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FactorLoading Class Reference

#include <FactorLoading.h>

Inheritance diagram for FactorLoading:

List of all members.

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Detailed Description

This class provides access to the factor loadings of an Ito integral and related covariation integrals. See book, 3.11.

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

Definition at line 93 of file FactorLoading.h.

Public Member Functions
int	getDimension () const
	FactorLoading (int dim)
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 UTRRealMatrix &	correlationMatrix () const
const UTRRealMatrix &	covariationMatrix (int p, int q, Real t, Real T) const
const UTRRealMatrix &	covariationMatrix (Real t, Real T) const
const UTRRealMatrix &	nu (Real t, int p) const
Protected Attributes
int	n

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Constructor & Destructor Documentation

FactorLoading::FactorLoading (  int    dim )  [inline]

Constructor. Parameters: dim  dimension n of Y. Definition at line 118 of file FactorLoading.h.

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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]

Instantaneous correlations of increments. Implemented in ConstantFactorLoading.

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

Volatility of . Parameters: i  components of . t  continuous time. Implemented in ConstantFactorLoading.

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. Implemented in ConstantFactorLoading.

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

Message and fields. Implemented in ConstantFactorLoading.

const UTRRealMatrix& FactorLoading::correlationMatrix (    )  const

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.

const UTRRealMatrix& FactorLoading::covariationMatrix (  Real    t, Real    T )  const

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

const UTRRealMatrix& FactorLoading::nu (  Real    t, int    p )  const

The factor loading computed as the upper triangular root of the matrix , where . This matrix satisfies . The index base is p, that is, natural indices when using the subscripting operator.

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Member Data Documentation

int FactorLoading::n [protected]

Definition at line 97 of file FactorLoading.h.

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The documentation for this class was generated from the following file:

• FactorLoading.h

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