Class FdmLocalVolFwdOp

Namespace

NanoQL.Methods

Assembly

NanoQL.dll

The local-volatility forward (Fokker-Planck) operator in the logarithm of the underlying, in one direction: the density's drift −(r − q − σ²/2) and half the local variance at each point, each on the columns of the first and second derivatives, over a time step.

[WorkingType]
public sealed class FdmLocalVolFwdOp : FdmLinearOpComposite

Inheritance

object

FdmLinearOp

FdmLinearOpComposite

FdmLocalVolFwdOp

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: SetTime(double, double) rewrites the operator's bands in place, through buffers it holds, by QuantLib's arithmetic in QuantLib's order, so a time step allocates nothing. The spot is QuantLib's constructor's argument, which QuantLib's operator doesn't read.

Its times run on the risk-free curve's day counter from the earliest reference date of its three structures, as Clock(GeneralizedBlackScholesProcess, FdmQuantoHelper?)'s, and each structure is read at the instants the step's times denote, on its own clock, where QuantLib reads them at the risk-free curve's times (the mismatched-dates class); structures that share the risk-free curve's times keep QuantLib's bits. A documented divergence.

Constructors

FdmLocalVolFwdOp(FdmMesher, double, YieldTermStructure, YieldTermStructure, LocalVolTermStructure, int)

Initializes a new instance of the FdmLocalVolFwdOp class.

public FdmLocalVolFwdOp(FdmMesher mesher, double spot, YieldTermStructure rTS, YieldTermStructure qTS, LocalVolTermStructure localVol, int direction = 0)

Parameters

mesher FdmMesher

The mesher.

spot double

The spot, which the operator doesn't read, as QuantLib's.

rTS YieldTermStructure

The risk-free curve.

qTS YieldTermStructure

The dividend curve.

localVol LocalVolTermStructure

The local volatility.

direction int

The direction of the underlying.

Exceptions

ArgumentNullException

An argument is null.

ArgumentOutOfRangeException

The direction isn't one of the layout's.

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.

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.

Exceptions

ArgumentException

t2 is before t1, or a curve can't be read.

NanoQLException

A curve or the local volatility can't be read.

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.

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.