LiborForwardModelProcess (3) - Linux Manuals

LiborForwardModelProcess: libor-forward-model process

NAME

QuantLib::LiborForwardModelProcess - libor-forward-model process

SYNOPSIS

#include <ql/legacy/libormarketmodels/lfmprocess.hpp>

Inherits QuantLib::StochasticProcess.

Public Member Functions

LiborForwardModelProcess (Size size, const boost::shared_ptr< IborIndex > &index)

Disposable< Array > initialValues () const
returns the initial values of the state variables
Disposable< Array > drift (Time t, const Array &x) const
returns the drift part of the equation, i.e., $ mu(t, mathrm{x}_t) $
Disposable< Matrix > diffusion (Time t, const Array &x) const
returns the diffusion part of the equation, i.e. $ igma(t, mathrm{x}_t) $
Disposable< Matrix > covariance (Time t0, const Array &x0, Time dt) const

Disposable< Array > apply (const Array &x0, const Array &dx) const

Disposable< Array > evolve (Time t0, const Array &x0, Time dt, const Array &dw) const

Size size () const
returns the number of dimensions of the stochastic process
Size factors () const
returns the number of independent factors of the process
boost::shared_ptr< IborIndex > index () const

Leg cashFlows (Real amount=1.0) const

void setCovarParam (const boost::shared_ptr< LfmCovarianceParameterization > &param)

boost::shared_ptr< LfmCovarianceParameterization > covarParam () const

Size nextIndexReset (Time t) const

const std::vector< Time > & fixingTimes () const

const std::vector< Date > & fixingDates () const

const std::vector< Time > & accrualStartTimes () const

const std::vector< Time > & accrualEndTimes () const

std::vector< DiscountFactor > discountBond (const std::vector< Rate > &rates) const

Detailed Description

libor-forward-model process

stochastic process of a libor forward model using the rolling forward measure incl. predictor-corrector step

References:

Glasserman, Paul, 2004, Monte Carlo Methods in Financial Engineering, Springer, Section 3.7

Antoon Pelsser, 2000, Efficient Methods for Valuing Interest Rate Derivatives, Springer, 8

Hull, John, White, Alan, 1999, Forward Rate Volatilities, Swap Rate Volatilities and the Implementation of the Libor Market Model (<http://www.rotman.utoronto.ca/~amackay/fin/libormktmodel2.pdf>)

Tests

the correctness is tested by Monte-Carlo reproduction of caplet & ratchet NPVs and comparison with Black pricing.

Warning

this class does not work correctly with Visual C++ 6.

Member Function Documentation

Disposable<Matrix> covariance (Time t0, const Array & x0, Time dt) const [virtual]

returns the covariance $ V(mathrm{x}_{t_0 + Delta t} | mathrm{x}_{t_0} = mathrm{x}_0) $ of the process after a time interval $ Delta t $ according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

Reimplemented from StochasticProcess.

Disposable<Array> apply (const Array & x0, const Array & dx) const [virtual]

applies a change to the asset value. By default, it returns $ mathrm{x} + Delta mathrm{x} $.

Reimplemented from StochasticProcess.

Disposable<Array> evolve (Time t0, const Array & x0, Time dt, const Array & dw) const [virtual]

returns the asset value after a time interval $ Delta t $ according to the given discretization. By default, it returns [ E(mathrm{x}_0,t_0,Delta t) + S(mathrm{x}_0,t_0,Delta t) dot Delta mathrm{w} ] where $ E $ is the expectation and $ S $ the standard deviation.

Reimplemented from StochasticProcess.

Author

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