Class LsmBasisSystem

Namespace

NanoQL.Methods

Assembly

NanoQL.dll

The basis systems of the Longstaff-Schwartz early-exercise Monte Carlo regressions.

public static class LsmBasisSystem

Inheritance

object

LsmBasisSystem

Inherited Members

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

A static class, as QuantLib's static members: each system is an immutable array of functions, the polynomials of orders 0 to the order given, the orthogonal ones weighted by the square root of their weight function.

Methods

MultiPathBasisSystem(int, int, LsmBasisSystemPolynomialType)

The multi-factor basis: the products over the factors of the one-factor polynomials whose orders sum to at most order, the constant first, then each total order's terms in increasing lexicographic order of their orders.

public static ImmutableArray<Func<Vector, double>> MultiPathBasisSystem(int dim, int order, LsmBasisSystemPolynomialType type)

Parameters

dim int

The number of factors.

order int

The highest total order.

type LsmBasisSystemPolynomialType

The polynomial family.

Returns

ImmutableArray<Func<Vector, double>>

The basis functions, each of a vector with one element per factor.

Exceptions

ArgumentOutOfRangeException

order is negative.

NanoQLException

dim isn't positive ("zero dimension"), or the family is unknown.

PathBasisSystem(int, LsmBasisSystemPolynomialType)

The one-factor basis: the polynomials of orders 0 to order.

public static ImmutableArray<Func<double, double>> PathBasisSystem(int order, LsmBasisSystemPolynomialType type)

Parameters

order int

The highest order.

type LsmBasisSystemPolynomialType

The polynomial family.

Returns

ImmutableArray<Func<double, double>>

The basis functions, order + 1 of them.

Exceptions

ArgumentOutOfRangeException

order is negative.

NanoQLException

The family is unknown.