LiborForwardModelProcess Class Reference

### A free/open-source library for quantitative finance

Public Member Functions
LiborForwardModelProcess Class Reference
Stochastic processes

libor-forward-model process More...

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

Inheritance diagram for LiborForwardModelProcess:
[legend]

List of all members.

## 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.,
Disposable< Matrix > | diffusion (Time t, const Array &x) const
| returns the diffusion part of the equation, i.e.
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 of the process after a time interval 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 .

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 according to the given discretization. By default, it returns

where is the expectation and the standard deviation.

Reimplemented from StochasticProcess.