//! Calibrate to a set of market instruments (caps/swaptions)
/*! An additional constraint can be passed which must be
* satisfied in addition to the constraints of the model.
*/
//public void calibrate(List<CalibrationHelper> instruments, OptimizationMethod method, EndCriteria endCriteria,
// Constraint constraint = new Constraint(), List<double> weights = new List<double>()) {
public void calibrate(List <CalibrationHelper> instruments, OptimizationMethod method, EndCriteria endCriteria,
Constraint additionalConstraint, List <double> weights)
{
if (!(weights.Count == 0 || weights.Count == instruments.Count))
{
throw new ApplicationException("mismatch between number of instruments and weights");
}
Constraint c;
if (additionalConstraint.empty())
{
c = constraint_;
}
else
{
c = new CompositeConstraint(constraint_, additionalConstraint);
}
List <double> w = weights.Count == 0 ? new InitializedList <double>(instruments.Count, 1.0): weights;
CalibrationFunction f = new CalibrationFunction(this, instruments, w);
Problem prob = new Problem(f, c, parameters());
shortRateEndCriteria_ = method.minimize(prob, endCriteria);
Vector result = new Vector(prob.currentValue());
setParams(result);
// recheck
Vector shortRateProblemValues_ = prob.values(result);
notifyObservers();
}
public DVPLI.EstimationResult Estimate(List <object> data, DVPLI.IEstimationSettings settings = null, DVPLI.IController controller = null, Dictionary <string, object> properties = null)
{
DVPLI.InterestRateMarketData irmd = data[0] as DVPLI.InterestRateMarketData;
//Date today = new Date(15, Month.February, 2002);
//Date settlement = new Date(19, Month.February, 2002);
Settings.setEvaluationDate(irmd.Date);
Handle <YieldTermStructure> termStructure = new Handle <YieldTermStructure>(new Utilities.ZeroRateFunction(irmd.Date, irmd.ZRMarketDates, irmd.ZRMarket));
//termStructure.link
HullWhite model = new HullWhite(termStructure);
IborIndex index = new Euribor6M(termStructure);
IPricingEngine engine = new JamshidianSwaptionEngine(model);
List <CalibrationHelper> swaptions = new List <CalibrationHelper>();
for (int i = 0; i < irmd.SwapDates.Length; i++)
{
for (int j = 0; j < irmd.SwapDuration.Length; j++)
{
Quote vol = new SimpleQuote(irmd.SwaptionsVolatility[j, i]);
CalibrationHelper helper =
new SwaptionHelper(new Period((int)irmd.SwapDates[i], TimeUnit.Years),
new Period((int)irmd.SwapDuration[j], TimeUnit.Years),
new Handle <Quote>(vol),
index,
new Period(1, TimeUnit.Years),
new Thirty360(),
new Actual360(),
termStructure,
false);
helper.setPricingEngine(engine);
swaptions.Add(helper);
}
}
// Set up the optimization problem
LevenbergMarquardt optimizationMethod = new LevenbergMarquardt(1.0e-8, 1.0e-8, 1.0e-8);
EndCriteria endCriteria = new EndCriteria(10000, 100, 1e-6, 1e-8, 1e-8);
//Optimize
model.calibrate(swaptions, optimizationMethod, endCriteria, new Constraint(), new List <double>());
EndCriteria.Type ecType = model.endCriteria();
Vector xMinCalculated = model.parameters();
double yMinCalculated = model.value(xMinCalculated, swaptions);
Vector xMinExpected = new Vector(2);
double yMinExpected = model.value(xMinExpected, swaptions);
DVPLI.EstimationResult r = new DVPLI.EstimationResult(new string[] { "Alpha", "Sigma" }, new double[] { xMinCalculated[0], xMinCalculated[1] });
return(r);
}
//! Perform line search
public override double value(Problem P, ref EndCriteria.Type ecType, EndCriteria endCriteria, double t_ini)
{
Constraint constraint = P.constraint();
succeed_ = true;
bool maxIter = false;
double qtold;
double t = t_ini;
int loopNumber = 0;
double q0 = P.functionValue();
double qp0 = P.gradientNormValue();
qt_ = q0;
qpt_ = (gradient_.Count == 0) ? qp0 : -Vector.DotProduct(gradient_, searchDirection_);
// Initialize gradient
gradient_ = new Vector(P.currentValue().Count);
// Compute new point
xtd_ = P.currentValue().Clone();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
// Enter in the loop if the criterion is not satisfied
if ((qt_ - q0) > -alpha_ * t * qpt_)
{
do
{
loopNumber++;
// Decrease step
t *= beta_;
// Store old value of the function
qtold = qt_;
// New point value
xtd_ = P.currentValue();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
P.gradient(ref gradient_, xtd_);
// and it squared norm
maxIter = endCriteria.checkMaxIterations(loopNumber, ref ecType);
}while ((((qt_ - q0) > (-alpha_ * t * qpt_)) || ((qtold - q0) <= (-alpha_ * t * qpt_ / beta_))) &&
(!maxIter));
}
if (maxIter)
{
succeed_ = false;
}
// Compute new gradient
P.gradient(ref gradient_, xtd_);
// and it squared norm
qpt_ = Vector.DotProduct(gradient_, gradient_);
// Return new step value
return(t);
}
//! minimize the optimization problem P
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
int stationaryStateIterationNumber_ = 0;
lineSearch_.searchDirection = new Vector(x_.Count);
bool end;
// function and squared norm of gradient values;
double normdiff;
// classical initial value for line-search step
double t = 1.0;
// Set gold at the size of the optimization problem search direction
Vector gold = new Vector(lineSearch_.searchDirection.Count);
Vector gdiff = new Vector(lineSearch_.searchDirection.Count);
P.setFunctionValue(P.valueAndGradient(gold, x_));
lineSearch_.searchDirection = gold * -1.0;
P.setGradientNormValue(Vector.DotProduct(gold, gold));
normdiff = Math.Sqrt(P.gradientNormValue());
do
{
// Linesearch
t = lineSearch_.value(P, ref ecType, endCriteria, t);
if (!(lineSearch_.succeed()))
{
throw new ApplicationException("line-search failed!");
}
// End criteria
// FIXME: it's never been used! ???
// , normdiff
end = endCriteria.value(iterationNumber_, ref stationaryStateIterationNumber_, true, P.functionValue(), Math.Sqrt(P.gradientNormValue()), lineSearch_.lastFunctionValue(), Math.Sqrt(lineSearch_.lastGradientNorm2()), ref ecType);
// Updates
// New point
x_ = lineSearch_.lastX();
// New function value
P.setFunctionValue(lineSearch_.lastFunctionValue());
// New gradient and search direction vectors
gdiff = gold - lineSearch_.lastGradient();
normdiff = Math.Sqrt(Vector.DotProduct(gdiff, gdiff));
gold = lineSearch_.lastGradient();
lineSearch_.searchDirection = gold * -1.0;
// New gradient squared norm
P.setGradientNormValue(lineSearch_.lastGradientNorm2());
// Increase interation number
++iterationNumber_;
} while (end == false);
P.setCurrentValue(x_);
return(ecType);
}
//! Calibrate to a set of market instruments (caps/swaptions)
/*! An additional constraint can be passed which must be
* satisfied in addition to the constraints of the model.
*/
//public void calibrate(List<CalibrationHelper> instruments, OptimizationMethod method, EndCriteria endCriteria,
// Constraint constraint = new Constraint(), List<double> weights = new List<double>()) {
public void calibrate(List <CalibrationHelper> instruments,
OptimizationMethod method,
EndCriteria endCriteria,
Constraint additionalConstraint = null,
List <double> weights = null,
List <bool> fixParameters = null)
{
if (weights == null)
{
weights = new List <double>();
}
if (additionalConstraint == null)
{
additionalConstraint = new Constraint();
}
Utils.QL_REQUIRE(weights.empty() || weights.Count == instruments.Count, () =>
"mismatch between number of instruments (" +
instruments.Count + ") and weights(" +
weights.Count + ")");
Constraint c;
if (additionalConstraint.empty())
{
c = constraint_;
}
else
{
c = new CompositeConstraint(constraint_, additionalConstraint);
}
List <double> w = weights.Count == 0 ? new InitializedList <double>(instruments.Count, 1.0): weights;
Vector prms = parameters();
List <bool> all = new InitializedList <bool>(prms.size(), false);
Projection proj = new Projection(prms, fixParameters ?? all);
CalibrationFunction f = new CalibrationFunction(this, instruments, w, proj);
ProjectedConstraint pc = new ProjectedConstraint(c, proj);
Problem prob = new Problem(f, pc, proj.project(prms));
shortRateEndCriteria_ = method.minimize(prob, endCriteria);
Vector result = new Vector(prob.currentValue());
setParams(proj.include(result));
Vector shortRateProblemValues_ = prob.values(result);
notifyObservers();
//CalibrationFunction f = new CalibrationFunction(this, instruments, w);
//Problem prob = new Problem(f, c, parameters());
//shortRateEndCriteria_ = method.minimize(prob, endCriteria);
//Vector result = new Vector(prob.currentValue());
//setParams(result);
//// recheck
//Vector shortRateProblemValues_ = prob.values(result);
//notifyObservers();
}
public EndCriteria.Type endCriteria()
{
EndCriteria.Type ret = (EndCriteria.Type)NQuantLibcPINVOKE.ShortRateModelHandle_endCriteria(swigCPtr);
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
return(ret);
}
public EndCriteria.Type endCriteria()
{
EndCriteria.Type ret = (EndCriteria.Type)NQuantLibcPINVOKE.NoArbSabrInterpolatedSmileSection_endCriteria(swigCPtr);
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
return(ret);
}
public bool checkZeroGradientNorm(double gradientNorm, ref EndCriteria.Type ecType)
{
if (gradientNorm >= gradientNormEpsilon_)
{
return(false);
}
ecType = Type.ZeroGradientNorm;
return(true);
}
public EndCriteria.Type endCriteria()
{
EndCriteria.Type ret = (EndCriteria.Type)NQuantLibcPINVOKE.MarkovFunctional_endCriteria(swigCPtr);
if (NQuantLibcPINVOKE.SWIGPendingException.Pending)
{
throw NQuantLibcPINVOKE.SWIGPendingException.Retrieve();
}
return(ret);
}
//! Test if the number of iteration is below MaxIterations
public bool checkMaxIterations(int iteration, ref EndCriteria.Type ecType)
{
if (iteration < maxIterations_)
{
return(false);
}
ecType = Type.MaxIterations;
return(true);
}
public void OptimizersTest()
{
//("Testing optimizers...");
setup();
// Loop over problems (currently there is only 1 problem)
for (int i = 0; i < costFunctions_.Count; ++i)
{
Problem problem = new Problem(costFunctions_[i], constraints_[i], initialValues_[i]);
Vector initialValues = problem.currentValue();
// Loop over optimizers
for (int j = 0; j < (optimizationMethods_[i]).Count; ++j)
{
double rootEpsilon = endCriterias_[i].rootEpsilon();
int endCriteriaTests = 1;
// Loop over rootEpsilon
for (int k = 0; k < endCriteriaTests; ++k)
{
problem.setCurrentValue(initialValues);
EndCriteria endCriteria = new EndCriteria(endCriterias_[i].maxIterations(),
endCriterias_[i].maxStationaryStateIterations(),
rootEpsilon,
endCriterias_[i].functionEpsilon(),
endCriterias_[i].gradientNormEpsilon());
rootEpsilon *= .1;
EndCriteria.Type endCriteriaResult =
optimizationMethods_[i][j].optimizationMethod.minimize(problem, endCriteria);
Vector xMinCalculated = problem.currentValue();
Vector yMinCalculated = problem.values(xMinCalculated);
// Check optimization results vs known solution
if (endCriteriaResult == EndCriteria.Type.None ||
endCriteriaResult == EndCriteria.Type.MaxIterations ||
endCriteriaResult == EndCriteria.Type.Unknown)
{
Assert.Fail("function evaluations: " + problem.functionEvaluation() +
" gradient evaluations: " + problem.gradientEvaluation() +
" x expected: " + xMinExpected_[i] +
" x calculated: " + xMinCalculated +
" x difference: " + (xMinExpected_[i] - xMinCalculated) +
" rootEpsilon: " + endCriteria.rootEpsilon() +
" y expected: " + yMinExpected_[i] +
" y calculated: " + yMinCalculated +
" y difference: " + (yMinExpected_[i] - yMinCalculated) +
" functionEpsilon: " + endCriteria.functionEpsilon() +
" endCriteriaResult: " + endCriteriaResult);
}
}
}
}
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
EndCriteria.Type ecType = EndCriteria.Type.None;
upperBound_ = P.constraint().upperBound(P.currentValue());
lowerBound_ = P.constraint().lowerBound(P.currentValue());
currGenSizeWeights_ = new Vector(configuration().populationMembers,
configuration().stepsizeWeight);
currGenCrossover_ = new Vector(configuration().populationMembers,
configuration().crossoverProbability);
List <Candidate> population = new InitializedList <Candidate>(configuration().populationMembers);
population.ForEach((ii, vv) => population[ii] = new Candidate(P.currentValue().size()));
fillInitialPopulation(population, P);
//original quantlib use partial_sort as only first elements is needed
double fxOld = population.Min(x => x.cost);
bestMemberEver_ = (Candidate)population.First(x => x.cost.IsEqual(fxOld)).Clone();
int iteration = 0, stationaryPointIteration = 0;
// main loop - calculate consecutive emerging populations
while (!endCriteria.checkMaxIterations(iteration++, ref ecType))
{
calculateNextGeneration(population, P.costFunction());
double fxNew = population.Min(x => x.cost);
Candidate tmp = (Candidate)population.First(x => x.cost.IsEqual(fxNew)).Clone();
if (fxNew < bestMemberEver_.cost)
{
bestMemberEver_ = tmp;
}
if (endCriteria.checkStationaryFunctionValue(fxOld, fxNew, ref stationaryPointIteration,
ref ecType))
{
break;
}
fxOld = fxNew;
}
P.setCurrentValue(bestMemberEver_.values);
P.setFunctionValue(bestMemberEver_.cost);
return(ecType);
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
int stationaryStateIterations_ = 0;
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x = P.currentValue();
iteration_ = 0;
n_ = x.size();
ptry_ = new Vector(n_, 0.0);
// build vertices
vertices_ = new InitializedList <Vector>(n_ + 1, x);
for (i_ = 0; i_ < n_; i_++)
{
Vector direction = new Vector(n_, 0.0);
direction[i_] = 1.0;
Vector tmp = vertices_[i_ + 1];
P.constraint().update(ref tmp, direction, lambda_);
vertices_[i_ + 1] = tmp;
}
values_ = new Vector(n_ + 1, 0.0);
for (i_ = 0; i_ <= n_; i_++)
{
if (!P.constraint().test(vertices_[i_]))
{
values_[i_] = Double.MaxValue;
}
else
{
values_[i_] = P.value(vertices_[i_]);
}
if (Double.IsNaN(ytry_))
{
// handle NAN
values_[i_] = Double.MaxValue;
}
}
// minimize
T_ = T0_;
yb_ = Double.MaxValue;
pb_ = new Vector(n_, 0.0);
do
{
iterationT_ = iteration_;
do
{
sum_ = new Vector(n_, 0.0);
for (i_ = 0; i_ <= n_; i_++)
{
sum_ += vertices_[i_];
}
tt_ = -T_;
ilo_ = 0;
ihi_ = 1;
ynhi_ = values_[0] + tt_ * Math.Log(rng_.next().value);
ylo_ = ynhi_;
yhi_ = values_[1] + tt_ * Math.Log(rng_.next().value);
if (ylo_ > yhi_)
{
ihi_ = 0;
ilo_ = 1;
ynhi_ = yhi_;
yhi_ = ylo_;
ylo_ = ynhi_;
}
for (i_ = 2; i_ < n_ + 1; i_++)
{
yt_ = values_[i_] + tt_ * Math.Log(rng_.next().value);
if (yt_ <= ylo_)
{
ilo_ = i_;
ylo_ = yt_;
}
if (yt_ > yhi_)
{
ynhi_ = yhi_;
ihi_ = i_;
yhi_ = yt_;
}
else
{
if (yt_ > ynhi_)
{
ynhi_ = yt_;
}
}
}
// GSL end criterion in x (cf. above)
if (endCriteria.checkStationaryPoint(simplexSize(), 0.0,
ref stationaryStateIterations_,
ref ecType) ||
endCriteria.checkMaxIterations(iteration_, ref ecType))
{
// no matter what, we return the best ever point !
P.setCurrentValue(pb_);
P.setFunctionValue(yb_);
return(ecType);
}
iteration_ += 2;
amotsa(P, -1.0);
if (ytry_ <= ylo_)
{
amotsa(P, 2.0);
}
else
{
if (ytry_ >= ynhi_)
{
ysave_ = yhi_;
amotsa(P, 0.5);
if (ytry_ >= ysave_)
{
for (i_ = 0; i_ < n_ + 1; i_++)
{
if (i_ != ilo_)
{
for (j_ = 0; j_ < n_; j_++)
{
sum_[j_] = 0.5 * (vertices_[i_][j_] +
vertices_[ilo_][j_]);
vertices_[i_][j_] = sum_[j_];
}
values_[i_] = P.value(sum_);
}
}
iteration_ += n_;
for (i_ = 0; i_ < n_; i_++)
{
sum_[i_] = 0.0;
}
for (i_ = 0; i_ <= n_; i_++)
{
sum_ += vertices_[i_];
}
}
}
else
{
iteration_ += 1;
}
}
}while (iteration_ <
iterationT_ + (scheme_ == Scheme.ConstantFactor ? m_ : 1));
switch (scheme_)
{
case Scheme.ConstantFactor:
T_ *= (1.0 - epsilon_);
break;
case Scheme.ConstantBudget:
if (iteration_ <= K_)
{
T_ = T0_ *
Math.Pow(1.0 - Convert.ToDouble(iteration_) / Convert.ToDouble(K_), alpha_);
}
else
{
T_ = 0.0;
}
break;
}
}while (true);
}
//! solve the optimization problem P
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// Initializations
double ftol = endCriteria.functionEpsilon();
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None; // reset end criteria
P.reset(); // reset problem
Vector x_ = P.currentValue(); // store the starting point
int iterationNumber_ = 0; // stationaryStateIterationNumber_=0
lineSearch_.searchDirection = new Vector(x_.Count); // dimension line search
bool done = false;
// function and squared norm of gradient values;
double fnew;
double fold;
double gold2;
double c;
double fdiff;
double normdiff;
// classical initial value for line-search step
double t = 1.0;
// Set gradient g at the size of the optimization problem search direction
int sz = lineSearch_.searchDirection.Count;
Vector g = new Vector(sz);
Vector d = new Vector(sz);
Vector sddiff = new Vector(sz);
// Initialize cost function, gradient g and search direction
P.setFunctionValue(P.valueAndGradient(g, x_));
P.setGradientNormValue(Vector.DotProduct(g, g));
lineSearch_.searchDirection = g * -1.0;
// Loop over iterations
do
{
// Linesearch
t = lineSearch_.value(P, ref ecType, endCriteria, t);
// don't throw: it can fail just because maxIterations exceeded
//QL_REQUIRE(lineSearch_->succeed(), "line-search failed!");
if (lineSearch_.succeed())
{
// Updates
d = lineSearch_.searchDirection;
// New point
x_ = lineSearch_.lastX();
// New function value
fold = P.functionValue();
P.setFunctionValue(lineSearch_.lastFunctionValue());
// New gradient and search direction vectors
g = lineSearch_.lastGradient();
// orthogonalization coef
gold2 = P.gradientNormValue();
P.setGradientNormValue(lineSearch_.lastGradientNorm2());
c = P.gradientNormValue() / gold2;
// conjugate gradient search direction
sddiff = ((g * -1.0) + c * d) - lineSearch_.searchDirection;
normdiff = Math.Sqrt(Vector.DotProduct(sddiff, sddiff));
lineSearch_.searchDirection = (g * -1.0) + c * d;
// Now compute accuracy and check end criteria
// Numerical Recipes exit strategy on fx (see NR in C++, p.423)
fnew = P.functionValue();
fdiff = 2.0 * Math.Abs(fnew - fold) / (Math.Abs(fnew) + Math.Abs(fold) + Double.Epsilon);
if (fdiff < ftol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryFunctionValue(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
return(ecType);
}
//done = endCriteria(iterationNumber_,
// stationaryStateIterationNumber_,
// true, //FIXME: it should be in the problem
// fold,
// std::sqrt(gold2),
// P.functionValue(),
// std::sqrt(P.gradientNormValue()),
// ecType);
P.setCurrentValue(x_); // update problem current value
++iterationNumber_; // Increase iteration number
}
else
{
done = true;
}
} while (!done);
P.setCurrentValue(x_);
return(ecType);
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
currentProblem_ = P;
initCostValues_ = P.costFunction().values(x_);
int m = initCostValues_.size();
int n = x_.size();
if (useCostFunctionsJacobian_)
{
initJacobian_ = new Matrix(m, n);
P.costFunction().jacobian(initJacobian_, x_);
}
Vector xx = new Vector(x_);
Vector fvec = new Vector(m), diag = new Vector(n);
int mode = 1;
double factor = 1;
int nprint = 0;
int info = 0;
int nfev = 0;
Matrix fjac = new Matrix(m, n);
int ldfjac = m;
List <int> ipvt = new InitializedList <int>(n);
Vector qtf = new Vector(n), wa1 = new Vector(n), wa2 = new Vector(n), wa3 = new Vector(n), wa4 = new Vector(m);
// call lmdif to minimize the sum of the squares of m functions
// in n variables by the Levenberg-Marquardt algorithm.
Func <int, int, Vector, int, Matrix> j = null;
if (useCostFunctionsJacobian_)
{
j = jacFcn;
}
// requirements; check here to get more detailed error messages.
Utils.QL_REQUIRE(n > 0, () => "no variables given");
Utils.QL_REQUIRE(m >= n, () => $"less functions ({m}) than available variables ({n})");
Utils.QL_REQUIRE(endCriteria.functionEpsilon() >= 0.0, () => "negative f tolerance");
Utils.QL_REQUIRE(xtol_ >= 0.0, () => "negative x tolerance");
Utils.QL_REQUIRE(gtol_ >= 0.0, () => "negative g tolerance");
Utils.QL_REQUIRE(endCriteria.maxIterations() > 0, () => "null number of evaluations");
MINPACK.lmdif(m, n, xx, ref fvec,
endCriteria.functionEpsilon(),
xtol_,
gtol_,
endCriteria.maxIterations(),
epsfcn_,
diag, mode, factor,
nprint, ref info, ref nfev, ref fjac,
ldfjac, ref ipvt, ref qtf,
wa1, wa2, wa3, wa4,
fcn, j);
info_ = info;
// check requirements & endCriteria evaluation
Utils.QL_REQUIRE(info != 0, () => "MINPACK: improper input parameters");
if (info != 6)
{
ecType = EndCriteria.Type.StationaryFunctionValue;
}
endCriteria.checkMaxIterations(nfev, ref ecType);
Utils.QL_REQUIRE(info != 7, () => "MINPACK: xtol is too small. no further " +
"improvement in the approximate " +
"solution x is possible.");
Utils.QL_REQUIRE(info != 8, () => "MINPACK: gtol is too small. fvec is " +
"orthogonal to the columns of the " +
"jacobian to machine precision.");
// set problem
x_ = new Vector(xx.GetRange(0, n));
P.setCurrentValue(x_);
P.setFunctionValue(P.costFunction().value(x_));
return(ecType);
}
public CalibratedModel(int nArguments)
{
arguments_ = new InitializedList<Parameter>(nArguments);
constraint_ = new PrivateConstraint(arguments_);
shortRateEndCriteria_ = EndCriteria.Type.None;
}
//! Test if the function value is below functionEpsilon
public bool checkStationaryFunctionAccuracy(double f, bool positiveOptimization, ref EndCriteria.Type ecType)
{
if (!positiveOptimization)
{
return(false);
}
if (f >= functionEpsilon_)
{
return(false);
}
ecType = Type.StationaryFunctionAccuracy;
return(true);
}
//! Test if the function variation is below functionEpsilon
public bool checkStationaryFunctionValue(double fxOld, double fxNew, ref int statStateIterations, ref EndCriteria.Type ecType)
{
if (Math.Abs(fxNew - fxOld) >= functionEpsilon_)
{
statStateIterations = 0;
return(false);
}
++statStateIterations;
if (statStateIterations <= maxStationaryStateIterations_)
{
return(false);
}
ecType = Type.StationaryFunctionValue;
return(true);
}
//! Test if the root variation is below rootEpsilon
public bool checkStationaryPoint(double xOld, double xNew, ref int statStateIterations, ref EndCriteria.Type ecType)
{
if (Math.Abs(xNew - xOld) >= rootEpsilon_)
{
statStateIterations = 0;
return(false);
}
++statStateIterations;
if (statStateIterations <= maxStationaryStateIterations_)
{
return(false);
}
ecType = Type.StationaryPoint;
return(true);
}
// ! Test if the number of iterations is not too big
// and if a minimum point is not reached
public bool value(int iteration, ref int statStateIterations, bool positiveOptimization, double fold, double UnnamedParameter1, double fnew, double normgnew, ref EndCriteria.Type ecType)
{
return(checkMaxIterations(iteration, ref ecType) || checkStationaryFunctionValue(fold, fnew, ref statStateIterations, ref ecType) || checkStationaryFunctionAccuracy(fnew, positiveOptimization, ref ecType) || checkZeroGradientNorm(normgnew, ref ecType));
}
public void calculate()
{
validCurve_ = false;
int nInsts = ts_.instruments_.Count, i;
// ensure rate helpers are sorted
ts_.instruments_.Sort((x, y) => x.latestDate().CompareTo(y.latestDate()));
// check that there is no instruments with the same maturity
for (i = 1; i < nInsts; ++i)
{
Date m1 = ts_.instruments_[i - 1].latestDate(),
m2 = ts_.instruments_[i].latestDate();
Utils.QL_REQUIRE(m1 != m2, () => "two instruments have the same maturity (" + m1 + ")");
}
// check that there is no instruments with invalid quote
Utils.QL_REQUIRE((i = ts_.instruments_.FindIndex(x => !x.quoteIsValid())) == -1, () =>
"instrument " + i + " (maturity: " + ts_.instruments_[i].latestDate() + ") has an invalid quote");
// setup instruments and register with them
ts_.instruments_.ForEach((x, j) => ts_.setTermStructure(j));
// set initial guess only if the current curve cannot be used as guess
if (validCurve_)
{
Utils.QL_REQUIRE(ts_.data_.Count == nInsts + 1, () =>
"dimension mismatch: expected " + nInsts + 1 + ", actual " + ts_.data_.Count);
}
else
{
ts_.data_ = new InitializedList <double>(nInsts + 1);
ts_.data_[0] = ts_.initialValue();
}
// calculate dates and times
ts_.dates_ = new InitializedList <Date>(nInsts + 1);
ts_.times_ = new InitializedList <double>(nInsts + 1);
ts_.dates_[0] = ts_.initialDate();
ts_.times_[0] = ts_.timeFromReference(ts_.dates_[0]);
for (i = 0; i < nInsts; ++i)
{
ts_.dates_[i + 1] = ts_.instruments_[i].latestDate();
ts_.times_[i + 1] = ts_.timeFromReference(ts_.dates_[i + 1]);
if (!validCurve_)
{
ts_.data_[i + 1] = ts_.data_[i];
}
}
LevenbergMarquardt solver = new LevenbergMarquardt(ts_.accuracy_, ts_.accuracy_, ts_.accuracy_);
EndCriteria endCriteria = new EndCriteria(100, 10, 0.00, ts_.accuracy_, 0.00);
PositiveConstraint posConstraint = new PositiveConstraint();
NoConstraint noConstraint = new NoConstraint();
Constraint solverConstraint = forcePositive_ ? (Constraint)posConstraint : (Constraint)noConstraint;
// now start the bootstrapping.
int iInst = localisation_ - 1;
int dataAdjust = (ts_.interpolator_ as ConvexMonotone).dataSizeAdjustment;
do
{
int initialDataPt = iInst + 1 - localisation_ + dataAdjust;
Vector startArray = new Vector(localisation_ + 1 - dataAdjust);
for (int j = 0; j < startArray.size() - 1; ++j)
{
startArray[j] = ts_.data_[initialDataPt + j];
}
// here we are extending the interpolation a point at a
// time... but the local interpolator can make an
// approximation for the final localisation period.
// e.g. if the localisation is 2, then the first section
// of the curve will be solved using the first 2
// instruments... with the local interpolator making
// suitable boundary conditions.
ts_.interpolation_ = (ts_.interpolator_ as ConvexMonotone).localInterpolate(ts_.times_, iInst + 2, ts_.data_,
localisation_, ts_.interpolation_ as ConvexMonotoneInterpolation, nInsts + 1);
if (iInst >= localisation_)
{
startArray[localisation_ - dataAdjust] = ts_.guess(iInst, ts_, false, 0);
}
else
{
startArray[localisation_ - dataAdjust] = ts_.data_[0];
}
var currentCost = new PenaltyFunction <T, U>(ts_, initialDataPt, ts_.instruments_,
iInst - localisation_ + 1, iInst + 1);
Problem toSolve = new Problem(currentCost, solverConstraint, startArray);
EndCriteria.Type endType = solver.minimize(toSolve, endCriteria);
// check the end criteria
Utils.QL_REQUIRE(endType == EndCriteria.Type.StationaryFunctionAccuracy ||
endType == EndCriteria.Type.StationaryFunctionValue, () =>
"Unable to strip yieldcurve to required accuracy ");
++iInst;
}while (iInst < nInsts);
validCurve_ = true;
}
public CalibratedModel(int nArguments)
{
arguments_ = new InitializedList <Parameter>(nArguments);
constraint_ = new PrivateConstraint(arguments_);
shortRateEndCriteria_ = EndCriteria.Type.None;
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
currentProblem_ = P;
initCostValues_ = P.costFunction().values(x_);
int m = initCostValues_.size();
int n = x_.size();
if (useCostFunctionsJacobian_)
{
initJacobian_ = new Matrix(m, n);
P.costFunction().jacobian(initJacobian_, x_);
}
Vector xx = new Vector(x_);
Vector fvec = new Vector(m), diag = new Vector(n);
int mode = 1;
double factor = 1;
int nprint = 0;
int info = 0;
int nfev = 0;
Matrix fjac = new Matrix(m, n);
int ldfjac = m;
List <int> ipvt = new InitializedList <int>(n);
Vector qtf = new Vector(n), wa1 = new Vector(n), wa2 = new Vector(n), wa3 = new Vector(n), wa4 = new Vector(m);
// call lmdif to minimize the sum of the squares of m functions
// in n variables by the Levenberg-Marquardt algorithm.
Func <int, int, Vector, int, Matrix> j = null;
if (useCostFunctionsJacobian_)
{
j = jacFcn;
}
MINPACK.lmdif(m, n, xx, ref fvec,
endCriteria.functionEpsilon(),
xtol_,
gtol_,
endCriteria.maxIterations(),
epsfcn_,
diag, mode, factor,
nprint, ref info, ref nfev, ref fjac,
ldfjac, ref ipvt, ref qtf,
wa1, wa2, wa3, wa4,
fcn, j);
info_ = info;
// check requirements & endCriteria evaluation
if (info == 0)
{
throw new ApplicationException("MINPACK: improper input parameters");
}
//if(info == 6) throw new ApplicationException("MINPACK: ftol is too small. no further " +
// "reduction in the sum of squares is possible.");
if (info != 6)
{
ecType = EndCriteria.Type.StationaryFunctionValue;
}
//QL_REQUIRE(info != 5, "MINPACK: number of calls to fcn has reached or exceeded maxfev.");
endCriteria.checkMaxIterations(nfev, ref ecType);
if (info == 7)
{
throw new ApplicationException("MINPACK: xtol is too small. no further " +
"improvement in the approximate " +
"solution x is possible.");
}
if (info == 8)
{
throw new ApplicationException("MINPACK: gtol is too small. fvec is " +
"orthogonal to the columns of the " +
"jacobian to machine precision.");
}
// set problem
x_ = new Vector(xx.GetRange(0, n));
P.setCurrentValue(x_);
P.setFunctionValue(P.costFunction().value(x_));
return(ecType);
}
//! Calibrate to a set of market instruments (caps/swaptions)
/*! An additional constraint can be passed which must be
satisfied in addition to the constraints of the model.
*/
//public void calibrate(List<CalibrationHelper> instruments, OptimizationMethod method, EndCriteria endCriteria,
// Constraint constraint = new Constraint(), List<double> weights = new List<double>()) {
public void calibrate(List<CalibrationHelper> instruments, OptimizationMethod method, EndCriteria endCriteria,
Constraint additionalConstraint, List<double> weights)
{
if (!(weights.Count == 0 || weights.Count == instruments.Count))
throw new ApplicationException("mismatch between number of instruments and weights");
Constraint c;
if (additionalConstraint.empty())
c = constraint_;
else
c = new CompositeConstraint(constraint_,additionalConstraint);
List<double> w = weights.Count == 0 ? new InitializedList<double>(instruments.Count, 1.0): weights;
CalibrationFunction f = new CalibrationFunction(this, instruments, w);
Problem prob = new Problem(f, c, parameters());
shortRateEndCriteria_ = method.minimize(prob, endCriteria);
Vector result = new Vector(prob.currentValue());
setParams(result);
// recheck
Vector shortRateProblemValues_ = prob.values(result);
notifyObservers();
}
//! Perform line search
public override double value(Problem P, // Optimization problem
ref EndCriteria.Type ecType,
EndCriteria endCriteria,
double t_ini) // initial value of line-search step
{
Constraint constraint = P.constraint();
succeed_ = true;
bool maxIter = false;
double t = t_ini;
int loopNumber = 0;
double q0 = P.functionValue();
double qp0 = P.gradientNormValue();
double tl = 0.0;
double tr = 0.0;
qt_ = q0;
qpt_ = (gradient_.empty()) ? qp0 : -Vector.DotProduct(gradient_, searchDirection_);
// Initialize gradient
gradient_ = new Vector(P.currentValue().size());
// Compute new point
xtd_ = P.currentValue();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
while ((qt_ - q0) < -beta_ * t * qpt_ || (qt_ - q0) > -alpha_ * t * qpt_)
{
if ((qt_ - q0) > -alpha_ * t * qpt_)
{
tr = t;
}
else
{
tl = t;
}
++loopNumber;
// calculate the new step
if (Utils.close_enough(tr, 0.0))
{
t *= extrapolation_;
}
else
{
t = (tl + tr) / 2.0;
}
// New point value
xtd_ = P.currentValue();
t = update(ref xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value(xtd_);
P.gradient(gradient_, xtd_);
// and it squared norm
maxIter = endCriteria.checkMaxIterations(loopNumber, ref ecType);
if (maxIter)
{
break;
}
}
if (maxIter)
{
succeed_ = false;
}
// Compute new gradient
P.gradient(gradient_, xtd_);
// and it squared norm
qpt_ = Vector.DotProduct(gradient_, gradient_);
// Return new step value
return(t);
}
public void testCachedHullWhite()
{
//("Testing Hull-White calibration against cached values...");
Date today = new Date(15, Month.February, 2002);
Date settlement = new Date(19, Month.February, 2002);
Settings.setEvaluationDate(today);
Handle <YieldTermStructure> termStructure =
new Handle <YieldTermStructure>(Utilities.flatRate(settlement, 0.04875825, new Actual365Fixed()));
//termStructure.link
HullWhite model = new HullWhite(termStructure);
CalibrationData[] data = { new CalibrationData(1, 5, 0.1148),
new CalibrationData(2, 4, 0.1108),
new CalibrationData(3, 3, 0.1070),
new CalibrationData(4, 2, 0.1021),
new CalibrationData(5, 1, 0.1000) };
IborIndex index = new Euribor6M(termStructure);
IPricingEngine engine = new JamshidianSwaptionEngine(model);
List <CalibrationHelper> swaptions = new List <CalibrationHelper>();
for (int i = 0; i < data.Length; i++)
{
Quote vol = new SimpleQuote(data[i].volatility);
CalibrationHelper helper =
new SwaptionHelper(new Period(data[i].start, TimeUnit.Years),
new Period(data[i].length, TimeUnit.Years),
new Handle <Quote>(vol),
index,
new Period(1, TimeUnit.Years),
new Thirty360(),
new Actual360(),
termStructure,
false);
helper.setPricingEngine(engine);
swaptions.Add(helper);
}
// Set up the optimization problem
// Real simplexLambda = 0.1;
// Simplex optimizationMethod(simplexLambda);
LevenbergMarquardt optimizationMethod = new LevenbergMarquardt(1.0e-8, 1.0e-8, 1.0e-8);
EndCriteria endCriteria = new EndCriteria(10000, 100, 1e-6, 1e-8, 1e-8);
//Optimize
model.calibrate(swaptions, optimizationMethod, endCriteria, new Constraint(), new List <double>());
EndCriteria.Type ecType = model.endCriteria();
// Check and print out results
#if QL_USE_INDEXED_COUPON
double cachedA = 0.0488199, cachedSigma = 0.00593579;
#else
double cachedA = 0.0488565, cachedSigma = 0.00593662;
#endif
double tolerance = 1.120e-5;
//double tolerance = 1.0e-6;
Vector xMinCalculated = model.parameters();
double yMinCalculated = model.value(xMinCalculated, swaptions);
Vector xMinExpected = new Vector(2);
xMinExpected[0] = cachedA;
xMinExpected[1] = cachedSigma;
double yMinExpected = model.value(xMinExpected, swaptions);
if (Math.Abs(xMinCalculated[0] - cachedA) > tolerance ||
Math.Abs(xMinCalculated[1] - cachedSigma) > tolerance)
{
Assert.Fail("Failed to reproduce cached calibration results:\n"
+ "calculated: a = " + xMinCalculated[0] + ", "
+ "sigma = " + xMinCalculated[1] + ", "
+ "f(a) = " + yMinCalculated + ",\n"
+ "expected: a = " + xMinExpected[0] + ", "
+ "sigma = " + xMinExpected[1] + ", "
+ "f(a) = " + yMinExpected + ",\n"
+ "difference: a = " + (xMinCalculated[0] - xMinExpected[0]) + ", "
+ "sigma = " + (xMinCalculated[1] - xMinExpected[1]) + ", "
+ "f(a) = " + (yMinCalculated - yMinExpected) + ",\n"
+ "end criteria = " + ecType);
}
}
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// set up of the problem
//double ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
double xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None;
P.reset();
Vector x_ = P.currentValue();
int iterationNumber_ = 0;
// Initialize vertices of the simplex
bool end = false;
int n = x_.Count;
vertices_ = new InitializedList <Vector>(n + 1, x_);
for (int i = 0; i < n; i++)
{
Vector direction = new Vector(n, 0.0);
Vector vertice = vertices_[i + 1];
direction[i] = 1.0;
P.constraint().update(ref vertice, direction, lambda_);
vertices_[i + 1] = vertice;
}
// Initialize function values at the vertices of the simplex
values_ = new Vector(n + 1, 0.0);
for (int i = 0; i <= n; i++)
{
values_[i] = P.value(vertices_[i]);
}
// Loop looking for minimum
do
{
sum_ = new Vector(n, 0.0);
for (int i = 0; i <= n; i++)
{
sum_ += vertices_[i];
}
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
int iLowest = 0;
int iHighest;
int iNextHighest;
if (values_[0] < values_[1])
{
iHighest = 1;
iNextHighest = 0;
}
else
{
iHighest = 0;
iNextHighest = 1;
}
for (int i = 1; i <= n; i++)
{
if (values_[i] > values_[iHighest])
{
iNextHighest = iHighest;
iHighest = i;
}
else
{
if ((values_[i] > values_[iNextHighest]) && i != iHighest)
{
iNextHighest = i;
}
}
if (values_[i] < values_[iLowest])
{
iLowest = i;
}
}
// Now compute accuracy, update iteration number and check end criteria
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//double low = values_[iLowest];
//double high = values_[iHighest];
//double rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
double simplexSize = Utils.computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol || endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryPoint(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(ecType);
}
// If end criteria is not met, continue
double factor = -1.0;
double vTry = extrapolate(ref P, iHighest, ref factor);
if ((vTry <= values_[iLowest]) && (factor == -1.0))
{
factor = 2.0;
extrapolate(ref P, iHighest, ref factor);
}
else if (Math.Abs(factor) > Const.QL_EPSILON)
{
if (vTry >= values_[iNextHighest])
{
double vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(ref P, iHighest, ref factor);
if (vTry >= vSave && Math.Abs(factor) > Const.QL_EPSILON)
{
for (int i = 0; i <= n; i++)
{
if (i != iLowest)
{
#if QL_ARRAY_EXPRESSIONS
vertices_[i] = 0.5 * (vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (Math.Abs(factor) <= Const.QL_EPSILON)
{
x_ = vertices_[iLowest];
double low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return(EndCriteria.Type.StationaryFunctionValue);
}
} while (end == false);
throw new Exception("optimization failed: unexpected behaviour");
}
//! Perform line search public abstract double value(Problem P, ref EndCriteria.Type ecType, EndCriteria NamelessParameter3, double t_ini); // initial value of line-search step
public override EndCriteria.Type minimize(Problem P, EndCriteria endCriteria)
{
// Initializations
double ftol = endCriteria.functionEpsilon();
int maxStationaryStateIterations_ = endCriteria.maxStationaryStateIterations();
EndCriteria.Type ecType = EndCriteria.Type.None; // reset end criteria
P.reset(); // reset problem
Vector x_ = P.currentValue(); // store the starting point
int iterationNumber_ = 0;
// dimension line search
lineSearch_.searchDirection = new Vector(x_.size());
bool done = false;
// function and squared norm of gradient values
double fnew, fold, gold2;
double fdiff;
// classical initial value for line-search step
double t = 1.0;
// Set gradient g at the size of the optimization problem
// search direction
int sz = lineSearch_.searchDirection.size();
Vector prevGradient = new Vector(sz), d = new Vector(sz), sddiff = new Vector(sz), direction = new Vector(sz);
// Initialize cost function, gradient prevGradient and search direction
P.setFunctionValue(P.valueAndGradient(prevGradient, x_));
P.setGradientNormValue(Vector.DotProduct(prevGradient, prevGradient));
lineSearch_.searchDirection = prevGradient * -1;
bool first_time = true;
// Loop over iterations
do
{
// Linesearch
if (!first_time)
{
prevGradient = lineSearch_.lastGradient();
}
t = (lineSearch_.value(P, ref ecType, endCriteria, t));
// don't throw: it can fail just because maxIterations exceeded
if (lineSearch_.succeed())
{
// Updates
// New point
x_ = lineSearch_.lastX();
// New function value
fold = P.functionValue();
P.setFunctionValue(lineSearch_.lastFunctionValue());
// New gradient and search direction vectors
// orthogonalization coef
gold2 = P.gradientNormValue();
P.setGradientNormValue(lineSearch_.lastGradientNorm2());
// conjugate gradient search direction
direction = getUpdatedDirection(P, gold2, prevGradient);
sddiff = direction - lineSearch_.searchDirection;
lineSearch_.searchDirection = direction;
// Now compute accuracy and check end criteria
// Numerical Recipes exit strategy on fx (see NR in C++, p.423)
fnew = P.functionValue();
fdiff = 2.0 * Math.Abs(fnew - fold) /
(Math.Abs(fnew) + Math.Abs(fold) + Const.QL_EPSILON);
if (fdiff < ftol ||
endCriteria.checkMaxIterations(iterationNumber_, ref ecType))
{
endCriteria.checkStationaryFunctionValue(0.0, 0.0, ref maxStationaryStateIterations_, ref ecType);
endCriteria.checkMaxIterations(iterationNumber_, ref ecType);
return(ecType);
}
P.setCurrentValue(x_); // update problem current value
++iterationNumber_; // Increase iteration number
first_time = false;
}
else
{
done = true;
}
}while (!done);
P.setCurrentValue(x_);
return(ecType);
}