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`#include <FactorLoading.h>`

List of all members.

## Detailed Description

This Ito integral is the unbounded variation part ("volatility part") of several interesting stochastic processes or their component wise logarithms, see LiborMarketModel, BlackScholesBasket.

We assume that is a matrix with rows of the form , where is a scalar function and a constant unit vector. Setting we have

Here is the instantaneous volatility of and the instantaneous correlation of .

With continuous times, set and

and let be the matrix

Here angular brackets denote the covariation process as usual and is the covariation matrix of Y on the interval . This matrix and its upper triangular root are used in the simulation of the time step t->T for the process Y and related processes.

The class `FactorLoading` has abstract methods to compute various covariation integrals (which obviously depend on the concrete volatility and correlation structure) and uses these to compute the various matrices needed for path simulation.

Author:
Michael J. Meyer

## Public Member Functions

int getDimension () const
virtual Real rho (int i, int j) const=0
virtual Real sigma (int i, Real t) const=0
virtual Real integral_sgi_sgj_rhoij (int i, int j, Real t, Real T) const=0
virtual std::ostream & printSelf (std::ostream &os) const=0
const UTRRealMatrixcorrelationMatrix () const
const UTRRealMatrixcovariationMatrix (int p, int q, Real t, Real T) const
const UTRRealMatrixcovariationMatrix (Real t, Real T) const
const UTRRealMatrixnu (Real t, int p) const

int n

## Constructor & Destructor Documentation

 FactorLoading::FactorLoading ( int dim ) ` [inline]`

Constructor.

Parameters:
 dim dimension n of Y.

## Member Function Documentation

 int FactorLoading::getDimension ( ) const` [inline]`
 Number `n` of forward Libors including `L_0`. Definition at line 107 of file FactorLoading.h.

 virtual Real FactorLoading::rho ( int i, int j ) const` [pure virtual]`

 virtual Real FactorLoading::sigma ( int i, Real t ) const` [pure virtual]`

Volatility of .

Parameters:
 i components of . t continuous time.

 virtual Real FactorLoading::integral_sgi_sgj_rhoij ( int i, int j, Real t, Real T ) const` [pure virtual]`

The integral

Parameters:
 i,j components of . t,T continuous times.

 virtual std::ostream& FactorLoading::printSelf ( std::ostream & os ) const` [pure virtual]`

 The constant correlation matrix of the .

 const UTRRealMatrix& FactorLoading::covariationMatrix ( int p, int q, Real t, Real T ) const
 The matrix CV of covariations where . Index base p, natural indices.

 The full matrix CV of covariations where . Index base 0.

 int FactorLoading::n` [protected]`