functions to compute delta or delta-gamma VaR numbers More...

#include <qle/math/covariancesalvage.hpp>
#include <ql/math/comparison.hpp>
#include <ql/math/array.hpp>
#include <ql/math/matrix.hpp>
#include <ql/math/matrixutilities/choleskydecomposition.hpp>
#include <ql/math/matrixutilities/pseudosqrt.hpp>
#include <ql/math/randomnumbers/rngtraits.hpp>
#include <boost/accumulators/accumulators.hpp>
#include <boost/accumulators/statistics/stats.hpp>
#include <boost/accumulators/statistics/tail_quantile.hpp>
#include <boost/foreach.hpp>

Functions
Real	deltaVar (const Matrix &omega, const Array &delta, const Real p, const CovarianceSalvage &sal=NoCovarianceSalvage())
	function that computes a delta VaR More...

Real	deltaGammaVarNormal (const Matrix &omega, const Array &delta, const Matrix &gamma, const Real p, const CovarianceSalvage &sal=NoCovarianceSalvage())
	function that computes a delta-gamma normal VaR More...

template<class RNG >
Real	deltaGammaVarMc (const Matrix &omega, const Array &delta, const Matrix &gamma, const Real p, const Size paths, const Size seed, const CovarianceSalvage &sal=NoCovarianceSalvage())
	function that computes a delta-gamma VaR using Monte Carlo (single quantile) More...

template<class RNG >
std::vector< Real >	deltaGammaVarMc (const Matrix &omega, const Array &delta, const Matrix &gamma, const std::vector< Real > &p, const Size paths, const Size seed, const CovarianceSalvage &sal=NoCovarianceSalvage())
	function that computes a delta-gamma VaR using Monte Carlo (multiple quantiles) More...

void	check (const Real p)

void	check (const Matrix &omega, const Array &delta)

void	check (const Matrix &omega, const Array &delta, const Matrix &gamma)

template<typename A >
Real	absMax (const A &a)

Real	deltaGammaVarCornishFisher (const Matrix &omega, const Array &delta, const Matrix &gamma, const Real p, const CovarianceSalvage &sal=NoCovarianceSalvage())

Real	deltaGammaVarSaddlepoint (const Matrix &omega, const Array &delta, const Matrix &gamma, const Real p, const CovarianceSalvage &sal=NoCovarianceSalvage())

Detailed Description

functions to compute delta or delta-gamma VaR numbers

Function Documentation

◆ deltaVar()

Real QuantExt::deltaVar	(	const Matrix &	omega,
		const Array &	delta,
		const Real	p,
		const CovarianceSalvage &	sal = `NoCovarianceSalvage()`
	)

function that computes a delta VaR

For a given covariance matrix and a delta vector this function computes a parametric var w.r.t. a given confidence level for multivariate normal risk factors.

◆ deltaGammaVarNormal()

Real QuantExt::deltaGammaVarNormal	(	const Matrix &	omega,
		const Array &	delta,
		const Matrix &	gamma,
		const Real	p,
		const CovarianceSalvage &	sal = `NoCovarianceSalvage()`
	)

function that computes a delta-gamma normal VaR

For a given a covariance matrix, a delta vector and a gamma matrix this function computes a parametric var w.r.t. a given confidence level. The gamma matrix is taken into account when computing the variance of the PL distribution, but the PL distribution is still assumed to be normal.

◆ deltaGammaVarMc() [1/2]

Real deltaGammaVarMc	(	const Matrix &	omega,
		const Array &	delta,
		const Matrix &	gamma,
		const Real	p,
		const Size	paths,
		const Size	seed,
		const CovarianceSalvage &	sal = `NoCovarianceSalvage()`
	)

function that computes a delta-gamma VaR using Monte Carlo (single quantile)

For a given a covariance matrix, a delta vector and a gamma matrix this function computes a parametric var w.r.t. a given confidence level. The var quantile is estimated from Monte-Carlo realisations of a second order sensitivity based PL.

◆ deltaGammaVarMc() [2/2]

std::vector< Real > deltaGammaVarMc	(	const Matrix &	omega,
		const Array &	delta,
		const Matrix &	gamma,
		const std::vector< Real > &	p,
		const Size	paths,
		const Size	seed,
		const CovarianceSalvage &	sal = `NoCovarianceSalvage()`
	)

function that computes a delta-gamma VaR using Monte Carlo (multiple quantiles)