Class FdmZabrOp

Namespace

NanoQL.Experimental

Assembly

NanoQL.dll

The ZABR pricing operator on a mesher whose first direction is the forward F and second the volatility v: ½v²F^2β·∂²/∂F² + ½ν²v^2γ·∂²/∂v² + νρ|v|^γ+1F^β·∂²/∂F∂v; γ = 1 is SABR.

[Experimental("NQL0001")]
[WorkingType]
public sealed class FdmZabrOp : FdmLinearOpComposite

Inheritance

object

FdmLinearOp

FdmLinearOpComposite

FdmZabrOp

Inherited Members

FdmLinearOpComposite.ApplyMixed(Vector)

FdmLinearOpComposite.ApplyDirection(int, Vector)

FdmLinearOpComposite.SolveSplitting(int, Vector, double)

FdmLinearOpComposite.Preconditioner(Vector, double)

FdmLinearOpComposite.ToMatrix()

FdmLinearOp.Apply(Vector)

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

A working type: its bands are built at construction and never change, and the sum Apply(ReadOnlySpan<double>, Span<double>) forms is written through buffers it holds, so a step allocates nothing; not thread-safe. Experimental, as in QuantLib.

Constructors

FdmZabrOp(FdmMesher, double, double, double, double)

Initializes a new instance of the FdmZabrOp class.

public FdmZabrOp(FdmMesher mesher, double beta, double nu, double rho, double gamma = 1)

Parameters

mesher FdmMesher

The mesher: the forward, then the volatility.

beta double

β.

nu double

ν.

rho double

ρ.

gamma double

γ; 1 recovers the classic SABR model.

Exceptions

ArgumentNullException

mesher is null.

Properties

Size

Gets the number of directions.

public override int Size { get; }

Property Value

int

Methods

Apply(ReadOnlySpan<double>, Span<double>)

Applies the operator to r, writing the result into the caller's span.

public override void Apply(ReadOnlySpan<double> r, Span<double> result)

Parameters

r ReadOnlySpan<double>

The values, one per point.

result Span<double>

The result, of r's length; it mustn't overlap r.

ApplyDirection(int, ReadOnlySpan<double>, Span<double>)

Applies the operator's part in one direction, writing the result into the caller's span.

public override void ApplyDirection(int direction, ReadOnlySpan<double> r, Span<double> result)

Parameters

direction int

The direction.

r ReadOnlySpan<double>

The values, one per point.

result Span<double>

The result, of r's length.

Exceptions

ArgumentOutOfRangeException

direction is neither 0 nor 1.

ApplyMixed(ReadOnlySpan<double>, Span<double>)

Applies the operator's mixed part, writing the result into the caller's span.

public override void ApplyMixed(ReadOnlySpan<double> r, Span<double> result)

Parameters

r ReadOnlySpan<double>

The values, one per point.

result Span<double>

The result, of r's length.

Preconditioner(ReadOnlySpan<double>, double, Span<double>)

Applies the preconditioner of (1 + s·A), writing the result into the caller's span.

public override void Preconditioner(ReadOnlySpan<double> r, double s, Span<double> result)

Parameters

r ReadOnlySpan<double>

The values, one per point.

s double

The scale of the operator.

result Span<double>

The result, of r's length.

SetTime(double, double)

Sets the operator for the interval [t1, t2].

public override void SetTime(double t1, double t2)

Parameters

t1 double

The start time.

t2 double

The end time, not before t1.

SolveSplitting(int, ReadOnlySpan<double>, double, Span<double>)

Solves (1 + s·A_direction) x = r for x, writing it into the caller's span.

public override void SolveSplitting(int direction, ReadOnlySpan<double> r, double s, Span<double> result)

Parameters

direction int

The direction.

r ReadOnlySpan<double>

The right-hand side, one value per point.

s double

The scale of the direction's operator.

result Span<double>

The solution, of r's length.

Exceptions

ArgumentOutOfRangeException

direction is neither 0 nor 1.

ToMatrixDecomp()

The operator as sparse matrices, one per part.

public override ImmutableArray<SparseMatrix> ToMatrixDecomp()

Returns

ImmutableArray<SparseMatrix>

The matrices.

Exceptions

NanoQLException

The operator has no sparse representation.