Class AbcdCalibration

Namespace

NanoQL.TermStructures

Assembly

NanoQL.dll

The abcd instantaneous volatility fitted to Black volatilities by their maturities: the root-mean-square error of the abcd Black volatilities, minimized over a, b, c and d through QuantLib's transformation (c, d and a + d positive), the fixed parameters at their guesses.

public sealed class AbcdCalibration

Inheritance

object

AbcdCalibration

Inherited Members

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

Immutable: Compute() returns the fitted calibration, where QuantLib's compute() changes the object; before it the parameters are the guesses, and the weights 1/n.

One of QuantLib's refusals is narrowed: QuantLib's transformation leaves b free, so its optimizer can step to a trial point the abcd function's validation refuses, and the fit throws. Here such a trial point's residuals are 1.0 each, a guard that keeps every fit QuantLib completes bit for bit, since none of them reaches such a point. A fit on which the guard acted is returned where it ends inside the valid region and refused with QuantLib's text, its first invalid trial point's, where it ends against the zero floor: its lowest instantaneous volatility below 1% of the smallest Black volatility given, as for data whose total variance shrinks, which no valid curve fits.

One of QuantLib's defects is fixed: its transformation gives a as a positive a + d less d, so with a fixed and d free it fixes a + d, and the fit moves a by what it moves d. Here a fixed keeps its guess, and d stays above max(0, −a), the same region; every other choice of fixed parameters is QuantLib's.

Constructors

AbcdCalibration(IEnumerable<double>, IEnumerable<double>, double, double, double, double, bool, bool, bool, bool, bool, EndCriteria?, OptimizationMethod?)

Initializes a new instance of the AbcdCalibration class, not yet fitted.

public AbcdCalibration(IEnumerable<double> t, IEnumerable<double> blackVols, double aGuess = -0.06, double bGuess = 0.17, double cGuess = 0.54, double dGuess = 0.17, bool aIsFixed = false, bool bIsFixed = false, bool cIsFixed = false, bool dIsFixed = false, bool vegaWeighted = false, EndCriteria? endCriteria = null, OptimizationMethod? method = null)

Parameters

t IEnumerable<double>

The maturities.

blackVols IEnumerable<double>

The Black volatilities, one per maturity.

aGuess double

a's guess.

bGuess double

b's guess.

cGuess double

c's guess, positive.

dGuess double

d's guess, non-negative.

aIsFixed bool

Whether a is fixed at its guess.

bIsFixed bool

Whether b is fixed at its guess.

cIsFixed bool

Whether c is fixed at its guess.

dIsFixed bool

Whether d is fixed at its guess.

vegaWeighted bool

Whether the errors are weighted by the at-the-money vegas.

endCriteria EndCriteria

The end criteria, or null for QuantLib's EndCriteria(10000, 1000, 1e-8, 0.3e-4, 0.3e-4).

method OptimizationMethod

The optimizer, or null for QuantLib's LevenbergMarquardt(1e-8, 1e-8, 1e-8, false).

Exceptions

ArgumentNullException

t or blackVols is null.

ArgumentException

The guesses fail Validate(double, double, double, double), or the sizes differ.

Properties

A

Gets a: the guess, or the fit.

public double A { get; }

Property Value

double

AIsFixed

Gets a value indicating whether a is fixed.

public bool AIsFixed { get; }

Property Value

bool

B

Gets b: the guess, or the fit.

public double B { get; }

Property Value

double

BIsFixed

Gets a value indicating whether b is fixed.

public bool BIsFixed { get; }

Property Value

bool

C

Gets c: the guess, or the fit.

public double C { get; }

Property Value

double

CIsFixed

Gets a value indicating whether c is fixed.

public bool CIsFixed { get; }

Property Value

bool

D

Gets d: the guess, or the fit.

public double D { get; }

Property Value

double

DIsFixed

Gets a value indicating whether d is fixed.

public bool DIsFixed { get; }

Property Value

bool

EndCriteria

Gets the end criterion the fit met: None before Compute() and with every parameter fixed.

public EndCriteriaType EndCriteria { get; }

Property Value

EndCriteriaType

Transformation

Gets the parameters' transformation the fit used, or null before a fit, QuantLib's empty pointer.

public ParametersTransformation? Transformation { get; }

Property Value

ParametersTransformation

Methods

Compute()

The fit, from the guesses: QuantLib's compute(), the receiver unchanged.

public AbcdCalibration Compute()

Returns

AbcdCalibration

The fitted calibration.

Exceptions

NanoQLException

The optimizer fails, or the fit ends against the zero floor after reaching a trial point QuantLib's validation refuses, with that refusal's text.

Error()

The weighted root-mean-square error, √(n·Σwᵢeᵢ²/(n − 1)).

public double Error()

Returns

double

The error.

Errors()

The weighted errors, eᵢ·√wᵢ.

public Vector Errors()

Returns

Vector

The errors.

K(IEnumerable<double>, IEnumerable<double>)

The adjustment factors that match the Black volatilities: each volatility over the fitted one.

public ImmutableArray<double> K(IEnumerable<double> t, IEnumerable<double> blackVols)

Parameters

t IEnumerable<double>

The maturities.

blackVols IEnumerable<double>

The Black volatilities, one per maturity.

Returns

ImmutableArray<double>

The factors.

Exceptions

ArgumentNullException

An argument is null.

ArgumentException

The sizes differ.

MaxError()

The largest absolute error.

public double MaxError()

Returns

double

The error.

Value(double)

The fitted abcd Black volatility at a maturity.

public double Value(double x)

Parameters

x double

The maturity.

Returns

double

The volatility.

Exceptions

ArgumentException

The parameters fail Validate(double, double, double, double), or the maturity is negative.