Public Member Functions | List of all members
LiborForwardModelProcess Class Reference
Stochastic processes

libor-forward-model process More...

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

Inheritance diagram for LiborForwardModelProcess:
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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. $ \sigma(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
 
- Public Member Functions inherited from StochasticProcess
virtual Disposable< Array > expectation (Time t0, const Array &x0, Time dt) const
 
virtual Disposable< Matrix > stdDeviation (Time t0, const Array &x0, Time dt) const
 
virtual Time time (const Date &) const
 
void update ()
 
- Public Member Functions inherited from Observer
 Observer (const Observer &)
 
Observer & operator= (const Observer &)
 
std::pair< std::set
< boost::shared_ptr
< Observable > >::iterator,
bool > 		registerWith (const boost::shared_ptr< Observable > &)
 
Size unregisterWith (const boost::shared_ptr< Observable > &)
 
void unregisterWithAll ()
 
- Public Member Functions inherited from Observable
 Observable (const Observable &)
 
Observable & operator= (const Observable &)
 
void notifyObservers ()
 

Additional Inherited Members

- Protected Member Functions inherited from StochasticProcess
 StochasticProcess (const boost::shared_ptr< discretization > &)
 
- Protected Attributes inherited from StochasticProcess
boost::shared_ptr< discretization > discretization_
 

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

\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]

where $ E $ is the expectation and $ S $ the standard deviation.

Reimplemented from StochasticProcess.

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