Class FdmHestonSolver

Namespace

NanoQL.Methods

Assembly

NanoQL.dll

The finite-difference Heston solver: FdmHestonOp on the problem's grid in the logarithm of the underlying by the variance, rolled back by the two-dimensional solver, read at a spot and a variance.

public sealed class FdmHestonSolver

Inheritance

object

FdmHestonSolver

Inherited Members

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

Computed at construction, where QuantLib's lazy object computes at the first read, and immutable after (Fdm2DimSolver's form). The problem's times are Clock(HestonProcess, FdmQuantoHelper?, LocalVolTermStructure?)'s.

The delta and gamma are the first and second derivatives with respect to the spot, not the model-implied ones (Fabio Mercurio, Massimo Morini, "A Note on Hedging with Local and Stochastic Volatility Models"); the mean-variance delta and gamma add the variance's moves along its correlation with the spot.

Constructors

FdmHestonSolver(HestonProcess, FdmSolverDesc, FdmSchemeDesc?, FdmQuantoHelper?, LocalVolTermStructure?, double)

Initializes a new instance of the FdmHestonSolver class, and solves the problem.

public FdmHestonSolver(HestonProcess process, FdmSolverDesc solverDesc, FdmSchemeDesc? schemeDesc = null, FdmQuantoHelper? quantoHelper = null, LocalVolTermStructure? leverageFct = null, double mixingFactor = 1)

Parameters

process HestonProcess

The Heston process.

solverDesc FdmSolverDesc

The problem, on Clock(HestonProcess, FdmQuantoHelper?, LocalVolTermStructure?)'s times.

schemeDesc FdmSchemeDesc?

The scheme; Hundsdorfer's by default, QuantLib's.

quantoHelper FdmQuantoHelper

The quanto helper, or null for none.

leverageFct LocalVolTermStructure

The leverage function, or null for none.

mixingFactor double

The factor scaling the variance's volatility σ.

Exceptions

ArgumentNullException

The process or the problem is null.

ArgumentException

The rollback's arguments are refused.

NanoQLException

A step or the spline fails.

Methods

DeltaAt(double, double)

The first derivative with respect to the spot at a spot and a variance.

public double DeltaAt(double s, double v)

Parameters

s double

The spot.

v double

The variance.

Returns

double

The delta.

GammaAt(double, double)

The second derivative with respect to the spot at a spot and a variance.

public double GammaAt(double s, double v)

Parameters

s double

The spot.

v double

The variance.

Returns

double

The gamma.

MeanVarianceDeltaAt(double, double)

The mean-variance delta at a spot and a variance: the delta plus ρσ/s times the derivative with respect to the variance.

public double MeanVarianceDeltaAt(double s, double v)

Parameters

s double

The spot.

v double

The variance.

Returns

double

The mean-variance delta.

MeanVarianceGammaAt(double, double)

The mean-variance gamma at a spot and a variance.

public double MeanVarianceGammaAt(double s, double v)

Parameters

s double

The spot.

v double

The variance.

Returns

double

The mean-variance gamma.

ThetaAt(double, double)

The theta at a spot and a variance.

public double? ThetaAt(double s, double v)

Parameters

s double

The spot.

v double

The variance.

Returns

double?

The theta; null when the problem's first stopping time is time 0.

ValueAt(double, double)

The value at a spot and a variance.

public double ValueAt(double s, double v)

Parameters

s double

The spot.

v double

The variance.

Returns

double

The value.