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PredictorCorrectorLMM Class Reference

#include <PredictorCorrectorLMM.h>

Inheritance diagram for PredictorCorrectorLMM:

List of all members.

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Detailed Description

Libor Market Model with time dependent deterministic log-Libor volatilities and constant log-Libor correlations. The volatilities and correlations are encapsulated in the FactorLoading. Two types of FactorLoadings are implemented.

The state variables are the Libors themselves and paths are generated using a predictor corrector simulation of the true Libor dynamics, see book, 6.5.1.

Time steps move directly from one point on the tenor structure to the following point and are simulated in the forward martingale measure at the terminal time . The stochastic dynamics is either pseudo random (MC) based on the Mersenne Twister or quasi random (QMC) based on the Sobol sequence.

Author:

Michael J. Meyer

Definition at line 82 of file PredictorCorrectorLMM.h.

Public Member Functions
void	switchToQMC ()
void	switchToMC ()
Real	XL (int j, int t) const
const RealVector &	XLvect (int t, int p)
	PredictorCorrectorLMM (LiborFactorLoading *fl)
void	newWienerIncrements (int t)
void	printWienerIncrements (int t, int s) const
int	effectiveDimension (int t, int s) const
void	timeStep (int t, int p)
void	timeStep (int t)
Real	capletAggregateVolatility (int i) const
Real	swaptionAggregateVolatility (int p, int q, int t) const
std::ostream &	printSelf (std::ostream &os) const
Static Public Member Functions
LiborMarketModel *	sample (int n, int volType, int corrType)

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Constructor & Destructor Documentation

PredictorCorrectorLMM::PredictorCorrectorLMM (  LiborFactorLoading *    fl )

Constructor, sets default stochastic generator: Mersenne Twister. Parameters: fl  volatility and correlation structure, see FactorLoading.

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Member Function Documentation

void PredictorCorrectorLMM::switchToQMC (    )

Switches to quasi random dynamics based on Sobol sequence.

void PredictorCorrectorLMM::switchToMC (    )

Switches to pseudo random dynamics based on Mersenne Twister.

Real PredictorCorrectorLMM::XL (  int    j, int    t )  const [virtual]

X-Libor , value in current path. Parameters: j  Libor index. t  discrete time. Implements LiborMarketModel.

const RealVector& PredictorCorrectorLMM::XLvect (  int    t, int    p )  [virtual]

X-Libor vector , value in current path. Index base p, natural indices. Parameters: p  index of first Libor. t  discrete time. Implements LiborMarketModel.

LiborMarketModel* PredictorCorrectorLMM::sample (  int    n, int    volType, int    corrType )  [static]

Sample LMM, quarterly accrual. Parameters: n  dimension (number of accrual intervals). volType  type of volatility surface (VolSurface::JR,M,CONST). corrType  type of correlations (Correlations::JR,CS).

void PredictorCorrectorLMM::newWienerIncrements (  int    t )  [virtual]

Writes a new set of standard normal increments driving a full Libor path to time t into the field Z. Forwards the request to the StochasticGenerator. Reimplemented from LiborMarketModel.

void PredictorCorrectorLMM::printWienerIncrements (  int    t, int    s )  const [virtual]

Prints the matrix Z of current Wiener increments, method is used for testing only. Reimplemented from LiborMarketModel.

int PredictorCorrectorLMM::effectiveDimension (  int    t, int    s )  const [inline, virtual]

The effective dimension of the simulation, that is, the number of standard normal deviates needed to compute one path. This is the dimension of the low discrepancy sequence generator needed for QMC simulation. Note: if this is too high (>623 for Mersenne Twister) a random number generator may not be able to ensure equidistribution in this dimension calling into question the mathematical basis for Monte Carlo expectations. Reimplemented from LiborMarketModel. Definition at line 202 of file PredictorCorrectorLMM.h.

void PredictorCorrectorLMM::timeStep (  int    t, int    p )  [virtual]

Time step of the X-Libors . (discrete time t -> t+1) using a predictor-corrector algorithm and the current matrix Z of standard normal increments. See book, 6.5.1. Parameters: t  discrete time (continuous time ). p  Libors evolved are . Implements LiborMarketModel. Referenced by timeStep().

void PredictorCorrectorLMM::timeStep (  int    t )  [inline]

Evolves the full set of Libors from discrete time t to time t+1 in a single time step using the current matrix Z of standard normal increments. Parameters: t  current discrete time (continuous time T_t). Definition at line 227 of file PredictorCorrectorLMM.h. References timeStep().

Real PredictorCorrectorLMM::capletAggregateVolatility (  int    i )  const [virtual]

Analytic approximation for the aggregate caplet volatility where . Exact if Libors have deterministic volatility. Quantity is needed for Black caplet fromula. Parameters: i  caplet on . Reimplemented from LiborMarketModel.

Real PredictorCorrectorLMM::swaptionAggregateVolatility (  int    p, int    q, int    t )  const [virtual]

Analytic forecast for the swap rate volatility where is the logarithm of the swap rate. Quantity is needed for Black approximate swaption formula. Parameters: p,q  swap along on . t  swaption exercise at time . Reimplemented from LiborMarketModel.

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

Message and fields. Implements LiborMarketModel.

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

• PredictorCorrectorLMM.h

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