QuantLib
A free/open-source library for quantitative finance
Reference manual - version 1.5
Public Member Functions | Protected Member Functions | Friends | List of all members
MarkovFunctional Class Reference

#include <ql/experimental/models/markovfunctional.hpp>

+ Inheritance diagram for MarkovFunctional:

Public Member Functions

 MarkovFunctional (const Handle< YieldTermStructure > &termStructure, const Real reversion, const std::vector< Date > &volstepdates, const std::vector< Real > &volatilities, const Handle< SwaptionVolatilityStructure > &swaptionVol, const std::vector< Date > &swaptionExpiries, const std::vector< Period > &swaptionTenors, const boost::shared_ptr< SwapIndex > &swapIndexBase, const MarkovFunctional::ModelSettings &modelSettings=ModelSettings())
 
 MarkovFunctional (const Handle< YieldTermStructure > &termStructure, const Real reversion, const std::vector< Date > &volstepdates, const std::vector< Real > &volatilities, const Handle< OptionletVolatilityStructure > &capletVol, const std::vector< Date > &capletExpiries, const boost::shared_ptr< IborIndex > &iborIndex, const MarkovFunctional::ModelSettings &modelSettings=ModelSettings())
 
const ModelSettings & modelSettings () const
 
const ModelOutputs & modelOutputs () const
 
const DatenumeraireDate () const
 
const TimenumeraireTime () const
 
const Arrayvolatility () const
 
void calibrate (const std::vector< boost::shared_ptr< CalibrationHelper > > &helper, OptimizationMethod &method, const EndCriteria &endCriteria, const Constraint &constraint=Constraint(), const std::vector< Real > &weights=std::vector< Real >(), const std::vector< bool > &fixParameters=std::vector< bool >())
 Calibrate to a set of market instruments (caps/swaptions) More...
 
void update ()
 
- Public Member Functions inherited from Gaussian1dModel
const boost::shared_ptr
< StochasticProcess1D
stateProcess () const
 
const Real numeraire (const Time t, const Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >()) const
 
const Real zerobond (const Time T, const Time t=0.0, const Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >()) const
 
const Real numeraire (const Date &referenceDate, const Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >()) const
 
const Real zerobond (const Date &maturity, const Date &referenceDate=Null< Date >(), const Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >()) const
 
const Real zerobondOption (const Option::Type &type, const Date &expiry, const Date &valueDate, const Date &maturity, const Rate strike, const Date &referenceDate=Null< Date >(), const Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >(), const Real yStdDevs=7.0, const Size yGridPoints=64, const bool extrapolatePayoff=true, const bool flatPayoffExtrapolation=false) const
 
const Real forwardRate (const Date &fixing, const Date &referenceDate=Null< Date >(), const Real y=0.0, boost::shared_ptr< IborIndex > iborIdx=boost::shared_ptr< IborIndex >()) const
 
const Real swapRate (const Date &fixing, const Period &tenor, const Date &referenceDate=Null< Date >(), const Real y=0.0, boost::shared_ptr< SwapIndex > swapIdx=boost::shared_ptr< SwapIndex >()) const
 
const Real swapAnnuity (const Date &fixing, const Period &tenor, const Date &referenceDate=Null< Date >(), const Real y=0.0, boost::shared_ptr< SwapIndex > swapIdx=boost::shared_ptr< SwapIndex >()) const
 
const Disposable< ArrayyGrid (const Real yStdDevs, const int gridPoints, const Real T=1.0, const Real t=0, const Real y=0) const
 
- Public Member Functions inherited from TermStructureConsistentModel
 TermStructureConsistentModel (const Handle< YieldTermStructure > &termStructure)
 
const Handle
< YieldTermStructure > & 
termStructure () const
 
- Public Member Functions inherited from Observable
 Observable (const Observable &)
 
Observableoperator= (const Observable &)
 
void notifyObservers ()
 
- Public Member Functions inherited from LazyObject
void update ()
 
void recalculate ()
 
void freeze ()
 
void unfreeze ()
 
- Public Member Functions inherited from Observer
 Observer (const Observer &)
 
Observeroperator= (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 CalibratedModel
 CalibratedModel (Size nArguments)
 
void update ()
 
Real value (const Array &params, const std::vector< boost::shared_ptr< CalibrationHelper > > &)
 
const boost::shared_ptr
< Constraint > & 
constraint () const
 
EndCriteria::Type endCriteria ()
 returns end criteria result
 
Disposable< Arrayparams () const
 Returns array of arguments on which calibration is done.
 
virtual void setParams (const Array &params)
 

Protected Member Functions

const Real numeraireImpl (const Time t, const Real y, const Handle< YieldTermStructure > &yts) const
 
const Real zerobondImpl (const Time T, const Time t, const Real y, const Handle< YieldTermStructure > &yts) const
 
void generateArguments ()
 
void performCalculations () const
 
Disposable< std::vector< bool > > FixedFirstVolatility () const
 
- Protected Member Functions inherited from Gaussian1dModel
 Gaussian1dModel (const Handle< YieldTermStructure > &yieldTermStructure)
 
void generateArguments ()
 
boost::shared_ptr< VanillaSwapunderlyingSwap (const boost::shared_ptr< SwapIndex > &index, const Date &expiry, const Period &tenor) const
 
- Protected Member Functions inherited from LazyObject
virtual void calculate () const
 

Friends

class ZeroHelper
 

Additional Inherited Members

- Static Public Member Functions inherited from Gaussian1dModel
static const Real gaussianPolynomialIntegral (const Real a, const Real b, const Real c, const Real d, const Real e, const Real x0, const Real x1)
 
static const Real gaussianShiftedPolynomialIntegral (const Real a, const Real b, const Real c, const Real d, const Real e, const Real h, const Real x0, const Real x1)
 
- Protected Attributes inherited from Gaussian1dModel
boost::shared_ptr
< StochasticProcess1D
stateProcess_
 
Date evaluationDate_
 
bool enforcesTodaysHistoricFixings_
 
- Protected Attributes inherited from LazyObject
bool calculated_
 
bool frozen_
 
- Protected Attributes inherited from CalibratedModel
std::vector< Parameterarguments_
 
boost::shared_ptr< Constraintconstraint_
 
EndCriteria::Type shortRateEndCriteria_
 

Detailed Description

One factor Markov Functional model class. Some documentation is available here http://ssrn.com/abstract_id=2183721 http://quantlib.org/slides/qlws13/caspers.pdf

The model requires a suitable input smile which means it should be arbitrage free, smooth (at least implying a C^1 call price function) and with a call price function not decreasing too slow in strike direction.

A method for arbitrage free extra- and interpolation due to Kahale is provided and may be used to improve an input smile. Alternatively a SABR smile with arbitrage free wings can be fitted to the input smile to provide an appropriate input smile.

If you use the Kahale or SABR method for smile pretreatment then this implies zero density for negative underlying rates. This means that in this case the market yield term structure must imply positive underlying atm forward rates. In principle the mf model is able to produce negative rates. To make this work the smileSection provided as input must have an digitalOptionPrice (or an optionPrice) implementation that is consistent with such a yield term structure and the model setting lowerRateBound must be set appropriately as a lower limit for the underlying rates.

If you do not use a smile pretreatment you should ensure that the input smileSection is arbitrage free and that the input smileSection covers the strikes from lowerRateBound to upperRateBound.

During calibration a monocurve setup is assumed with the given yield term structure determining the rates throughout, no matter what curves are linked to the indices in the volatility term structures. The yield term structure should therefore be the main risk curve, i.e. the forwarding curve for the respective swaption or cap underlyings.

The model uses a simplified formula for the npv of a swaps floating leg namely $P(t,T_0)-P(t,T_1)$ with $T_0$ being the start date of the leg and $T_1$ being the last payment date, which is an approximation to the true npv.

The model calibrates to slightly modified market options in the sense that the start date is set equal to the fixing date, i.e. there is no delay. The model diagnostic outputs refer to this modified instrument. In general the actual market instrument including the delay is still matched very well though the calibration is done on a slightly different instrument.

AdjustYts and AdjustDigitals are experimental options. Specifying AdjustYts may have a negative impact on the volatility smile match, so it should be used with special care. For long term calibration it seems an interesting option though.

A bad fit to the initial yield term structure may be due to a non suitable input smile or accumulating numerical errors in very long term calibrations. The former point is adressed by smile pretreatment options. The latter point may be tackled by higher values for the numerical parameters possibly together with NTL high precision computing.

Member Function Documentation

void calibrate ( const std::vector< boost::shared_ptr< CalibrationHelper > > &  ,
OptimizationMethod method,
const EndCriteria endCriteria,
const Constraint constraint = Constraint(),
const std::vector< Real > &  weights = std::vector< Real >(),
const std::vector< bool > &  fixParameters = std::vector< bool >() 
)
virtual

Calibrate to a set of market instruments (caps/swaptions)

An additional constraint can be passed which must be satisfied in addition to the constraints of the model.

Reimplemented from CalibratedModel.

void update ( )
virtual

This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.

Implements Observer.

void performCalculations ( ) const
protectedvirtual

This method must implement any calculations which must be (re)done in order to calculate the desired results.

Reimplemented from Gaussian1dModel.