MarkovFunctional Class Reference

`#include <ql/models/shortrate/onefactormodels/markovfunctional.hpp>`

Inheritance diagram for MarkovFunctional:
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## Public Member Functions

MarkovFunctional (const Handle< YieldTermStructure > &termStructure, 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 ext::shared_ptr< SwapIndex > &swapIndexBase, const MarkovFunctional::ModelSettings &modelSettings=ModelSettings())

| MarkovFunctional (const Handle< YieldTermStructure > &termStructure, Real reversion, const std::vector< Date > &volstepdates, const std::vector< Real > &volatilities, const Handle< OptionletVolatilityStructure > &capletVol, const std::vector< Date > &capletExpiries, const ext::shared_ptr< IborIndex > &iborIndex, const MarkovFunctional::ModelSettings &modelSettings=ModelSettings())
const ModelSettings & | modelSettings () const
const ModelOutputs & | modelOutputs () const
const Date & | numeraireDate () const
const Time & | numeraireTime () const
const Array & | volatility () const
void | calibrate (const std::vector< ext::shared_ptr< CalibrationHelper > > &helpers, 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 (usually caps/swaptions) More...
void | calibrate (const std::vector< ext::shared_ptr< BlackCalibrationHelper > > &helpers, 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 >())
void | update ()
std::vector< std::pair< Size, Size > > | arbitrageIndices () const
void | forceArbitrageIndices (const std::vector< std::pair< Size, Size > > &indices)
Public Member Functions inherited from Gaussian1dModel
ext::shared_ptr< StochasticProcess1D > | stateProcess () const
Real | numeraire (Time t, Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >()) const
Real | zerobond (Time T, Time t=0.0, Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >()) const
Real | numeraire (const Date &referenceDate, Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >()) const
Real | zerobond (const Date &maturity, const Date &referenceDate=Null< Date >(), Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >()) const
Real | zerobondOption (const Option::Type &type, const Date &expiry, const Date &valueDate, const Date &maturity, Rate strike, const Date &referenceDate=Null< Date >(), Real y=0.0, const Handle< YieldTermStructure > &yts=Handle< YieldTermStructure >(), Real yStdDevs=7.0, Size yGridPoints=64, bool extrapolatePayoff=true, bool flatPayoffExtrapolation=false) const
Real | forwardRate (const Date &fixing, const Date &referenceDate=Null< Date >(), Real y=0.0, const ext::shared_ptr< IborIndex > &iborIdx=ext::shared_ptr< IborIndex >()) const
Real | swapRate (const Date &fixing, const Period &tenor, const Date &referenceDate=Null< Date >(), Real y=0.0, const ext::shared_ptr< SwapIndex > &swapIdx=ext::shared_ptr< SwapIndex >()) const
Real | swapAnnuity (const Date &fixing, const Period &tenor, const Date &referenceDate=Null< Date >(), Real y=0.0, const ext::shared_ptr< SwapIndex > &swapIdx=ext::shared_ptr< SwapIndex >()) const
Disposable< Array > | yGrid (Real yStdDevs, int gridPoints, Real T=1.0, Real t=0, 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 &)
Observable & | operator= (const Observable &)
void | notifyObservers ()
Public Member Functions inherited from LazyObject
void | update ()
void | recalculate ()
void | freeze ()
void | unfreeze ()
void | alwaysForwardNotifications ()
Public Member Functions inherited from Observer
| Observer (const Observer &)
Observer & | operator= (const 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 | deepUpdate ()
Public Member Functions inherited from CalibratedModel
| CalibratedModel (Size nArguments)
Real | value (const Array &params, const std::vector< ext::shared_ptr< CalibrationHelper > > &)
QL_DEPRECATED Real | value (const Array &params, const std::vector< ext::shared_ptr< BlackCalibrationHelper > > &)
const ext::shared_ptr< Constraint > & | constraint () const
EndCriteria::Type | endCriteria () const
| Returns end criteria result.
const Array & | problemValues () const
| Returns the problem values.
Disposable< Array > | params () const
| Returns array of arguments on which calibration is done.
virtual void | setParams (const Array &params)
Integer | functionEvaluation () const

## Protected Member Functions

Real | numeraireImpl (Time t, Real y, const Handle< YieldTermStructure > &yts) const
Real | zerobondImpl (Time T, Time t, 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 ()
ext::shared_ptr< VanillaSwap > | underlyingSwap (const ext::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

Public Types inherited from Observer
typedef boost::unordered_set< ext::shared_ptr< Observable > > | set_type
typedef set_type::iterator | iterator
Static Public Member Functions inherited from Gaussian1dModel
static Real | gaussianPolynomialIntegral (Real a, Real b, Real c, Real d, Real e, Real x0, Real x1)
static Real | gaussianShiftedPolynomialIntegral (Real a, Real b, Real c, Real d, Real e, Real h, Real x0, Real x1)
Protected Attributes inherited from Gaussian1dModel
ext::shared_ptr< StochasticProcess1D > | stateProcess_
Date | evaluationDate_
bool | enforcesTodaysHistoricFixings_
Protected Attributes inherited from LazyObject
bool | calculated_
bool | frozen_
bool | alwaysForward_
Protected Attributes inherited from CalibratedModel
std::vector< Parameter > | arguments_
ext::shared_ptr< Constraint > | constraint_
EndCriteria::Type | shortRateEndCriteria_
Array | problemValues_
Integer | functionEvaluation_

## 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 underlying rates below minus the displacement parameter. This means that in this case the market yield term structure must imply underlying atm forward rates greater than minus displacement.

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.

When using a shifted lognormal smile input the lower rate bound is adjusted by the shift so that a lower bound of 0.0 always corresponds to the lower bound of the shifted distribution.

If a custom smile is used, this will take full responsibility of inverting digital prices to market rates, so digitalGap, marketRateAccuracy, lowerRateBound, upperRateBound are irrelavant and the smile moneyness checkpoints are only used for the debug model output in this setup.

## Member Function Documentation

## calibrate() [1/2]

void calibrate | ( | const std::vector< ext::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 (usually caps/swaptions)

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

Reimplemented from CalibratedModel.

## calibrate() [2/2]

void calibrate | ( | const std::vector< ext::shared_ptr< BlackCalibrationHelper > > & | ,
|  | 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

Deprecated:
  Use the other overload. Deprecated in version 1.18.

Reimplemented from CalibratedModel.

## update()

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.

Reimplemented from CalibratedModel.

## performCalculations()

void performCalculations | ( |  | ) | const

protected virtual

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

Reimplemented from Gaussian1dModel.