316,-0.01412414,
0.97939148, 0.13492952,-0.15028753,
0.95970595,-0.00000000,-0.28100621,
0.97939148,-0.13492952,-0.15028753,
0.96438280,-0.26413316,-0.01412414,
0.91915359,-0.37716089, 0.11360610,
0.85549771,-0.46707264, 0.22353259};
Matrix volaComp=new Matrix(9,3);
List<double> lcompValues=new InitializedList<double>(27,0);
List<double> ltemp = new InitializedList<double>(3, 0);
lcompValues=compValues.ToList();
//std::copy(compValues, compValues+9*3, volaComp.begin());
for (int i = 0; i < 9; i++)
{
ltemp = lcompValues.GetRange(3*i, 3);
for (int j = 0; j < 3; j++)
volaComp[i, j] = ltemp[j];
}
LiborForwardModelProcess process1 = makeProcess();
LiborForwardModelProcess process2 = makeProcess(volaComp);
List<double> tmp = process1.fixingTimes();
TimeGrid grid=new TimeGrid(tmp ,12);
List<int> location=new List<int>();
for (int i=0; i < tmp.Count; ++i) {
location.Add(grid.index(tmp[i])) ;
}
// set-up a small Monte-Carlo simulation to price caplets
// and ratchet caps using a one- and a three factor libor market model
ulong seed = 42;
LowDiscrepancy.icInstance = new InverseCumulativeNormal();
IRNG rsg1 = (IRNG)new LowDiscrepancy().make_sequence_generator(
process1.factors()*(grid.size()-1), seed);
IRNG rsg2 = (IRNG)new LowDiscrepancy().make_sequence_generator(
process2.factors()*(grid.size()-1), seed);
MultiPathGenerator<IRNG> generator1=new MultiPathGenerator<IRNG> (process1, grid, rsg1, false);
MultiPathGenerator<IRNG> generator2=new MultiPathGenerator<IRNG> (process2, grid, rsg2, false);
const int nrTrails = 250000;
List<GeneralStatistics> stat1 = new InitializedList<GeneralStatistics>(process1.size());
List<GeneralStatistics> stat2 = new InitializedList<GeneralStatistics>(process2.size());
List<GeneralStatistics> stat3 = new InitializedList<GeneralStatistics>(process2.size() - 1);
for (int i=0; i<nrTrails; ++i) {
Sample<MultiPath> path1 = generator1.next();
Sample<MultiPath> path2 = generator2.next();
List<double> rates1=new InitializedList<double>(len);
List<double> rates2 = new InitializedList<double>(len);
for (int j=0; j<process1.size(); ++j) {
rates1[j] = path1.value[j][location[j]];
rates2[j] = path2.value[j][location[j]];
}
List<double> dis1 = process1.discountBond(rates1);
List<double> dis2 = process2.discountBond(rates2);
for (int k=0; k<process1.size(); ++k) {
double accrualPeriod = process1.accrualEndTimes()[k]
- process1.accrualStartTimes()[k];
// caplet payoff function, cap rate at 4%
double payoff1 = Math.Max(rates1[k] - 0.04, 0.0) * accrualPeriod;
double payoff2 = Math.Max(rates2[k] - 0.04, 0.0) * accrualPeriod;
stat1[k].add(dis1[k] * payoff1);
stat2[k].add(dis2[k] * payoff2);
if (k != 0) {
// ratchet cap payoff function
double payoff3 = Math.Max(rates2[k] - (rates2[k-1]+0.0025), 0.0)
* accrualPeriod;
stat3[k-1].add(dis2[k] * payoff3);
}
}
}
double[] capletNpv = {0.000000000000, 0.000002841629, 0.002533279333,
0.009577143571, 0.017746502618, 0.025216116835,
0.031608230268, 0.036645683881, 0.039792254012,
0.041829864365};
double[] ratchetNpv = {0.0082644895, 0.0082754754, 0.0082159966,
0.0082982822, 0.0083803357, 0.0084366961,
0.0084173270, 0.0081803406, 0.0079533814};
for (int k=0; k < process1.size(); ++k) {
double calculated1 = stat1[k].mean();
double tolerance1 = stat1[k].errorEstimate();
double expected = capletNpv[k];
if (Math.Abs(calculated1 - expected) > tolerance1) {
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated1
+ "\n error int: " + tolerance1
+ "\n expected: " + expected);
}
double calculated2 = stat2[k].mean();
double tolerance2 = stat2[k].errorEstimate();
if (Math.Abs(calculated2 - expected) > tolerance2) {
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated2
+ "\n error int: " + tolerance2
+ "\n expected: " + expected);
}
if (k != 0) {
double calculated3 = stat3[k-1].mean();
double tolerance3 = stat3[k-1].errorEstimate();
expected = ratchetNpv[k-1];
double refError = 1e-5; // 1e-5. error bars of the reference values
if (Math.Abs(calculated3 - expected) > tolerance3 + refError) {
Assert.Fail("Failed to reproduce expected caplet NPV"
+ "\n calculated: " + calculated3
+ "\n error int: " + tolerance3 + refError
+ "\n expected: " + expected);
}
}
}
}
public abstract Lattice tree(TimeGrid t);
public void testSwaptionPricing()
{
//"Testing forward swap and swaption pricing...");
//SavedSettings backup;
const int size = 10;
const int steps = 8*size;
#if QL_USE_INDEXED_COUPON
const double tolerance = 1e-6;
#else
const double tolerance = 1e-12;
#endif
List<Date> dates = new List<Date>();
List<double> rates = new List<double>();
dates.Add(new Date(4,9,2005));
dates.Add(new Date(4,9,2011));
rates.Add(0.04);
rates.Add(0.08);
IborIndex index = makeIndex(dates, rates);
LiborForwardModelProcess process = new LiborForwardModelProcess(size, index);
LmCorrelationModel corrModel = new LmExponentialCorrelationModel(size, 0.5);
LmVolatilityModel volaModel = new LmLinearExponentialVolatilityModel(process.fixingTimes(),
0.291, 1.483, 0.116, 0.00001);
// set-up pricing engine
process.setCovarParam((LfmCovarianceParameterization)
new LfmCovarianceProxy(volaModel, corrModel));
// set-up a small Monte-Carlo simulation to price swations
List<double> tmp = process.fixingTimes();
TimeGrid grid=new TimeGrid(tmp ,steps);
List<int> location=new List<int>();
for (int i=0; i < tmp.Count; ++i) {
location.Add(grid.index(tmp[i])) ;
}
ulong seed=42;
const int nrTrails = 5000;
LowDiscrepancy.icInstance = new InverseCumulativeNormal();
IRNG rsg = (InverseCumulativeRsg<RandomSequenceGenerator<MersenneTwisterUniformRng>
,InverseCumulativeNormal>)
new PseudoRandom().make_sequence_generator(process.factors()*(grid.size()-1),seed);
MultiPathGenerator<IRNG> generator=new MultiPathGenerator<IRNG>(process,
grid,
rsg, false);
LiborForwardModel liborModel = new LiborForwardModel(process, volaModel, corrModel);
Calendar calendar = index.fixingCalendar();
DayCounter dayCounter = index.forwardingTermStructure().link.dayCounter();
BusinessDayConvention convention = index.businessDayConvention();
Date settlement = index.forwardingTermStructure().link.referenceDate();
SwaptionVolatilityMatrix m = liborModel.getSwaptionVolatilityMatrix();
for (int i=1; i < size; ++i) {
for (int j=1; j <= size-i; ++j) {
Date fwdStart = settlement + new Period(6*i, TimeUnit.Months);
Date fwdMaturity = fwdStart + new Period(6*j, TimeUnit.Months);
Schedule schedule =new Schedule(fwdStart, fwdMaturity, index.tenor(), calendar,
convention, convention, DateGeneration.Rule.Forward, false);
double swapRate = 0.0404;
VanillaSwap forwardSwap = new VanillaSwap(VanillaSwap.Type.Receiver, 1.0,
schedule, swapRate, dayCounter,
schedule, index, 0.0, index.dayCounter());
forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure()));
// check forward pricing first
double expected = forwardSwap.fairRate();
double calculated = liborModel.S_0(i-1,i+j-1);
if (Math.Abs(expected - calculated) > tolerance)
Assert.Fail("Failed to reproduce fair forward swap rate"
+ "\n calculated: " + calculated
+ "\n expected: " + expected);
swapRate = forwardSwap.fairRate();
forwardSwap =
new VanillaSwap(VanillaSwap.Type.Receiver, 1.0,
schedule, swapRate, dayCounter,
schedule, index, 0.0, index.dayCounter());
forwardSwap.setPricingEngine(new DiscountingSwapEngine(index.forwardingTermStructure()));
if (i == j && i<=size/2) {
IPricingEngine engine =
new LfmSwaptionEngine(liborModel, index.forwardingTermStructure());
Exercise exercise =
new EuropeanExercise(process.fixingDates()[i]);
Swaption swaption =
new Swaption(forwardSwap, exercise);
swaption.setPricingEngine(engine);
GeneralStatistics stat = new GeneralStatistics();
for (int n=0; n<nrTrails; ++n) {
Sample<MultiPath> path = (n%2!=0) ? generator.antithetic()
: generator.next();
//Sample<MultiPath> path = generator.next();
List<double> rates_ = new InitializedList<double>(size);
for (int k=0; k<process.size(); ++k) {
rates_[k] = path.value[k][location[i]];
}
List<double> dis = process.discountBond(rates_);
double npv=0.0;
for (int k=i; k < i+j; ++k) {
npv += (swapRate - rates_[k])
* ( process.accrualEndTimes()[k]
- process.accrualStartTimes()[k])*dis[k];
}
stat.add(Math.Max(npv, 0.0));
}
if (Math.Abs(swaption.NPV() - stat.mean())
> stat.errorEstimate()*2.35)
Assert.Fail("Failed to reproduce swaption npv"
+ "\n calculated: " + stat.mean()
+ "\n expected: " + swaption.NPV());
}
}
}
}
static void Main(string[] args)
{
DateTime timer = DateTime.Now;
Date todaysDate = new Date(15, 2, 2002);
Calendar calendar = new TARGET();
Date settlementDate = new Date(19, 2, 2002);
Settings.setEvaluationDate(todaysDate);
// flat yield term structure impling 1x5 swap at 5%
Quote flatRate = new SimpleQuote(0.04875825);
Handle<YieldTermStructure> rhTermStructure = new Handle<YieldTermStructure>(
new FlatForward(settlementDate, new Handle<Quote>(flatRate),
new Actual365Fixed()));
// Define the ATM/OTM/ITM swaps
Frequency fixedLegFrequency = Frequency.Annual;
BusinessDayConvention fixedLegConvention = BusinessDayConvention.Unadjusted;
BusinessDayConvention floatingLegConvention = BusinessDayConvention.ModifiedFollowing;
DayCounter fixedLegDayCounter = new Thirty360(Thirty360.Thirty360Convention.European);
Frequency floatingLegFrequency = Frequency.Semiannual;
VanillaSwap.Type type = VanillaSwap.Type.Payer;
double dummyFixedRate = 0.03;
IborIndex indexSixMonths = new Euribor6M(rhTermStructure);
Date startDate = calendar.advance(settlementDate, 1, TimeUnit.Years,
floatingLegConvention);
Date maturity = calendar.advance(startDate, 5, TimeUnit.Years,
floatingLegConvention);
Schedule fixedSchedule = new Schedule(startDate, maturity, new Period(fixedLegFrequency),
calendar, fixedLegConvention, fixedLegConvention,
DateGeneration.Rule.Forward, false);
Schedule floatSchedule = new Schedule(startDate, maturity, new Period(floatingLegFrequency),
calendar, floatingLegConvention, floatingLegConvention,
DateGeneration.Rule.Forward, false);
VanillaSwap swap = new VanillaSwap(
type, 1000.0,
fixedSchedule, dummyFixedRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
swap.setPricingEngine(new DiscountingSwapEngine(rhTermStructure));
double fixedAtmRate = swap.fairRate();
double fixedOtmRate = fixedAtmRate * 1.2;
double fixedItmRate = fixedAtmRate * 0.8;
VanillaSwap atmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedAtmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
VanillaSwap otmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedOtmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
VanillaSwap itmSwap = new VanillaSwap(
type, 1000.0,
fixedSchedule, fixedItmRate, fixedLegDayCounter,
floatSchedule, indexSixMonths, 0.0,
indexSixMonths.dayCounter());
// defining the swaptions to be used in model calibration
List<Period> swaptionMaturities = new List<Period>(5);
swaptionMaturities.Add(new Period(1, TimeUnit.Years));
swaptionMaturities.Add(new Period(2, TimeUnit.Years));
swaptionMaturities.Add(new Period(3, TimeUnit.Years));
swaptionMaturities.Add(new Period(4, TimeUnit.Years));
swaptionMaturities.Add(new Period(5, TimeUnit.Years));
List<CalibrationHelper> swaptions = new List<CalibrationHelper>();
// List of times that have to be included in the timegrid
List<double> times = new List<double>();
for (int i = 0; i < NumRows; i++)
{
int j = NumCols - i - 1; // 1x5, 2x4, 3x3, 4x2, 5x1
int k = i * NumCols + j;
Quote vol = new SimpleQuote(SwaptionVols[k]);
swaptions.Add(new SwaptionHelper(swaptionMaturities[i],
new Period(SwapLenghts[j], TimeUnit.Years),
new Handle<Quote>(vol),
indexSixMonths,
indexSixMonths.tenor(),
indexSixMonths.dayCounter(),
indexSixMonths.dayCounter(),
rhTermStructure, false));
swaptions.Last().addTimesTo(times);
}
// Building time-grid
TimeGrid grid = new TimeGrid(times, 30);
// defining the models
G2 modelG2 = new G2(rhTermStructure);
HullWhite modelHw = new HullWhite(rhTermStructure);
HullWhite modelHw2 = new HullWhite(rhTermStructure);
BlackKarasinski modelBk = new BlackKarasinski(rhTermStructure);
// model calibrations
Console.WriteLine("G2 (analytic formulae) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new G2SwaptionEngine(modelG2, 6.0, 16));
CalibrateModel(modelG2, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n" +
"b = {2:0.000000}, " +
"eta = {3:0.0000000}\n" +
"rho = {4:0.00000}\n",
modelG2.parameters()[0],
modelG2.parameters()[1],
modelG2.parameters()[2],
modelG2.parameters()[3],
modelG2.parameters()[4]);
Console.WriteLine("Hull-White (analytic formulae) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new JamshidianSwaptionEngine(modelHw));
CalibrateModel(modelHw, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n",
modelHw.parameters()[0],
modelHw.parameters()[1]);
Console.WriteLine("Hull-White (numerical) calibration");
for (int i = 0; i < swaptions.Count(); i++)
swaptions[i].setPricingEngine(new TreeSwaptionEngine(modelHw2, grid));
CalibrateModel(modelHw2, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.0000000}\n",
modelHw2.parameters()[0],
modelHw2.parameters()[1]);
Console.WriteLine("Black-Karasinski (numerical) calibration");
for (int i = 0; i < swaptions.Count; i++)
swaptions[i].setPricingEngine(new TreeSwaptionEngine(modelBk, grid));
CalibrateModel(modelBk, swaptions);
Console.WriteLine("calibrated to:\n" +
"a = {0:0.000000}, " +
"sigma = {1:0.00000}\n",
modelBk.parameters()[0],
modelBk.parameters()[1]);
// ATM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (ATM)",
fixedAtmRate);
List<Date> bermudanDates = new List<Date>();
List<CashFlow> leg = swap.fixedLeg();
for (int i = 0; i < leg.Count; i++)
{
Coupon coupon = (Coupon)leg[i];
bermudanDates.Add(coupon.accrualStartDate());
}
Exercise bermudanExercise = new BermudanExercise(bermudanDates);
Swaption bermudanSwaption = new Swaption(atmSwap, bermudanExercise);
// Do the pricing for each model
// G2 price the European swaption here, it should switch to bermudan
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.00}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.000}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", bermudanSwaption.NPV());
bermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.000}", bermudanSwaption.NPV());
// OTM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (OTM)",
fixedOtmRate);
Swaption otmBermudanSwaption = new Swaption(otmSwap, bermudanExercise);
// Do the pricing for each model
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.0000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.0000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", otmBermudanSwaption.NPV());
otmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.0000}", otmBermudanSwaption.NPV());
// ITM Bermudan swaption pricing
Console.WriteLine("Payer bermudan swaption "
+ "struck at {0:0.00000 %} (ITM)",
fixedItmRate);
Swaption itmBermudanSwaption = new Swaption(itmSwap, bermudanExercise);
// Do the pricing for each model
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelG2, 50));
Console.WriteLine("G2: {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw, 50));
Console.WriteLine("HW: {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelHw2, 50));
Console.WriteLine("HW (num): {0:0.000}", itmBermudanSwaption.NPV());
itmBermudanSwaption.setPricingEngine(new TreeSwaptionEngine(modelBk, 50));
Console.WriteLine("BK: {0:0.000}", itmBermudanSwaption.NPV());
Console.WriteLine(" \nRun completed in {0}", DateTime.Now - timer);
Console.WriteLine();
Console.Write("Press any key to continue ...");
Console.ReadKey();
}
public Path(TimeGrid timeGrid)
: this(timeGrid, new Vector())
{
}
public Lattice(TimeGrid timeGrid)
{
t_ = timeGrid;
}
