libor-forward-model process More...

#include <lfmprocess.hpp>

Inheritance diagram for LiborForwardModelProcess:

Collaboration diagram for LiborForwardModelProcess:

Public Member Functions
	LiborForwardModelProcess (Size size, ext::shared_ptr< IborIndex > index)

Array	initialValues () const override
	returns the initial values of the state variables More...

Array	drift (Time t, const Array &x) const override
	returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \) More...

Matrix	diffusion (Time t, const Array &x) const override
	returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \) More...

Matrix	covariance (Time t0, const Array &x0, Time dt) const override

Array	apply (const Array &x0, const Array &dx) const override

Array	evolve (Time t0, const Array &x0, Time dt, const Array &dw) const override

Size	size () const override
	returns the number of dimensions of the stochastic process More...

Size	factors () const override
	returns the number of independent factors of the process More...

ext::shared_ptr< IborIndex >	index () const

Leg	cashFlows (Real amount=1.0) const

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

ext::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
	~StochasticProcess () override=default

virtual Array	expectation (Time t0, const Array &x0, Time dt) const

virtual Matrix	stdDeviation (Time t0, const Array &x0, Time dt) const

virtual Time	time (const Date &) const

void	update () override

Public Member Functions inherited from Observer
	Observer ()=default

	Observer (const Observer &)

Observer &	operator= (const Observer &)

virtual	~Observer ()

std::pair< iterator, bool >	registerWith (const ext::shared_ptr< Observable > &)

void	registerWithObservables (const ext::shared_ptr< Observer > &)

Size	unregisterWith (const ext::shared_ptr< Observable > &)

void	unregisterWithAll ()

virtual void	update ()=0

virtual void	deepUpdate ()

Public Member Functions inherited from Observable
	Observable ()

	Observable (const Observable &)

Observable &	operator= (const Observable &)

	Observable (Observable &&)=delete

Observable &	operator= (Observable &&)=delete

virtual	~Observable ()=default

void	notifyObservers ()

Private Attributes
Size	size_

const ext::shared_ptr< IborIndex >	index_

ext::shared_ptr< LfmCovarianceParameterization >	lfmParam_

Array	initialValues_

std::vector< Time >	fixingTimes_

std::vector< Date >	fixingDates_

std::vector< Time >	accrualStartTimes_

std::vector< Time >	accrualEndTimes_

std::vector< Time >	accrualPeriod_

Array	m1

Array	m2

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator

Protected Member Functions inherited from StochasticProcess
	StochasticProcess ()=default

	StochasticProcess (ext::shared_ptr< discretization >)

Protected Attributes inherited from StochasticProcess
ext::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.

Definition at line 58 of file lfmprocess.hpp.

Constructor & Destructor Documentation

◆ LiborForwardModelProcess()

LiborForwardModelProcess	(	Size	size,
		ext::shared_ptr< IborIndex >	index
	)

Definition at line 33 of file lfmprocess.cpp.

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Member Function Documentation

◆ initialValues()

Array initialValues ( ) const

overridevirtual

returns the initial values of the state variables

Implements StochasticProcess.

Definition at line 147 of file lfmprocess.cpp.

◆ drift()

Array drift	(	Time	t,
		const Array &	x
	)		const

overridevirtual

returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)

Implements StochasticProcess.

Definition at line 68 of file lfmprocess.cpp.

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◆ diffusion()

Matrix diffusion	(	Time	t,
		const Array &	x
	)		const

overridevirtual

returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)

Implements StochasticProcess.

Definition at line 85 of file lfmprocess.cpp.

◆ covariance()

Matrix covariance	(	Time	t0,
		const Array &	x0,
		Time	dt
	)		const

overridevirtual

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.

Definition at line 89 of file lfmprocess.cpp.

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◆ apply()

Array apply	(	const Array &	x0,
		const Array &	dx
	)		const

overridevirtual

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

Reimplemented from StochasticProcess.

Definition at line 93 of file lfmprocess.cpp.

◆ evolve()

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

overridevirtual

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.

Definition at line 103 of file lfmprocess.cpp.

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◆ size()

Size size ( ) const

overridevirtual

returns the number of dimensions of the stochastic process

Implements StochasticProcess.

Definition at line 183 of file lfmprocess.cpp.

◆ factors()

Size factors ( ) const

overridevirtual

returns the number of independent factors of the process

Reimplemented from StochasticProcess.

Definition at line 187 of file lfmprocess.cpp.

◆ index()

ext::shared_ptr< IborIndex > index ( ) const

Definition at line 162 of file lfmprocess.cpp.

◆ cashFlows()

Leg cashFlows ( Real amount = 1.0 ) const

Definition at line 167 of file lfmprocess.cpp.

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◆ setCovarParam()

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

Definition at line 151 of file lfmprocess.cpp.

◆ covarParam()

ext::shared_ptr< LfmCovarianceParameterization > covarParam ( ) const

Definition at line 157 of file lfmprocess.cpp.

◆ nextIndexReset()

Size nextIndexReset ( Time t ) const

Definition at line 209 of file lfmprocess.cpp.

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◆ fixingTimes()

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

Definition at line 191 of file lfmprocess.cpp.

◆ fixingDates()

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

Definition at line 195 of file lfmprocess.cpp.

◆ accrualStartTimes()

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

Definition at line 200 of file lfmprocess.cpp.

◆ accrualEndTimes()

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

Definition at line 205 of file lfmprocess.cpp.

◆ discountBond()

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

Definition at line 214 of file lfmprocess.cpp.

Member Data Documentation

◆ size_

Size size_

private

Definition at line 93 of file lfmprocess.hpp.

◆ index_

const ext::shared_ptr<IborIndex> index_

private

Definition at line 95 of file lfmprocess.hpp.

◆ lfmParam_

ext::shared_ptr<LfmCovarianceParameterization> lfmParam_

private

Definition at line 96 of file lfmprocess.hpp.

◆ initialValues_

Array initialValues_

private

Definition at line 98 of file lfmprocess.hpp.

◆ fixingTimes_

std::vector<Time> fixingTimes_

private

Definition at line 100 of file lfmprocess.hpp.

◆ fixingDates_

std::vector<Date> fixingDates_

private

Definition at line 101 of file lfmprocess.hpp.

◆ accrualStartTimes_

std::vector<Time> accrualStartTimes_

private

Definition at line 102 of file lfmprocess.hpp.

◆ accrualEndTimes_

std::vector<Time> accrualEndTimes_

private

Definition at line 103 of file lfmprocess.hpp.

◆ accrualPeriod_

std::vector<Time> accrualPeriod_

private

Definition at line 104 of file lfmprocess.hpp.

◆ m1

Array m1

mutableprivate

Definition at line 106 of file lfmprocess.hpp.

◆ m2

Array m2

private

Definition at line 106 of file lfmprocess.hpp.

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ LiborForwardModelProcess()

Member Function Documentation

◆ initialValues()

◆ drift()

◆ diffusion()

◆ covariance()

◆ apply()

◆ evolve()

◆ size()

◆ factors()

◆ index()

◆ cashFlows()

◆ setCovarParam()

◆ covarParam()

◆ nextIndexReset()

◆ fixingTimes()

◆ fixingDates()

◆ accrualStartTimes()

◆ accrualEndTimes()

◆ discountBond()

Member Data Documentation

◆ size_

◆ index_

◆ lfmParam_

◆ initialValues_

◆ fixingTimes_

◆ fixingDates_

◆ accrualStartTimes_

◆ accrualEndTimes_

◆ accrualPeriod_

◆ m1

◆ m2