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CubicSpline B-splines fitting method

Fits a discount function to a set of cubic B-splines $ N_{i,3}(t) $, i.e., $$ d(t) = \sum_{i=0}^{n} c_i * N_{i,3}(t) $$

See: McCulloch, J. 1971, "Measuring the Term Structure of Interest Rates." Journal of Business, 44: 19-31

McCulloch, J. 1975, "The tax adjusted yield curve." Journal of Finance, XXX811-30

warning "The results are extremely sensitive to the number and location of the knot points, and there is no optimal way of selecting them." James, J. and N. Webber, "Interest Rate Modelling" John Wiley, 2000, pp. 440.

Hierarchy

Index

Properties

Private _N

Protected _constrainAtZero

_constrainAtZero: boolean

Protected _costFunction

_costFunction: FittingCost

_curve

Protected _guessSolution

_guessSolution: Real[]

_l2

_l2: Real[]

Private _size

_size: Size

_solution

_solution: Real[]

Private _splines

_splines: BSpline

_weights

_weights: Real[]

Methods

basisFunction

  • Parameters

    Returns Real

calculate

  • calculate(): void
  • Returns void

cbsfInit1

  • Parameters

    • knots: Time[]
    • Default value constrainAtZero: boolean = true
    • Default value weights: Real[] = []
    • Default value optimizationMethod: OptimizationMethod = null
    • Default value l2: Real[] = []

    Returns CubicBSplinesFitting

cbsfInit2

  • Parameters

    • knots: Time[]
    • constrainAtZero: boolean
    • weights: Real[]
    • l2: Real[]

    Returns CubicBSplinesFitting

clone

constrainAtZero

  • constrainAtZero(): boolean

discount

discountFunction

fmInit

  • Parameters

    • Default value constrainAtZero: boolean = true
    • Default value weights: Real[] = []
    • Default value optimizationMethod: OptimizationMethod = null
    • Default value l2: Real[] = []

    Returns FittingMethod

init

  • init(): void
  • Returns void

l2

  • Returns Real[]

minimumCostValue

  • minimumCostValue(): Real

numberOfIterations

optimizationMethod

size

  • Returns Size

solution

  • solution(): Real[]

weights