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LiborFactorLoading Class Reference

#include <LiborFactorLoading.h>

List of all members.

Detailed Description

FactorLoading for the log-Libors of a Libor Market Model. Volatilities based on a volatility surface provided by the class VolSurface. The factor loading contains the vector k of volatility scaling factors (book, 6.11.1, k=c). Log-Libor correlations provided by the class Correlations.

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 the on the interval . This matrix and its upper triangular root are used in the simulation of the time step s->t for the process Y and related processes.

More precisely to simulate the time step (here t is discrete time) we need the matrix ,

for the drift step as well as its upper triangular root R satisfying for the volatility step.

If a low factor model with r factors is desired we need an approximation , where R(t) has rank at most r and more precisely dimension . The best approximation is obtained by diagonalizing the matrix as where H is a unitary matrix and the eigenvalues of H. One then sets

where the are the columns of H.

Author:
Michael J. Meyer

Definition at line 131 of file LiborFactorLoading.h.

Public Member Functions

const LiborFactorLoadingType * getType () const
int getDimension () const
const RealArray1D & getDeltas () const
const RealArray1D & getTenorStructure () const
Real getT (int i) const
const RealArray1D & getInitialLibors () const
const RealArray1D & getInitialXLibors () const
RealArray1D & getScalingFactors ()
const UTRRealMatrix & getRho () const
VolSurface * getVolSurface ()
Correlations * getCorrelations ()
 LiborFactorLoading (const RealArray1D &L0, const RealArray1D &deltas, const RealArray1D &_k, VolSurface *vols, Correlations *corrs)
 ~LiborFactorLoading ()
void setParameters (const RealArray1D &u)
Real sigma (int i, Real t) const
Real integral_sgi_sgj_rhoij (int i, int j, Real s, Real t) const
Real annualVol (int i) const
const UTRRealMatrix & logLiborCovariationMatrix (int p, int q, Real s, Real t) const
const UTRRealMatrix & logLiborCovariationMatrix (int t) const
const UTRRealMatrix & logLiborCovariationMatrixRoot (int t) const
const RealMatrix & reducedRankLogLiborCovariationMatrixRoot (int t, int r) const
void factorAnalysis (int p, int q, Real s, Real t, int r) const
void factorAnalysis (int t, int r) const
void selfTest () const
void factorizationTest (int r) const
std::ostream & printSelf (std::ostream &os) const

Static Public Member Functions

LiborFactorLoading * sample (int n, int volType=VolSurface::JR, int corrType=Correlations::CS)

Protected Attributes

LiborFactorLoadingType flType
int n
RealArray1D delta
RealArray1D T
RealArray1D l
RealArray1D x
RealArray1D k
VolSurface * vol
Correlations * corr
Correlations & rho

Constructor & Destructor Documentation

LiborFactorLoading::LiborFactorLoading (  const RealArray1D &    L0,
const RealArray1D &    deltas,
const RealArray1D &    _k,
VolSurface *    vols,
Correlations *    corrs
) 
 

Parameters:
L0 initial libors .
deltas array of accrual interval lengths .
_k scaling factors for Libor vols.
vols volatility surface.
corrs correlations.

LiborFactorLoading::~LiborFactorLoading (    )  [inline]
 

Definition at line 211 of file LiborFactorLoading.h.

Member Function Documentation

const LiborFactorLoadingType* LiborFactorLoading::getType (    )  const [inline]
 

Type object, contains integer and string IDs of the VolSurface and Correlations.

Definition at line 156 of file LiborFactorLoading.h.

int LiborFactorLoading::getDimension (    )  const [inline]
 

Number n of forward Libors including .

Definition at line 160 of file LiborFactorLoading.h.

const RealArray1D& LiborFactorLoading::getDeltas (    )  const [inline]
 

Array of accrual intervals .

Definition at line 164 of file LiborFactorLoading.h.

const RealArray1D& LiborFactorLoading::getTenorStructure (    )  const [inline]
 

Array of continuous Libor reset times .

Definition at line 168 of file LiborFactorLoading.h.

Real LiborFactorLoading::getT (  int    i )  const [inline]
 

Libor reset date .

Definition at line 171 of file LiborFactorLoading.h.

References Real.

const RealArray1D& LiborFactorLoading::getInitialLibors (    )  const [inline]
 

The array of initial Libors .

Definition at line 175 of file LiborFactorLoading.h.

const RealArray1D& LiborFactorLoading::getInitialXLibors (    )  const [inline]
 

The array of initial XLibors .

Definition at line 179 of file LiborFactorLoading.h.

RealArray1D& LiborFactorLoading::getScalingFactors (    )  [inline]
 

The scaling factor . See book, 6.11.1.

Definition at line 183 of file LiborFactorLoading.h.

const UTRRealMatrix& LiborFactorLoading::getRho (    )  const
 

The instantaneous log-Libor correlations.

VolSurface* LiborFactorLoading::getVolSurface (    )  [inline]
 

The VolSurface of the factor loading.

Definition at line 190 of file LiborFactorLoading.h.

Correlations* LiborFactorLoading::getCorrelations (    )  [inline]
 

The Correlations of the factor loading.

Definition at line 193 of file LiborFactorLoading.h.

void LiborFactorLoading::setParameters (  const RealArray1D &    u ) 
 

Set the parameters of the factorloading from the vector X. The first 4 coordinates populate the VolSurface the rest goes to the Correlations. Index base of u must be zero.

Real LiborFactorLoading::sigma (  int    i,
Real    t
)  const
 

Volatility of forward Libor . See book, 6.4.

Parameters:
i Libor index.
t continuous time.

Real LiborFactorLoading::integral_sgi_sgj_rhoij (  int    i,
int    j,
Real    s,
Real    t
)  const
 

The integral

neeeded for the distribution of time step increments s->t. See book, 6.5.1.

Parameters:
i,j forward Libor indices.
s,t continuous integration bounds (times).

Real LiborFactorLoading::annualVol (  int    i )  const
 

Annualized volatility of Libor .

const UTRRealMatrix& LiborFactorLoading::logLiborCovariationMatrix (  int    p,
int    q,
Real    s,
Real    t
)  const
 

The upper triangular half of the covariation matrix CV(p,q,s,t).

Parameters:
p,q Libors .
s,t continuous times .

const UTRRealMatrix& LiborFactorLoading::logLiborCovariationMatrix (  int    t )  const
 

The upper triangular half of the covariation matrix CV(t). This is the matrix needed for the drift part of the Libor process time step .

Parameters:
t discrete time.

const UTRRealMatrix& LiborFactorLoading::logLiborCovariationMatrixRoot (  int    t )  const
 

The upper triangular root R of the covariation matrix CV(t). This matrix is needed for the volatility part of the Libor process time step .

Parameters:
t discrete time.

const RealMatrix& LiborFactorLoading::reducedRankLogLiborCovariationMatrixRoot (  int    t,
int    r
)  const
 

Rank r approximate root R of the covariation matrix CV(t). Best approximation , with R of rank at most r. This matrix is needed for the volatility part of the Libor process time step .

Parameters:
t discrete time.
r rank (number of factors).

void LiborFactorLoading::factorAnalysis (  int    p,
int    q,
Real    s,
Real    t,
int    r
)  const
 

Examines how dominant are the first r eigenvalues of the covariation matrix CV(p,q,s,t)=(C_ij) with entries

This matrix is needed for the Libor time step s->t.

void LiborFactorLoading::factorAnalysis (  int    t,
int    r
)  const
 

Examines how dominant are the first r eigenvalues of the covariation matrix CV(t)=(C_ij) with entries

This matrix is needed for the Libor time step .

void LiborFactorLoading::selfTest (    )  const
 

Test the roots of all logLiborCovariationMatrix(int t).

void LiborFactorLoading::factorizationTest (  int    r )  const
 

Computes approximate rank r factorizations C(t)=R(t)R(t)' for all the matrices logLiborCovariationMatrix(int t) and prints the relative error.

LiborFactorLoading* LiborFactorLoading::sample (  int    n,
int    volType = VolSurface::JR,
int    corrType = Correlations::CS
)  [static]
 

Returns sample factor loading in dimension n.

Parameters:
volType type of VolSurface (VolSurface::CONST, JR, M)
corrType type of Correlation (Correlation::JR, CS)

std::ostream& LiborFactorLoading::printSelf (  std::ostream &    os )  const
 

Message and fields.

Member Data Documentation

LiborFactorLoadingType LiborFactorLoading::flType [protected]
 

Definition at line 135 of file LiborFactorLoading.h.

int LiborFactorLoading::n [protected]
 

Definition at line 137 of file LiborFactorLoading.h.

RealArray1D LiborFactorLoading::delta [protected]
 

Definition at line 139 of file LiborFactorLoading.h.

RealArray1D LiborFactorLoading::T [protected]
 

Definition at line 140 of file LiborFactorLoading.h.

RealArray1D LiborFactorLoading::l [protected]
 

Definition at line 141 of file LiborFactorLoading.h.

RealArray1D LiborFactorLoading::x [protected]
 

Definition at line 142 of file LiborFactorLoading.h.

RealArray1D LiborFactorLoading::k [protected]
 

Definition at line 143 of file LiborFactorLoading.h.

VolSurface* LiborFactorLoading::vol [protected]
 

Definition at line 145 of file LiborFactorLoading.h.

Correlations* LiborFactorLoading::corr [protected]
 

Definition at line 146 of file LiborFactorLoading.h.

Correlations& LiborFactorLoading::rho [protected]
 

Definition at line 147 of file LiborFactorLoading.h.

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