- java.lang.Object
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- net.finmath.montecarlo.model.AbstractProcessModel
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- net.finmath.montecarlo.interestrate.models.HullWhiteModel
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- All Implemented Interfaces:
Serializable
,IndependentModelParameterProvider
,LIBORModel
,ShortRateModel
,TermStructureModel
,ProcessModel
public class HullWhiteModel extends AbstractProcessModel implements ShortRateModel, LIBORModel, Serializable
Implements a Hull-White model with time dependent mean reversion speed and time dependent short rate volatility.Model Dynamics
The Hull-While model assumes the following dynamic for the short rate: \[ d r(t) = ( \theta(t) - a(t) r(t) ) d t + \sigma(t) d W(t) \text{,} \quad r(t_{0}) = r_{0} \text{,} \] where the function \( \theta \) determines the calibration to the initial forward curve, \( a \) is the mean reversion and \( \sigma \) is the instantaneous volatility. The dynamic above is under the equivalent martingale measure corresponding to the numeraire \[ N(t) = \exp\left( \int_0^t r(\tau) \mathrm{d}\tau \right) \text{.} \] The main task of this class is to provide the risk-neutral drift and the volatility to the numerical scheme (given the volatility model), simulating \( r(t_{i}) \). The class then also provides and the corresponding numeraire and forward rates (LIBORs).Time Discrete Model
Assuming piecewise constant coefficients (mean reversion speed \( a \) and short rate volatility \( \sigma \) the class specifies the drift and factor loadings as piecewise constant functions for an Euler-scheme. The class provides the exact Euler step for the joint distribution of \( (r,N) \), where \( r \) denotes the short rate and \( N \) denotes the numeraire, following the scheme in ssrn.com/abstract=2737091. More specifically (assuming a constant mean reversion speed \( a \) for a moment), considering \[ \Delta \bar{r}(t_{i}) = \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} d r(t) \] we find from \[ \exp(-a t) \ \left( \mathrm{d} \left( \exp(a t) r(t) \right) \right) \ = \ a r(t) + \mathrm{d} r(t) \ = \ \theta(t) \mathrm{d}t + \sigma(t) \mathrm{d}W(t) \] that \[ \exp(a t_{i+1}) r(t_{i+1}) - \exp(a t_{i}) r(t_{i}) \ = \ \int_{t_{i}}^{t_{i+1}} \left[ \exp(a t) \theta(t) \mathrm{d}t + \exp(a t) \sigma(t) \mathrm{d}W(t) \right] \] that is \[ r(t_{i+1}) - r(t_{i}) \ = \ -(1-\exp(-a (t_{i+1}-t_{i})) r(t_{i}) + \int_{t_{i}}^{t_{i+1}} \left[ \exp(-a (t_{i+1}-t)) \theta(t) \mathrm{d}t + \exp(-a (t_{i+1}-t)) \sigma(t) \mathrm{d}W(t) \right] \] Assuming piecewise constant \( \sigma \) and \( \theta \), being constant over \( (t_{i},t_{i}+\Delta t_{i}) \), we thus find \[ r(t_{i+1}) - r(t_{i}) \ = \ \frac{1-\exp(-a \Delta t_{i})}{a \Delta t_{i}} \left( ( \theta(t_{i}) - a \bar{r}(t_{i})) \Delta t_{i} \right) + \sqrt{\frac{1-\exp(-2 a \Delta t_{i})}{2 a \Delta t_{i}}} \sigma(t_{i}) \Delta W(t_{i}) \] . In other words, the Euler scheme is exact if the mean reversion \( a \) is replaced by the effective mean reversion \( \frac{1-\exp(-a \Delta t_{i})}{a \Delta t_{i}} a \) and the volatility is replaced by the effective volatility \( \sqrt{\frac{1-\exp(-2 a \Delta t_{i})}{2 a \Delta t_{i}}} \sigma(t_{i}) \). In the calculations above the mean reversion speed is treated as a constants, but it is straight forward to see that the same holds for piecewise constant mean reversion speeds, replacing the expression \( a \ t \) by \( \int_{0}^t a(s) \mathrm{d}s \).Calibration
The drift of the short rate is calibrated to the given forward curve using \[ \theta(t) = \frac{\partial}{\partial T} f(0,t) + a(t) f(0,t) + \phi(t) \text{,} \] where the function \( f \) denotes the instantanenous forward rate and \( \phi(t) = \frac{1}{2} a \sigma^{2}(t) B(t)^{2} + \sigma^{2}(t) B(t) \frac{\partial}{\partial t} B(t) \) with \( B(t) = \frac{1-\exp(-a t)}{a} \).Volatility Model
The Hull-White model is essentially equivalent to LIBOR Market Model where the forward rate normal volatility \( \sigma(t,T) \) is given by \[ \sigma(t,T_{i}) \ = \ (1 + L_{i}(t) (T_{i+1}-T_{i})) \sigma(t) \exp(-a (T_{i}-t)) \frac{1-\exp(-a (T_{i+1}-T_{i}))}{a (T_{i+1}-T_{i})} \] (where \( \{ T_{i} \} \) is the forward rates tenor time discretization (note that this is the normal volatility, not the log-normal volatility) (see ssrn.com/abstract=2737091 for details on the derivation). Hence, we interpret both, short rate mean reversion speed and short rate volatility as part of the volatility model. The mean reversion speed and the short rate volatility have to be provided to this class via an object implementingShortRateVolatilityModel
. This implementation supports different method for the interpolation of the curves. The property"isInterpolateDiscountFactorsOnLiborPeriodDiscretization"
is a boolean. If true, the given curves are used only at the discretization points given byliborPeriodDiscretization
. This implies that the model reports only a limited set of risk factors in the methodsgetModelParameters()
.- Version:
- 1.4
- Author:
- Christian Fries
- See Also:
ShortRateVolatilityModel
, ssrn.com/abstract=2737091, Serialized Form
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Constructor Summary
Constructors Constructor Description HullWhiteModel(RandomVariableFactory abstractRandomVariableFactory, TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, ShortRateVolatilityModel volatilityModel, Map<String,Object> properties)
Creates a Hull-White model which implementsLIBORMarketModel
.HullWhiteModel(TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, ShortRateVolatilityModel volatilityModel, Map<String,Object> properties)
Creates a Hull-White model which implementsLIBORMarketModel
.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description RandomVariable
applyStateSpaceTransform(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)
Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.RandomVariable
applyStateSpaceTransformInverse(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)
Applies the inverse state space transform f-1i to the given random variable such that Xi → f-1i(Xi) =: Yi.AnalyticModel
getAnalyticModel()
Return the associated analytic model, a collection of market date object like discount curve, forward curve and volatility surfaces.LIBORModel
getCloneWithModifiedData(Map<String,Object> dataModified)
Create a new object implementing LIBORModel, using the new data.HullWhiteModel
getCloneWithModifiedVolatilityModel(ShortRateVolatilityModel volatilityModel)
Create a new object implementing ShortRateModel, using the new volatility model.DiscountCurve
getDiscountCurve()
Return the discount curve associated the forwards.RandomVariable[]
getDrift(MonteCarloProcess process, int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor)
This method has to be implemented to return the drift, i.e.RandomVariable[]
getFactorLoading(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable[] realizationAtTimeIndex)
This method has to be implemented to return the factor loadings, i.e.RandomVariable
getForwardDiscountBond(MonteCarloProcess process, double time, double maturity)
Returns the time \( t \) forward bond derived from the numeraire, i.e., \( P(T;t) = E( \frac{N(t)}{N(T)} \vert \mathcal{F}_{t} ) \).ForwardCurve
getForwardRateCurve()
Return the initial forward rate curve.RandomVariable[]
getInitialState(MonteCarloProcess process)
Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.RandomVariable
getIntegratedBondSquaredVolatility(double time, double maturity)
RandomVariable
getLIBOR(MonteCarloProcess process, double time, double periodStart, double periodEnd)
Returns the time \( t \) forward rate on the models forward curve.RandomVariable
getLIBOR(MonteCarloProcess process, int timeIndex, int liborIndex)
Return the forward rate at a given timeIndex and for a given liborIndex.double
getLiborPeriod(int timeIndex)
The period start corresponding to a given forward rate discretization index.TimeDiscretization
getLiborPeriodDiscretization()
The tenor time discretization of the forward rate curve.int
getLiborPeriodIndex(double time)
Same as java.util.Arrays.binarySearch(liborPeriodDiscretization,time).Map<String,RandomVariable>
getModelParameters()
Returns a map of independent model parameters of this model.int
getNumberOfComponents()
Returns the number of componentsint
getNumberOfFactors()
Return the number of factors.int
getNumberOfLibors()
Get the number of LIBORs in the LIBOR discretization.RandomVariable
getNumeraire(MonteCarloProcess process, double time)
Return the numeraire at a given time index.RandomVariable
getRandomVariableForConstant(double value)
Return a random variable initialized with a constant using the models random variable factory.LocalDateTime
getReferenceDate()
Returns the model's date corresponding to the time discretization's \( t = 0 \).RandomVariable
getShortRateConditionalVariance(double time, double maturity)
Calculates the variance \( \mathop{Var}(r(t) \vert r(s) ) \), that is \( \int_{s}^{t} \sigma^{2}(\tau) \exp(-2 \cdot \int_{\tau}^{t} a(u) \mathrm{d}u ) \ \mathrm{d}\tau \) where \( a \) is the meanReversion and \( \sigma \) is the short rate instantaneous volatility.ShortRateVolatilityModel
getVolatilityModel()
Return the volatility model.static HullWhiteModel
of(RandomVariableFactory abstractRandomVariableFactory, TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, ShortRateVolatilityModel volatilityModel, CalibrationProduct[] calibrationProducts, Map<String,Object> properties)
Creates a Hull-White model which implementsLIBORMarketModel
.String
toString()
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Methods inherited from class net.finmath.montecarlo.model.AbstractProcessModel
getInitialValue
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Constructor Detail
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HullWhiteModel
public HullWhiteModel(RandomVariableFactory abstractRandomVariableFactory, TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, ShortRateVolatilityModel volatilityModel, Map<String,Object> properties)
Creates a Hull-White model which implementsLIBORMarketModel
.- Parameters:
abstractRandomVariableFactory
- The factory to be used to construct random variables.liborPeriodDiscretization
- The forward rate discretization to be used in thegetLIBOR
method.analyticModel
- The analytic model to be used (currently not used, may be null).forwardRateCurve
- The forward curve to be used (currently not used, - the model uses disocuntCurve only.discountCurve
- The disocuntCurve (currently also used to determine the forward curve).volatilityModel
- The volatility model specifying mean reversion and instantaneous volatility of the short rate.properties
- A map specifying model properties.
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HullWhiteModel
public HullWhiteModel(TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, ShortRateVolatilityModel volatilityModel, Map<String,Object> properties)
Creates a Hull-White model which implementsLIBORMarketModel
.- Parameters:
liborPeriodDiscretization
- The forward rate discretization to be used in thegetLIBOR
method.analyticModel
- The analytic model to be used (currently not used, may be null).forwardRateCurve
- The forward curve to be used (currently not used, - the model uses disocuntCurve only.discountCurve
- The disocuntCurve (currently also used to determine the forward curve).volatilityModel
- The volatility model specifying mean reversion and instantaneous volatility of the short rate.properties
- A map specifying model properties (currently not used, may be null).
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Method Detail
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of
public static HullWhiteModel of(RandomVariableFactory abstractRandomVariableFactory, TimeDiscretization liborPeriodDiscretization, AnalyticModel analyticModel, ForwardCurve forwardRateCurve, DiscountCurve discountCurve, ShortRateVolatilityModel volatilityModel, CalibrationProduct[] calibrationProducts, Map<String,Object> properties) throws CalculationException
Creates a Hull-White model which implementsLIBORMarketModel
.- Parameters:
abstractRandomVariableFactory
- The randomVariableFactoryliborPeriodDiscretization
- The forward rate discretization to be used in thegetLIBOR
method.analyticModel
- The analytic model to be used (currently not used, may be null).forwardRateCurve
- The forward curve to be used (currently not used, - the model uses disocuntCurve only.discountCurve
- The disocuntCurve (currently also used to determine the forward curve).volatilityModel
- The volatility model specifying mean reversion and instantaneous volatility of the short rate.calibrationProducts
- The products to be used for calibrationproperties
- The calibration properties- Returns:
- A (possibly calibrated) Hull White model.
- Throws:
CalculationException
- Thrown if calibration fails.
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getReferenceDate
public LocalDateTime getReferenceDate()
Description copied from interface:ProcessModel
Returns the model's date corresponding to the time discretization's \( t = 0 \). Note: Currently not all models provide a reference date. This will change in future versions.- Specified by:
getReferenceDate
in interfaceProcessModel
- Overrides:
getReferenceDate
in classAbstractProcessModel
- Returns:
- The model's date corresponding to the time discretization's \( t = 0 \).
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getNumberOfComponents
public int getNumberOfComponents()
Description copied from interface:ProcessModel
Returns the number of components- Specified by:
getNumberOfComponents
in interfaceProcessModel
- Returns:
- The number of components
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getNumberOfFactors
public int getNumberOfFactors()
Description copied from interface:ShortRateModel
Return the number of factors.- Specified by:
getNumberOfFactors
in interfaceProcessModel
- Specified by:
getNumberOfFactors
in interfaceShortRateModel
- Returns:
- The number of factors.
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applyStateSpaceTransform
public RandomVariable applyStateSpaceTransform(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)
Description copied from interface:ProcessModel
Applies the state space transform fi to the given state random variable such that Yi → fi(Yi) =: Xi.- Specified by:
applyStateSpaceTransform
in interfaceProcessModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.timeIndex
- The time index (related to the model times discretization).componentIndex
- The component index i.randomVariable
- The state random variable Yi.- Returns:
- New random variable holding the result of the state space transformation.
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applyStateSpaceTransformInverse
public RandomVariable applyStateSpaceTransformInverse(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable randomVariable)
Description copied from interface:ProcessModel
Applies the inverse state space transform f-1i to the given random variable such that Xi → f-1i(Xi) =: Yi.- Specified by:
applyStateSpaceTransformInverse
in interfaceProcessModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.timeIndex
- The time index (related to the model times discretization).componentIndex
- The component index i.randomVariable
- The state random variable Xi.- Returns:
- New random variable holding the result of the state space transformation.
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getInitialState
public RandomVariable[] getInitialState(MonteCarloProcess process)
Description copied from interface:ProcessModel
Returns the initial value of the state variable of the process Y, not to be confused with the initial value of the model X (which is the state space transform applied to this state value.- Specified by:
getInitialState
in interfaceProcessModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.- Returns:
- The initial value of the state variable of the process Y(t=0).
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getNumeraire
public RandomVariable getNumeraire(MonteCarloProcess process, double time) throws CalculationException
Description copied from interface:ProcessModel
Return the numeraire at a given time index. Note: The random variable returned is a defensive copy and may be modified.- Specified by:
getNumeraire
in interfaceProcessModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.time
- The time t for which the numeraire N(t) should be returned.- Returns:
- The numeraire at the specified time as
RandomVariable
- Throws:
CalculationException
- Thrown if the valuation fails, specific cause may be available via thecause()
method.
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getForwardDiscountBond
public RandomVariable getForwardDiscountBond(MonteCarloProcess process, double time, double maturity) throws CalculationException
Description copied from interface:TermStructureModel
Returns the time \( t \) forward bond derived from the numeraire, i.e., \( P(T;t) = E( \frac{N(t)}{N(T)} \vert \mathcal{F}_{t} ) \). Note: It is guaranteed that the random variabble returned by this method is \( \mathcal{F}_{t} ) \)-measurable.- Specified by:
getForwardDiscountBond
in interfaceTermStructureModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.time
- The evaluation time.maturity
- The maturity.- Returns:
- The forward bond P(T;t).
- Throws:
CalculationException
- Thrown if model fails to calculate the random variable.
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getDrift
public RandomVariable[] getDrift(MonteCarloProcess process, int timeIndex, RandomVariable[] realizationAtTimeIndex, RandomVariable[] realizationPredictor)
Description copied from interface:ProcessModel
This method has to be implemented to return the drift, i.e. the coefficient vector
μ = (μ1, ..., μn) such that X = f(Y) and
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm
in an m-factor model. Here j denotes index of the component of the resulting process. Since the model is provided only on a time discretization, the method may also (should try to) return the drift as \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \).- Specified by:
getDrift
in interfaceProcessModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.timeIndex
- The time index (related to the model times discretization).realizationAtTimeIndex
- The given realization at timeIndexrealizationPredictor
- The given realization attimeIndex+1
or null if no predictor is available.- Returns:
- The drift or average drift from timeIndex to timeIndex+1, i.e. \( \frac{1}{t_{i+1}-t_{i}} \int_{t_{i}}^{t_{i+1}} \mu(\tau) \mathrm{d}\tau \) (or a suitable approximation).
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getFactorLoading
public RandomVariable[] getFactorLoading(MonteCarloProcess process, int timeIndex, int componentIndex, RandomVariable[] realizationAtTimeIndex)
Description copied from interface:ProcessModel
This method has to be implemented to return the factor loadings, i.e. the coefficient vector
λj = (λ1,j, ..., λm,j) such that X = f(Y) and
dYj = μj dt + λ1,j dW1 + ... + λm,j dWm
in an m-factor model. Here j denotes index of the component of the resulting process.- Specified by:
getFactorLoading
in interfaceProcessModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.timeIndex
- The time index (related to the model times discretization).componentIndex
- The index j of the driven component.realizationAtTimeIndex
- The realization of X at the time corresponding to timeIndex (in order to implement local and stochastic volatlity models).- Returns:
- The factor loading for given factor and component.
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getRandomVariableForConstant
public RandomVariable getRandomVariableForConstant(double value)
Description copied from interface:ProcessModel
Return a random variable initialized with a constant using the models random variable factory.- Specified by:
getRandomVariableForConstant
in interfaceProcessModel
- Parameters:
value
- The constant value.- Returns:
- A new random variable initialized with a constant value.
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getLIBOR
public RandomVariable getLIBOR(MonteCarloProcess process, double time, double periodStart, double periodEnd) throws CalculationException
Description copied from interface:TermStructureModel
Returns the time \( t \) forward rate on the models forward curve. Note: It is guaranteed that the random variable returned by this method is \( \mathcal{F}_{t} ) \)-measurable.- Specified by:
getLIBOR
in interfaceTermStructureModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.time
- The evaluation time.periodStart
- The period start of the forward rate.periodEnd
- The period end of the forward rate.- Returns:
- The forward rate.
- Throws:
CalculationException
- Thrown if model fails to calculate the random variable.
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getLIBOR
public RandomVariable getLIBOR(MonteCarloProcess process, int timeIndex, int liborIndex) throws CalculationException
Description copied from interface:LIBORModel
Return the forward rate at a given timeIndex and for a given liborIndex.- Specified by:
getLIBOR
in interfaceLIBORModel
- Parameters:
process
- The discretization process generating this model. The process provides call backs for TimeDiscretization and allows calls to getProcessValue for timeIndices less or equal the given one.timeIndex
- The time index (associated withProcess.getTimeDiscretization()
.liborIndex
- The forward rate index (associated withLIBORModel.getLiborPeriodDiscretization()
.- Returns:
- The forward rate.
- Throws:
CalculationException
- Thrown if calculation failed.
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getLiborPeriodDiscretization
public TimeDiscretization getLiborPeriodDiscretization()
Description copied from interface:LIBORModel
The tenor time discretization of the forward rate curve.- Specified by:
getLiborPeriodDiscretization
in interfaceLIBORModel
- Returns:
- The tenor time discretization of the forward rate curve.
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getNumberOfLibors
public int getNumberOfLibors()
Description copied from interface:LIBORModel
Get the number of LIBORs in the LIBOR discretization.- Specified by:
getNumberOfLibors
in interfaceLIBORModel
- Returns:
- The number of LIBORs in the LIBOR discretization
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getLiborPeriod
public double getLiborPeriod(int timeIndex)
Description copied from interface:LIBORModel
The period start corresponding to a given forward rate discretization index.- Specified by:
getLiborPeriod
in interfaceLIBORModel
- Parameters:
timeIndex
- The index corresponding to a given time (interpretation is start of period)- Returns:
- The period start corresponding to a given forward rate discretization index.
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getLiborPeriodIndex
public int getLiborPeriodIndex(double time)
Description copied from interface:LIBORModel
Same as java.util.Arrays.binarySearch(liborPeriodDiscretization,time). Will return a negative value if the time is not found, but then -index-1 corresponds to the index of the smallest time greater than the given one.- Specified by:
getLiborPeriodIndex
in interfaceLIBORModel
- Parameters:
time
- The period start.- Returns:
- The index corresponding to a given time (interpretation is start of period)
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getAnalyticModel
public AnalyticModel getAnalyticModel()
Description copied from interface:TermStructureModel
Return the associated analytic model, a collection of market date object like discount curve, forward curve and volatility surfaces.- Specified by:
getAnalyticModel
in interfaceTermStructureModel
- Returns:
- The associated analytic model.
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getDiscountCurve
public DiscountCurve getDiscountCurve()
Description copied from interface:TermStructureModel
Return the discount curve associated the forwards.- Specified by:
getDiscountCurve
in interfaceTermStructureModel
- Returns:
- the discount curve associated the forwards.
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getForwardRateCurve
public ForwardCurve getForwardRateCurve()
Description copied from interface:TermStructureModel
Return the initial forward rate curve.- Specified by:
getForwardRateCurve
in interfaceTermStructureModel
- Returns:
- the forward rate curve
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getCloneWithModifiedData
public LIBORModel getCloneWithModifiedData(Map<String,Object> dataModified)
Description copied from interface:LIBORModel
Create a new object implementing LIBORModel, using the new data.- Specified by:
getCloneWithModifiedData
in interfaceLIBORModel
- Specified by:
getCloneWithModifiedData
in interfaceProcessModel
- Specified by:
getCloneWithModifiedData
in interfaceTermStructureModel
- Parameters:
dataModified
- A map with values to be used in constructions (keys are identical to parameter names of the constructors).- Returns:
- A new object implementing LIBORModel, using the new data.
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getShortRateConditionalVariance
public RandomVariable getShortRateConditionalVariance(double time, double maturity)
Calculates the variance \( \mathop{Var}(r(t) \vert r(s) ) \), that is \( \int_{s}^{t} \sigma^{2}(\tau) \exp(-2 \cdot \int_{\tau}^{t} a(u) \mathrm{d}u ) \ \mathrm{d}\tau \) where \( a \) is the meanReversion and \( \sigma \) is the short rate instantaneous volatility.- Parameters:
time
- The parameter s in \( \int_{s}^{t} \sigma^{2}(\tau) \exp(-2 \cdot \int_{\tau}^{t} a(u) \mathrm{d}u ) \ \mathrm{d}\tau \)maturity
- The parameter t in \( \int_{s}^{t} \sigma^{2}(\tau) \exp(-2 \cdot \int_{\tau}^{t} a(u) \mathrm{d}u ) \ \mathrm{d}\tau \)- Returns:
- The conditional variance of the short rate, \( \mathop{Var}(r(t) \vert r(s) ) \).
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getIntegratedBondSquaredVolatility
public RandomVariable getIntegratedBondSquaredVolatility(double time, double maturity)
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getCloneWithModifiedVolatilityModel
public HullWhiteModel getCloneWithModifiedVolatilityModel(ShortRateVolatilityModel volatilityModel)
Description copied from interface:ShortRateModel
Create a new object implementing ShortRateModel, using the new volatility model.- Specified by:
getCloneWithModifiedVolatilityModel
in interfaceShortRateModel
- Parameters:
volatilityModel
- The new volatility model.- Returns:
- A new object implementing ShortRateModel, using the new volatility model.
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getVolatilityModel
public ShortRateVolatilityModel getVolatilityModel()
Description copied from interface:ShortRateModel
Return the volatility model.- Specified by:
getVolatilityModel
in interfaceShortRateModel
- Returns:
- The volatility model.
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getModelParameters
public Map<String,RandomVariable> getModelParameters()
Description copied from interface:IndependentModelParameterProvider
Returns a map of independent model parameters of this model.- Specified by:
getModelParameters
in interfaceIndependentModelParameterProvider
- Returns:
- Map of independent model parameters of this model.
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