Class CoxIngersollRoss
The Cox-Ingersoll-Ross model: dr(t) = k(θ − r(t))dt + σ√r(t) dW(t).
public class CoxIngersollRoss : OneFactorAffineModel, ICalibratedModel, IAffineModel- Inheritance
-
CoxIngersollRoss
- Implements
- Derived
- Inherited Members
- Extension Methods
Remarks
Its arguments are θ, k, σ and r₀, in that order, each a constant parameter, positive. QuantLib's header warns that the class "was not tested enough to guarantee its functionality". Its dynamics simulate the short rate directly, on CoxIngersollRossProcess's quadratic-exponential scheme.
The Feller constraint (K1): with it, the model's parameters satisfy σ² < 2kθ at each vector's own k and θ,
through ParametersConstraint(), and σ's own constraint is positivity: a divergence,
QuantLib's testing σ against the constructor's k and θ (coxingersollross.cpp:24-37), so a calibration can
leave the Feller region and σ stops at a bound the constructor set (Divergences/CirFellerConstraintTests.cs).
The constructor refuses a σ outside it with QuantLib's text.
The tree (K2): on QuantLib's dynamics before its 1.23, the square root y = √r of the short rate, of constant
volatility σ/2, Euler-discretized, the short rate y², which the trinomial tree's state-independent variance fits:
a divergence, QuantLib's tree reading CoxIngersollRossProcess, whose variance depends on the state,
at its initial value, so that its prices stall away from its own analytic ones
(Divergences/CirTreeConvergenceTests.cs).
An extension point, as in QuantLib: the extended Cox-Ingersoll-Ross model derives from it.
Constructors
CoxIngersollRoss(double, double, double, double, bool)
Initializes a new instance of the CoxIngersollRoss class.
public CoxIngersollRoss(double r0 = 0.05, double theta = 0.1, double k = 0.1, double sigma = 0.1, bool withFellerConstraint = true)Parameters
r0doubleThe initial short rate, positive.
thetadoubleThe level θ, positive.
kdoubleThe speed k, positive.
sigmadoubleThe volatility σ, positive, and with the Feller constraint below √(2kθ).
withFellerConstraintboolWhether the parameters satisfy the Feller condition σ² < 2kθ.
Exceptions
- ArgumentException
A parameter is outside its constraint.
Properties
K
Gets the speed k.
protected double K { get; }Property Value
Sigma
Gets the volatility σ.
protected double Sigma { get; }Property Value
Theta
Gets the level θ.
protected double Theta { get; }Property Value
X0
Gets the initial short rate.
protected double X0 { get; }Property Value
Methods
A(double, double)
The affine discount bond's A(t, T).
protected override double A(double t, double T)Parameters
Returns
- double
A(t, T).
B(double, double)
The affine discount bond's B(t, T).
protected override double B(double t, double T)Parameters
Returns
- double
B(t, T).
DiscountBondOption(OptionType, double, double, double)
The price of an option on a discount bond, by the non-central χ² distribution.
public override double DiscountBondOption(OptionType type, double strike, double maturity, double bondMaturity)Parameters
typeOptionTypeThe option's type.
strikedoubleThe strike, positive.
maturitydoubleThe option's maturity.
bondMaturitydoubleThe bond's maturity.
Returns
- double
The price.
Exceptions
- ArgumentException
strikeisn't positive.- ArgumentOutOfRangeException
typeisn't a member of its type.
Dynamics()
The model's short-rate dynamics: the short rate itself, a CoxIngersollRossProcess.
public override OneFactorModelShortRateDynamics Dynamics()Returns
- OneFactorModelShortRateDynamics
A new dynamics object.
ParametersConstraint()
The Feller condition σ² < 2kθ at the vector's own k and θ, when the model was built with it.
protected override Constraint? ParametersConstraint()Returns
- Constraint
The constraint, or null without the Feller constraint.
Tree(TimeGrid)
Builds the model's trinomial tree on a time grid, on the square root of the short rate.
public override Lattice Tree(TimeGrid grid)Parameters
gridTimeGridThe time grid.
Returns
- Lattice
The tree, an unfitted OneFactorModelShortRateTree.
Exceptions
- ArgumentNullException
gridis null.