Class AlphaFinder

Namespace

NanoQL.Models

Assembly

NanoQL.dll

The α of an alpha form, and the multipliers a and b, at which a swap rate's volatilities give a caplet its target variance: by the form's α at the initial guess where it works, by a bisection on the quadratic's turning point otherwise, or, with SolveWithMaxHomogeneity(double, int, ReadOnlySpan<double>, ReadOnlySpan<double>, ReadOnlySpan<double>, double, double, double, double, double, double, int, out double, out double, out double, Span<double>), at the α of the most homogeneous volatilities among those that work.

[WorkingType]
public sealed class AlphaFinder

Inheritance

object

AlphaFinder

Inherited Members

object.GetType()

object.ToString()

object.Equals(object)

object.Equals(object, object)

object.ReferenceEquals(object, object)

object.GetHashCode()

Remarks

A working type: each solve keeps its inputs, as QuantLib's members, and sets the form's α; the alpha calibration builds one per calibration around its own copy of the form. It isn't thread-safe.

QuantLib's master's finder (#2910; Divergences/AlphaFinderTests.cs), which fixes four of QuantLib 1.44's defects: the downward bracket search stops at its first acceptable α, testing the value it moves, where 1.44's tests the upward one's (alphafinder.cpp:372-373); the minimization's feasibility test reads the trial α, where 1.44's reads the objective's value there (:117, :145); the bisection returns at an exact root and where its point no longer moves; and Solve(double, int, ReadOnlySpan<double>, ReadOnlySpan<double>, ReadOnlySpan<double>, double, double, double, double, double, double, int, out double, out double, out double, Span<double>) and SolveWithMaxHomogeneity(double, int, ReadOnlySpan<double>, ReadOnlySpan<double>, ReadOnlySpan<double>, double, double, double, double, double, double, int, out double, out double, out double, Span<double>) return their final part's success, where 1.44's return true where it fails, at α₀ or at the search's α (:335-346, :405-415, :550-561), the swap rate's last volatility then left as the caller's. Two of nanoql's own: the searches and the minimization also stop where their point no longer moves, where QuantLib's never end at a tolerance of 0 (:30-111); and b is NaN where the final part fails, where QuantLib leaves the caller's value. The alpha calibration's fallback minimizes on 1.44's test of the objective's value. Inputs shorter than the step index reads, which QuantLib reads past, are refused.

Constructors

AlphaFinder(AlphaForm)

Initializes a new instance of the AlphaFinder class.

public AlphaFinder(AlphaForm parametricForm)

Parameters

parametricForm AlphaForm

The alpha form, whose α each solve sets.

Methods

Solve(double, int, ReadOnlySpan<double>, ReadOnlySpan<double>, ReadOnlySpan<double>, double, double, double, double, double, double, int, out double, out double, out double, Span<double>)

The α, a and b at which the second rate's volatilities give the caplet its target variance: the initial α where it works, a bracketed bisection on the quadratic's turning point otherwise.

public bool Solve(double alpha0, int stepIndex, ReadOnlySpan<double> rateOneVols, ReadOnlySpan<double> rateTwoHomogeneousVols, ReadOnlySpan<double> correlations, double w0, double w1, double targetVariance, double tolerance, double alphaMax, double alphaMin, int steps, out double alpha, out double a, out double b, Span<double> rateTwoVols)

Parameters

alpha0 double

The initial α.

stepIndex int

The caplet's index.

rateOneVols ReadOnlySpan<double>

The first rate's volatilities, at least the step index plus one.

rateTwoHomogeneousVols ReadOnlySpan<double>

The second rate's homogeneous volatilities, at least the step index plus two.

correlations ReadOnlySpan<double>

The two rates' correlations, at least the step index plus one.

w0 double

The first rate's weight.

w1 double

The second rate's weight.

targetVariance double

The caplet's target variance.

tolerance double

The bisection's tolerance.

alphaMax double

The largest α.

alphaMin double

The smallest α.

steps int

The bracket search's steps.

alpha double

The α found; NaN where none is.

a double

The multiplier of the second rate's volatilities to the caplet's reset.

b double

The multiplier of its volatility after it; NaN where the final part fails.

rateTwoVols Span<double>

The second rate's new volatilities, written to the step index plus one.

Returns

bool

Whether an α was found and its final part, the variance left for the second rate's last volatility, succeeded.

Exceptions

ArgumentException

A vector is shorter than the step index reads.

ArgumentOutOfRangeException

stepIndex is negative.

SolveWithMaxHomogeneity(double, int, ReadOnlySpan<double>, ReadOnlySpan<double>, ReadOnlySpan<double>, double, double, double, double, double, double, int, out double, out double, out double, Span<double>)

The α, a and b at which the second rate's volatilities give the caplet its target variance, at the α, among those that work, whose volatilities are the closest to the homogeneous ones.

public bool SolveWithMaxHomogeneity(double alpha0, int stepIndex, ReadOnlySpan<double> rateOneVols, ReadOnlySpan<double> rateTwoHomogeneousVols, ReadOnlySpan<double> correlations, double w0, double w1, double targetVariance, double tolerance, double alphaMax, double alphaMin, int steps, out double alpha, out double a, out double b, Span<double> rateTwoVols)

Parameters

alpha0 double

The initial α.

stepIndex int

The caplet's index.

rateOneVols ReadOnlySpan<double>

The first rate's volatilities, at least the step index plus one.

rateTwoHomogeneousVols ReadOnlySpan<double>

The second rate's homogeneous volatilities, at least the step index plus two.

correlations ReadOnlySpan<double>

The two rates' correlations, at least the step index plus one.

w0 double

The first rate's weight.

w1 double

The second rate's weight.

targetVariance double

The caplet's target variance.

tolerance double

The searches' tolerance.

alphaMax double

The largest α.

alphaMin double

The smallest α.

steps int

The search's steps where no end works.

alpha double

The α found; NaN where none is.

a double

The multiplier of the second rate's volatilities to the caplet's reset.

b double

The multiplier of its volatility after it; NaN where the final part fails.

rateTwoVols Span<double>

The second rate's new volatilities, written to the step index plus one.

Returns

bool

Whether an α was found and its final part, the variance left for the second rate's last volatility, succeeded.

Exceptions

ArgumentException

A vector is shorter than the step index reads.

ArgumentOutOfRangeException

stepIndex or steps is negative.