/
latentmodel.hpp
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/
latentmodel.hpp
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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Roland Lichters
Copyright (C) 2014 Jose Aparicio
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#ifndef quantlib_latent_model_hpp
#define quantlib_latent_model_hpp
#include <ql/experimental/math/multidimquadrature.hpp>
#include <ql/experimental/math/multidimintegrator.hpp>
#include <ql/math/integrals/trapezoidintegral.hpp>
#include <ql/math/randomnumbers/randomsequencegenerator.hpp>
// for template spezs
#include <ql/experimental/math/gaussiancopulapolicy.hpp>
#include <ql/experimental/math/tcopulapolicy.hpp>
#include <ql/math/randomnumbers/boxmullergaussianrng.hpp>
#include <ql/math/functional.hpp>
#include <ql/experimental/math/polarstudenttrng.hpp>
#include <ql/handle.hpp>
#include <ql/quote.hpp>
#include <ql/functional.hpp>
#include <vector>
/*! \file latentmodel.hpp
\brief Generic multifactor latent variable model.
*/
namespace QuantLib {
namespace detail {
// havent figured out how to do this in-place
struct multiplyV {
typedef Disposable<std::vector<Real> > result_type;
Disposable<std::vector<Real> >
operator()(Real d, Disposable<std::vector<Real> > v)
{
std::transform(v.begin(), v.end(), v.begin(),
multiply_by<Real>(d));
return v;
}
};
}
//! \name Latent model direct integration facility.
//@{
/* Things trying to achieve here:
1.- Unify the two branches of integrators in the library, they do not
hang from a common base class and here a common ptr for the
factory is needed.
2.- Have a common signature for the integration call.
3.- Factory construction so integrable latent models can choose the
integration algorithm separately.
*/
class LMIntegration {
public:
// Interface with actual integrators:
// integral of a scalar function
virtual Real integrate(const ext::function<Real (
const std::vector<Real>& arg)>& f) const = 0;
// integral of a vector function
/* I had to use a different name, since the compiler does not
recognise the overload; MSVC sees the argument as
ext::function<Signature> in both cases....
I could do the as with the quadratures and have this as a template
function and spez for the vector case but I prefer to understand
why the overload fails....
FIX ME
*/
virtual Disposable<std::vector<Real> > integrateV(
const ext::function<Disposable<std::vector<Real> > (
const std::vector<Real>& arg)>& f) const {
QL_FAIL("No vector integration provided");
}
virtual ~LMIntegration() = default;
};
//CRTP-ish for joining the integrations, class above to have the factory
template <class I_T>
class IntegrationBase :
public I_T, public LMIntegration {// diamond on 'integrate'
// this class template always to be fully specialized:
private:
IntegrationBase() = default;
~IntegrationBase() override = default;
};
//@}
// gcc reports value collision with heston engine (?!) thats why the name
namespace LatentModelIntegrationType {
enum LatentModelIntegrationType {
#ifndef QL_PATCH_SOLARIS
GaussianQuadrature,
#endif
Trapezoid
// etc....
};
}
#ifndef QL_PATCH_SOLARIS
/* class template specializations. I havent use CRTP type cast directly
because the signature of the integrators is different, grid integration
needs the domain. */
template<> class IntegrationBase<GaussianQuadMultidimIntegrator> :
public GaussianQuadMultidimIntegrator, public LMIntegration {
public:
IntegrationBase(Size dimension, Size order)
: GaussianQuadMultidimIntegrator(dimension, order) {}
Real integrate(const ext::function<Real(const std::vector<Real>& arg)>& f) const override {
return GaussianQuadMultidimIntegrator::integrate<Real>(f);
}
Disposable<std::vector<Real> > integrateV(
const ext::function<Disposable<std::vector<Real> >(const std::vector<Real>& arg)>& f)
const override {
return GaussianQuadMultidimIntegrator::integrate<Disposable<std::vector<Real> > >(f);
}
~IntegrationBase() override = default;
};
#endif
template<> class IntegrationBase<MultidimIntegral> :
public MultidimIntegral, public LMIntegration {
public:
IntegrationBase(
const std::vector<ext::shared_ptr<Integrator> >& integrators,
Real a, Real b)
: MultidimIntegral(integrators),
a_(integrators.size(),a), b_(integrators.size(),b) {}
Real integrate(const ext::function<Real(const std::vector<Real>& arg)>& f) const override {
return MultidimIntegral::operator()(f, a_, b_);
}
// disposable vector version here....
~IntegrationBase() override = default;
const std::vector<Real> a_, b_;
};
// Intended to replace OneFactorCopula
/*!
\brief Generic multifactor latent variable model.\par
In this model set up one considers latent (random) variables
\f$ Y_i \f$ described by:
\f[
\begin{array}{ccccc}
Y_1 & = & \sum_k M_k a_{1,k} & + \sqrt{1-\sum_k a_{1,k}^2} Z_1 &
\sim \Phi_{Y_1}\nonumber \\
... & = & ... & ... & \nonumber \\
Y_i & = & \sum_k M_k a_{i,k} & + \sqrt{1-\sum_k a_{i,k}^2} Z_i &
\sim \Phi_{Y_i}\nonumber \\
... & = & ... & ... & \nonumber \\
Y_N & = & \sum_k M_k a_{N,k} & + \sqrt{1-\sum_k a_{N,k}^2} Z_N &
\sim \Phi_{Y_N}
\end{array}
\f]
where the systemic \f$ M_k \f$ and idiosyncratic \f$ Z_i \f$ (this last
one known as error term in some contexts) random variables have
independent zero-mean unit-variance distributions. A restriction of the
model implemented here is that the N idiosyncratic variables all follow
the same probability law \f$ \Phi_Z(z)\f$ (but they are still
independent random variables) Also the model is normalized
so that: \f$-1\leq a_{i,k} \leq 1\f$ (technically the \f$Y_i\f$ are
convex linear combinations). The correlation between \f$Y_i\f$ and
\f$Y_j\f$ is then \f$\sum_k a_{i,k} a_{j,k}\f$.
\f$\Phi_{Y_i}\f$ denotes the cumulative distribution function of
\f$Y_i\f$ which in general differs for each latent variable.\par
In its single factor set up this model is usually employed in derivative
pricing and it is best to use it through integration of the desired
statistical properties of the model; in its multifactorial version (with
typically around a dozen factors) it is used in the context of portfolio
risk metrics; because of the number of variables it is best to opt for a
simulation to compute model properties/magnitudes.
For this reason this class template provides a random factor sample
interface and an integration interface that will be instantiated by
derived concrete models as needed. The class is neutral on the
integration and random generation algorithms\par
The latent variables are typically treated as unobservable magnitudes
and they serve to model one or several magnitudes related to them
through some function
\f[
\begin{array}{ccc}
F_i(Y_i) & = &
F_i(\sum_k M_k a_{i,k} + \sqrt{1-\sum_k a_{i,k}^2} Z_i )\nonumber \\
& = & F_i(M_1,..., M_k, ..., M_K, Z_i)
\end{array}
\f]
The transfer function can have a more generic form:
\f$F_i(Y_1,....,Y_N)\f$ but here the model is restricted to a one to
one relation between the latent variables and the modelled ones. Also
it is assumed that \f$F_i(y_i; \tau)\f$ is monotonic in \f$y_i\f$; it
can then be inverted and the relation of the cumulative probability of
\f$F_i\f$ and \f$Y_i\f$ is simple:
\f[
\int_{\infty}^b \phi_{F_i} df =
\int_{\infty}^{F_i^{-1}(b)} \phi_{Y_i} dy
\f]
If \f$t\f$ is some value of the functional or modelled variable,
\f$y\f$ is mapped to \f$t\f$ such that percentiles match, i.e.
\f$F_Y(y)=Q_i(t)\f$ or \f$y=F_Y^{-1}(Q_i(t))\f$.
The class provides an integration facility of arbitrary functions
dependent on the model states. It also provides random number generation
interfaces for usage of the model in monte carlo simulations.\par
Now let \f$\Phi_Z(z)\f$ be the cumulated distribution function of (all
equal as mentioned) \f$Z_i\f$. For a given realization of \f$M_k\f$,
this determines the distribution of \f$y\f$:
\f[
Prob \,(Y_i < y|M_k) = \Phi_Z \left( \frac{y-\sum_k a_{i,k}\,M_k}
{\sqrt{1-\sum_k a_{i,k}^2}}\right)
\qquad
\mbox{or}
\qquad
Prob \,(t_i < t|M) = \Phi_Z \left( \frac
{F_{Y_{i}}^{-1}(Q_i(t))-\sum_k a_{i,k}\,M_k}
{\sqrt{1-\sum_k a_{i,k}^2}}
\right)
\f]
The distribution functions of \f$ M_k, Z_i \f$ are specified in
specific copula template classes. The distribution function
of \f$ Y_i \f$ is then given by the convolution
\f[
F_{Y_{i}}(y) = Prob\,(Y_i<y) =
\int_{-\infty}^\infty\,\cdots\,\int_{-\infty}^{\infty}\:
D_Z(z)\,\prod_k D_{M_{k}}(m_k) \quad
\Theta \left(y - \sum_k a_{i,k}m_k -
\sqrt{1-\sum_k a_{i,k}^2}\,z\right)\,d\bar{m}\,dz,
\qquad
\Theta (x) = \left\{
\begin{array}{ll}
1 & x \geq 0 \\
0 & x < 0
\end{array}\right.
\f]
where \f$ D_Z(z) \f$ and \f$ D_M(m) \f$ are the probability
densities of \f$ Z\f$ and \f$ M, \f$ respectively.\par
This convolution can also be written
\f[
F_{Y_{i}}(y) = Prob \,(Y_i < y) =
\int_{-\infty}^\infty\,\cdots\,\int_{-\infty}^{\infty}
D_{M_{k}}(m_k)\,dm_k\:
\int_{-\infty}^{g(y,\vec{a},\vec{m})} D_Z(z)\,dz, \qquad
g(y,\vec{a},\vec{m}) = \frac{y - \sum_k a_{i,k}m_k}
{\sqrt{1-\sum_k a_{i,k}^2}}, \qquad \sum_k a_{i,k}^2 < 1
\f]
In general, \f$ F_{Y_{i}}(y) \f$ needs to be computed numerically.\par
The policy class template separates the copula function (the
distributions involved) and the functionality (i.e. what the latent
model represents: a default probability, a recovery...). Since the
copula methods for the
probabilities are to be called repeatedly from an integration or a MC
simulation, virtual tables are avoided and template parameter mechnics
is preferred.\par
There is nothing at this level enforncing the requirement
on the factor distributions to be of zero mean and unit variance. Thats
the user responsibility and the model fails to behave correctly if it
is not the case.\par
Derived classes should implement a modelled magnitude (default time,
etc) and will provide probability distributions and conditional values.
They could also provide functionality for the parameter inversion
problem, the (e.g.) time at which the modeled variable first takes a
given value. This problem has solution/sense depending on the transfer
function \f$F_i(Y_i)\f$ characteristics.
To make direct integration and simulation time efficient virtual
functions have been avoided in accessing methods in the copula policy
and in the sampling of the random factors
*/
template <class copulaPolicyImpl>
class LatentModel
: public virtual Observer , public virtual Observable
{//observer if factors as quotes
public:
void update() override;
//! \name Copula interface.
//@{
typedef copulaPolicyImpl copulaType;
/*! Cumulative probability of the \f$ Y_i \f$ modelled latent random
variable to take a given value.
*/
Probability cumulativeY(Real val, Size iVariable) const {
return copula_.cumulativeY(val, iVariable);
}
//! Cumulative distribution of Z, the idiosyncratic/error factors.
Probability cumulativeZ(Real z) const {
return copula_.cumulativeZ(z);
}
//! Density function of M, the market/systemic factors.
Probability density(const std::vector<Real>& m) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(m.size() == nFactors_,
"Factor size must match that of model.");
#endif
return copula_.density(m);
}
//! Inverse cumulative distribution of the systemic factor iFactor.
Real inverseCumulativeDensity(Probability p, Size iFactor) const {
return copula_.inverseCumulativeDensity(p, iFactor);
}
/*! Inverse cumulative value of the i-th random latent variable with a
given probability. */
Real inverseCumulativeY(Probability p, Size iVariable) const {
return copula_.inverseCumulativeY(p, iVariable);
}
/*! Inverse cumulative value of the idiosyncratic variable with a given
probability. */
Real inverseCumulativeZ(Probability p) const {
return copula_.inverseCumulativeZ(p);
}
/*! All factor cumulative inversion. Used in integrations and sampling.
Inverts all the cumulative random factors probabilities in the
model. These are all the systemic factors plus all the idiosyncratic
ones, so the size of the inversion is the number of systemic factors
plus the number of latent modelled variables*/
Disposable<std::vector<Real> >
allFactorCumulInverter(const std::vector<Real>& probs) const {
return copula_.allFactorCumulInverter(probs);
}
//@}
/*! The value of the latent variable Y_i conditional to
(given) a set of values of the factors.
The passed allFactors vector contains values for all the
independent factors in the model (systemic and
idiosyncratic, in that order). A full sample is required,
i.e. all the idiosyncratic values are expected to be
present even if only the relevant one is used.
*/
Real latentVarValue(const std::vector<Real>& allFactors,
Size iVar) const
{
return std::inner_product(factorWeights_[iVar].begin(),
// systemic term:
factorWeights_[iVar].end(), allFactors.begin(),
// idiosyncratic term:
allFactors[numFactors()+iVar] * idiosyncFctrs_[iVar]);
}
// \to do write variants of the above, although is the most common case
const copulaType& copula() const {
return copula_;
}
// protected:
//! \name Latent model random factor number generator facility.
//@{
/*! Allows generation or random samples of the latent variable.
Generates samples of all the factors in the latent model according
to the given copula as random sequence. The default implementation
given uses the inversion in the copula policy (which must be
present).
USNG is expected to be a uniform sequence generator in the default
implementation.
*/
/*
Several (very different) usages make the spez non trivial
The final goal is to obtain a sequence generator of the factor
samples, several routes are possible depending on the algorithms:
1.- URNG -> Sequence Gen -> CopulaInversion
e.g.: CopulaInversion(RandomSequenceGenerator<MersenneTwisterRNG>)
2.- PseudoRSG ------------> CopulaInversion
e.g.: CopulaInversion(SobolRSG)
3.- URNG -> SpecificMapping -> Sequence Gen (bypasses the copula
for performance)
e.g.: RandomSequenceGenerator<BoxMullerGaussianRng<
MersenneTwisterRNG> >
Notice that the order the three algorithms involved (uniform gen,
sequence construction, distribution mapping) is not always the same.
(in fact there could be some other ways to generate but these are
the ones in the library now.)
Difficulties arise when wanting to use situation 3.- whith a generic
RNG, leaving it unspecified
Derived classes might specialize (on the copula
type) to another type of generator if a more efficient algorithm
that the distribution inversion is available; rewritig then the
nextSequence method for a particular copula implementation.
Some combinations of generators might make no sense, while it
could be possible to block template classes corresponding to those
cases its not done (yet?) (e.g. a BoxMuller under a TCopula.)
Dimensionality coherence (between the generator and the copula)
should have been checked by the client code.
In multithread usage the sequence generator is expect to be already
in position.
To sample the latent variable itself users should call
LatentModel::latentVarValue with these samples.
*/
// Cant use InverseCumulativeRsg since the inverse there has to return a
// real number and here a vector is needed, the function inverted here
// is multivalued.
template <class USNG,
// dummy template parameter to allow for 'full' specialization of
// inner class without specialization of the outer.
bool = true>
class FactorSampler {
public:
typedef Sample<std::vector<Real> > sample_type;
explicit FactorSampler(const copulaType& copula,
BigNatural seed = 0)
: sequenceGen_(copula.numFactors(), seed), // base case construction
x_(std::vector<Real>(copula.numFactors()), 1.0),
copula_(copula) { }
/*! Returns a sample of the factor set \f$ M_k\,Z_i\f$.
This method has the vocation of being specialized at particular
types of the copula with a more efficient inversion to generate the
random variables modelled (e.g. Box-Muller for a gaussian).
Here a default implementation is provided based directly on the
inversion of the cumulative distribution from the copula.
Care has to be taken in potential specializations that the generator
algorithm is compatible with an eventual concurrence of the
simulations.
*/
const sample_type& nextSequence() const {
typename USNG::sample_type sample =
sequenceGen_.nextSequence();
//Not possible to overload operator member access in Disposable
//return copula_.allFactorCumulInverter(sample.value).value;
x_.value = copula_.allFactorCumulInverter(sample.value);
return x_;
}
private:
USNG sequenceGen_;// copy, we might be mutithreaded
mutable sample_type x_;
// no copies
const copulaType& copula_;
};
//@}
protected:
/* \todo Move integrator traits like number of quadrature points,
integration domain dimensions, etc to the copula through a static
member function. Since they depend on the nature of the probability
density distribution thats where they belong.
This is why theres one factory per copula policy template parameter
(even if this is not used...yet)
*/
class IntegrationFactory {
public:
static ext::shared_ptr<LMIntegration> createLMIntegration(
Size dimension,
LatentModelIntegrationType::LatentModelIntegrationType type =
#ifndef QL_PATCH_SOLARIS
LatentModelIntegrationType::GaussianQuadrature)
#else
LatentModelIntegrationType::Trapezoid)
#endif
{
switch(type) {
#ifndef QL_PATCH_SOLARIS
case LatentModelIntegrationType::GaussianQuadrature:
return
ext::make_shared<
IntegrationBase<GaussianQuadMultidimIntegrator> >(
dimension, 25);
#endif
case LatentModelIntegrationType::Trapezoid:
{
std::vector<ext::shared_ptr<Integrator> > integrals;
for(Size i=0; i<dimension; i++)
integrals.push_back(
ext::make_shared<TrapezoidIntegral<Default> >(
1.e-4, 20));
/* This integration domain is tailored for the T
distribution; it is too wide for normals or Ts of high
order.
\todo This needs to be solved by having the copula to
provide the integration traits for any integration
algorithm since it is the copula that knows the relevant
domain for its density distributions. Also to be able to
block integrations which will fail; like a quadrature
here in some cases.
*/
return
ext::make_shared<IntegrationBase<MultidimIntegral> >
(integrals, -35., 35.);
}
default:
QL_FAIL("Unknown latent model integration type.");
}
}
private:
IntegrationFactory() = default;
};
//@}
public:
// model size, number of latent variables modelled
Size size() const {return nVariables_;}
//! Number of systemic factors.
Size numFactors() const {return nFactors_;}
//! Number of total free random factors; systemic and idiosyncratic.
Size numTotalFactors() const { return nVariables_ + nFactors_; }
/*! Constructs a LM with an arbitrary number of latent variables
and factors given by the dimensions of the passed matrix.
@param factorsWeights Ordering is factorWeights_[iVar][iFactor]
@param ini Initialization variables. Trait type from the copula
policy to allow for static policies (this solution needs to be
revised, possibly drop the static policy and create a policy
member in LatentModel)
*/
explicit LatentModel(
const std::vector<std::vector<Real> >& factorsWeights,
const typename copulaType::initTraits& ini =
copulaType::initTraits());
/*! Constructs a LM with an arbitrary number of latent variables
depending only on one random factor but contributing to each latent
variable through different weights.
@param factorsWeight Ordering is factorWeights_[iVariable]
@param ini Initialization variables. Trait type from the copula
policy to allow for static policies (this solution needs to be
revised, possibly drop the static policy and create a policy
member in LatentModel)
*/
explicit LatentModel(const std::vector<Real>& factorsWeight,
const typename copulaType::initTraits& ini =
copulaType::initTraits());
/*! Constructs a LM with an arbitrary number of latent variables
depending only on one random factor with the same weight for all
latent variables.
correlSqr is the weight, same for all.
ini is a trait type from the copula policy, to allow for
static policies (this solution needs to be revised,
possibly drop the static policy and create a policy member
in LatentModel)
*/
explicit LatentModel(Real correlSqr,
Size nVariables,
const typename copulaType::initTraits& ini = copulaType::initTraits());
/*! Constructs a LM with an arbitrary number of latent variables
depending only on one random factor with the same weight for all
latent variables. The weight is observed and this constructor is
intended to be used when the model relates to a market value.
singleFactorCorrel is the weight/mkt-factor, same for all.
ini is a trait type from the copula policy, to allow for
static policies (this solution needs to be revised,
possibly drop the static policy and create a policy member
in LatentModel)
*/
explicit LatentModel(const Handle<Quote>& singleFactorCorrel,
Size nVariables,
const typename copulaType::initTraits& ini =
copulaType::initTraits());
//! Provides values of the factors \f$ a_{i,k} \f$
const std::vector<std::vector<Real> >& factorWeights() const {
return factorWeights_;
}
//! Provides values of the normalized idiosyncratic factors \f$ Z_i \f$
const std::vector<Real>& idiosyncFctrs() const {return idiosyncFctrs_;}
//! Latent variable correlations:
Real latentVariableCorrel(Size iVar1, Size iVar2) const {
// true for any normalized combination
Real init = (iVar1 == iVar2 ?
idiosyncFctrs_[iVar1] * idiosyncFctrs_[iVar1] : 0.);
return std::inner_product(factorWeights_[iVar1].begin(),
factorWeights_[iVar1].end(), factorWeights_[iVar2].begin(),
init);
}
//! \name Integration facility interface
//@{
/*! Integrates an arbitrary scalar function over the density domain(i.e.
computes its expected value).
*/
Real integratedExpectedValue(
const ext::function<Real(const std::vector<Real>& v1)>& f) const {
// function composition: composes the integrand with the density
// through a product.
return
integration()->integrate(
ext::bind(std::multiplies<Real>(),
ext::bind(&copulaPolicyImpl::density, copula_,
ext::placeholders::_1),
ext::bind(ext::cref(f),
ext::placeholders::_1)));
}
/*! Integrates an arbitrary vector function over the density domain(i.e.
computes its expected value).
*/
Disposable<std::vector<Real> > integratedExpectedValue(
// const ext::function<std::vector<Real>(
const ext::function<Disposable<std::vector<Real> >(
const std::vector<Real>& v1)>& f ) const {
return
integration()->integrateV(//see note in LMIntegrators base class
ext::bind<Disposable<std::vector<Real> > >(
detail::multiplyV(),
ext::bind(&copulaPolicyImpl::density, copula_,
ext::placeholders::_1),
ext::bind(ext::cref(f), ext::placeholders::_1)));
}
protected:
// Integrable models must provide their integrator.
// Arguable, not having the integration in the LM class saves that
// memory but have an entry in the VT...
virtual const ext::shared_ptr<LMIntegration>& integration() const {
QL_FAIL("Integration non implemented in Latent model.");
}
//@}
// Ordering is: factorWeights_[iVariable][iFactor]
mutable std::vector<std::vector<Real> > factorWeights_;
/* This is a duplicated value from the data above chosen for memory
reasons.
I have opted for this one value redundant memory rather than have the
memory load of the observable in all factors. Typically Latent models
are used in two very different ways: with many factors and not linked
to a market observable (typical matrix size above is of tens of
thousands entries) or with just one observable value and the matrix is
just a scalar. Otherwise, to remove the redundancy, the matrix
factorWeights_ should be one of Quotes Handles.
Yet it is not entirely true that quotes might be used only in pricing,
think sensitivity analysis....
\todo Reconsider this, see how expensive truly is.
*/
mutable Handle<Quote> cachedMktFactor_;
// updated only by correlation observability and constructors.
// \sqrt{1-\sum_k \beta_{i,k}^2} the addition being along the factors.
// It has therefore the size of the basket. Cached for perfomance
mutable std::vector<Real> idiosyncFctrs_;
//! Number of systemic factors.
mutable Size nFactors_;//matches idiosyncFctrs_[0].size();i=0 or any
//! Number of latent model variables, idiosyncratic terms or model dim
mutable Size nVariables_;// matches idiosyncFctrs_.size()
mutable copulaType copula_;
};
// Defines ----------------------------------------------------------------
#ifndef __DOXYGEN__
template <class Impl>
LatentModel<Impl>::LatentModel(
const std::vector<std::vector<Real> >& factorWeights,
const typename Impl::initTraits& ini)
: factorWeights_(factorWeights),
nFactors_(factorWeights[0].size()),
nVariables_(factorWeights.size()), copula_(factorWeights, ini)
{
for(Size i=0; i<factorWeights.size(); i++) {
idiosyncFctrs_.push_back(std::sqrt(1.-
std::inner_product(factorWeights[i].begin(),
factorWeights[i].end(),
factorWeights[i].begin(), 0.)));
// while at it, check sizes are coherent:
QL_REQUIRE(factorWeights[i].size() == nFactors_,
"Name " << i << " provides a different number of factors");
}
}
template <class Impl>
LatentModel<Impl>::LatentModel(
const std::vector<Real>& factorWeights,
const typename Impl::initTraits& ini)
: nFactors_(1),
nVariables_(factorWeights.size())
{
for(Size iName=0; iName < factorWeights.size(); iName++)
factorWeights_.push_back(std::vector<Real>(1,
factorWeights[iName]));
for(Size iName=0; iName < factorWeights.size(); iName++)
idiosyncFctrs_.push_back(std::sqrt(1. -
factorWeights[iName]*factorWeights[iName]));
//convert row to column vector....
copula_ = copulaType(factorWeights_, ini);
}
template <class Impl>
LatentModel<Impl>::LatentModel(
const Real correlSqr,
Size nVariables,
const typename Impl::initTraits& ini)
: factorWeights_(nVariables, std::vector<Real>(1, correlSqr)),
idiosyncFctrs_(nVariables,
std::sqrt(1.-correlSqr*correlSqr)),
nFactors_(1),
nVariables_(nVariables),
copula_(factorWeights_, ini)
{ }
template <class Impl>
LatentModel<Impl>::LatentModel(
const Handle<Quote>& singleFactorCorrel,
Size nVariables,
const typename Impl::initTraits& ini)
: factorWeights_(nVariables, std::vector<Real>(1,
std::sqrt(singleFactorCorrel->value()))),
cachedMktFactor_(singleFactorCorrel),
idiosyncFctrs_(nVariables,
std::sqrt(1.-singleFactorCorrel->value())),
nFactors_(1),
nVariables_(nVariables),
copula_(factorWeights_, ini)
{
registerWith(cachedMktFactor_);
}
#endif
template <class Impl>
void LatentModel<Impl>::update() {
/* only registration with the single market correl quote. If we get
register with something else remember that the quote stores correlation
and the model need factor values; which for one factor models are the
square root of the correlation.
*/
factorWeights_ = std::vector<std::vector<Real> >(nVariables_,
std::vector<Real>(1, std::sqrt(cachedMktFactor_->value())));
idiosyncFctrs_ = std::vector<Real>(nVariables_,
std::sqrt(1.-cachedMktFactor_->value()));
copula_ = copulaType(factorWeights_, copula_.getInitTraits());
notifyObservers();
}
#ifndef __DOXYGEN__
//----Template partial specializations of the random FactorSampler--------
/*
Notice that while the default template needs a sequence generator the
specializations need a number generator. This is forced at the time the
concrete policy class is used in the template parameter, if it has been
specialized it needs the sample type typedef to match at compilation.
Notice here the outer class template is specialized only, leaving the inner
generator still a class template. Apparently old versions of gcc (3.x) bug
on this one not recognizing the specialization.
*/
/*! \brief Specialization for direct Gaussian Box-Muller generation.\par
The implementation of Box-Muller in the library is the rejection variant so
do not use it within a multithreaded simulation.
*/
template<class TC> template<class URNG, bool dummy>
class LatentModel<TC>
::FactorSampler <RandomSequenceGenerator<BoxMullerGaussianRng<URNG> > ,
dummy> {
typedef URNG urng_type;
public:
//Size below must be == to the numb of factors idiosy + systemi
typedef Sample<std::vector<Real> > sample_type;
explicit FactorSampler(const GaussianCopulaPolicy& copula,
BigNatural seed = 0)
: boxMullRng_(copula.numFactors(),
BoxMullerGaussianRng<urng_type>(urng_type(seed))){ }
const sample_type& nextSequence() const {
return boxMullRng_.nextSequence();
}
private:
RandomSequenceGenerator<BoxMullerGaussianRng<urng_type> > boxMullRng_;
};
/*! \brief Specialization for direct T samples generation.\par
The PolarT is a rejection algorithm so do not use it within a
multithreaded simulation.
The RandomSequenceGenerator class does not admit heterogeneous
distribution samples so theres a trick here since the template parameter is
not what it is used internally.
*/
template<class TC> template<class URNG, bool dummy>//uniform number expected
class LatentModel<TC>
::FactorSampler<RandomSequenceGenerator<PolarStudentTRng<URNG> > ,
dummy> {
typedef URNG urng_type;
public:
typedef Sample<std::vector<Real> > sample_type;
explicit FactorSampler(const TCopulaPolicy& copula, BigNatural seed = 0)
: sequence_(std::vector<Real> (copula.numFactors()), 1.0),
urng_(seed) {
// 1 == urng.dimension() is enforced by the sample type
const std::vector<Real>& varF = copula.varianceFactors();
for(Size i=0; i<varF.size(); i++)// ...use back inserter lambda
trng_.push_back(
PolarStudentTRng<urng_type>(2./(1.-varF[i]*varF[i]), urng_));
}
const sample_type& nextSequence() const {
Size i=0;
for(; i<trng_.size(); i++)//systemic samples plus one idiosyncratic
sequence_.value[i] = trng_[i].next().value;
for(; i<sequence_.value.size(); i++)//rest of idiosyncratic samples
sequence_.value[i] = trng_.back().next().value;
return sequence_;
}
private:
mutable sample_type sequence_;
urng_type urng_;
mutable std::vector<PolarStudentTRng<urng_type> > trng_;
};
#endif
}
#endif