Class QdFpAmericanEngine

Namespace

NanoQL.PricingEngines

Assembly

NanoQL.dll

The high-performance, high-precision American engine based on a fixed-point iteration for the exercise boundary (L. Andersen, M. Lake and D. Offengenden, "High Performance American Option Pricing", 2015; L. Andersen and M. Lake, "Fast American Option Pricing: The Double-Boundary Case", 2021), seeded by QD+'s boundary.

public class QdFpAmericanEngine : QdPutCallParityEngine

Inheritance

object

QdPutCallParityEngine

QdFpAmericanEngine

Inherited Members

QdPutCallParityEngine.Calculate(VanillaOption, EvaluationContext)

QdPutCallParityEngine.Process

object.GetType()

object.MemberwiseClone()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

The engine reports the value. Immutable: the three schemes QuantLib keeps as function statics are static singletons; each price builds its boundary, and the fixed-point steps' new values give a new interpolation on the same nodes (WithY(ReadOnlySpan<double>)), which the boundary function reads, where QuantLib updates its interpolation in place. The static Calculate builds an engine and prices through it. An extension point, as in QuantLib.

Constructors

QdFpAmericanEngine(GeneralizedBlackScholesProcess, QdFpIterationScheme?, QdFpAmericanEngineFixedPointEquation)

Initializes a new instance of the QdFpAmericanEngine class.

public QdFpAmericanEngine(GeneralizedBlackScholesProcess bsProcess, QdFpIterationScheme? iterationScheme = null, QdFpAmericanEngineFixedPointEquation fpEquation = QdFpAmericanEngineFixedPointEquation.Auto)

Parameters

bsProcess GeneralizedBlackScholesProcess

The Black-Scholes process.

iterationScheme QdFpIterationScheme

The iteration scheme, or null for AccurateScheme().

fpEquation QdFpAmericanEngineFixedPointEquation

The fixed-point equation.

Exceptions

ArgumentNullException

bsProcess is null.

ArgumentOutOfRangeException

The equation isn't a member of its type.

Methods

AccurateScheme()

The accurate scheme, the default: Legendre-tanh-sinh (25, 5, 13)-1e-8.

public static QdFpIterationScheme AccurateScheme()

Returns

QdFpIterationScheme

The scheme, one instance.

Calculate(VanillaOption, EvaluationContext, GeneralizedBlackScholesProcess, QdFpIterationScheme?, QdFpAmericanEngineFixedPointEquation)

Prices an American vanilla option by the fixed-point iteration.

public static OneAssetOptionResults Calculate(VanillaOption option, EvaluationContext context, GeneralizedBlackScholesProcess bsProcess, QdFpIterationScheme? iterationScheme = null, QdFpAmericanEngineFixedPointEquation fpEquation = QdFpAmericanEngineFixedPointEquation.Auto)

Parameters

option VanillaOption

The option.

context EvaluationContext

The evaluation context.

bsProcess GeneralizedBlackScholesProcess

The Black-Scholes process.

iterationScheme QdFpIterationScheme

The iteration scheme, or null for AccurateScheme().

fpEquation QdFpAmericanEngineFixedPointEquation

The fixed-point equation.

Returns

OneAssetOptionResults

The option's results: the value.

Exceptions

ArgumentNullException

An argument is null.

NanoQLException

The engine refuses the option.

CalculatePut(double, double, double, double, double, double)

The value of an American put.

protected override double CalculatePut(double s, double k, double r, double q, double vol, double t)

Parameters

s double

The spot.

k double

The strike.

r double

The risk-free rate.

q double

The dividend yield.

vol double

The volatility.

t double

The time to expiry.

Returns

double

The value.

FastScheme()

The fast scheme: Gauss-Legendre (7, 2, 7)-27.

public static QdFpIterationScheme FastScheme()

Returns

QdFpIterationScheme

The scheme, one instance.

HighPrecisionScheme()

The high-precision scheme: tanh-sinh (10, 30)-1e-10.

public static QdFpIterationScheme HighPrecisionScheme()

Returns

QdFpIterationScheme

The scheme, one instance.