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switch to DataInterpolations instead of BSplineKit #141

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switch to DataInterpolations instead of BSplineKit #141

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5ad5903
switch to DataInterpolations
alecloudenback Oct 12, 2022
c539200
wip
alecloudenback Oct 12, 2022
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7 changes: 4 additions & 3 deletions Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -4,26 +4,27 @@ authors = ["Alec Loudenback <[email protected]> and contributors"]
version = "3.3.1"

[deps]
BSplineKit = "093aae92-e908-43d7-9660-e50ee39d5a0a"
DataInterpolations = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
FinanceCore = "b9b1ffdd-6612-4b69-8227-7663be06e089"
ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
LsqFit = "2fda8390-95c7-5789-9bda-21331edee243"
NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
Optim = "429524aa-4258-5aef-a3af-852621145aeb"
Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228"

[compat]
BSplineKit = "^0.8"
FinanceCore = "^1"
ForwardDiff = "^0.10"
LsqFit = "^0.12"
Optim = "^1"
Reexport = "^1.2"
Roots = "^1"
UnicodePlots = "^2"
julia = "^1.6"
Reexport = "^1.2"

[extras]
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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4 changes: 3 additions & 1 deletion src/Yields.jl
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@@ -1,11 +1,13 @@
module Yields

using Reexport
using StaticArrays
using FinanceCore
using FinanceCore: Rate, rate, discount, accumulation, Periodic, Continuous, forward
@reexport using FinanceCore: Rate, rate, discount, accumulation, Periodic, Continuous, forward
import BSplineKit
import DataInterpolations
import ForwardDiff
using NonlinearSolve
using LinearAlgebra
using UnicodePlots
import LsqFit
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79 changes: 22 additions & 57 deletions src/utils.jl
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Expand Up @@ -50,7 +50,7 @@ struct LinearSpline <: InterpolationKind end
Bootstrap the rates with the given maturities, treating the rates according to the periodic frequencies in settlement_frequency.

`interpolator` is any function that will take two vectors of inputs and output points and return a function that will estimate an output given a scalar input. That is
`interpolator` should be: `interpolator(xs, ys) -> f(x)` where `f(x)` is the interpolated value of `y` at `x`.
`interpolator` should be: `interpolator(ys, xs) -> f(x)` where `f(x)` is the interpolated value of `y` at `x`.

Built in `interpolator`s in Yields are:
- `QuadraticSpline()`: Quadratic spline interpolation.
Expand All @@ -70,11 +70,11 @@ end
# dispatch on the user-exposed InterpolationKind to the right
# internally named interpolation function
function _bootstrap_choose_interp(rates, maturities, settlement_frequency, i::QuadraticSpline)
return _bootstrap_inner(rates, maturities, settlement_frequency, cubic_interp)
return _bootstrap_inner(rates, maturities, settlement_frequency, DataInterpolations.QuadraticSpline)
end

function _bootstrap_choose_interp(rates, maturities, settlement_frequency, i::LinearSpline)
return _bootstrap_inner(rates, maturities, settlement_frequency, linear_interp)
return _bootstrap_inner(rates, maturities, settlement_frequency, DataInterpolations.LinearInterpolation)
end


Expand All @@ -85,6 +85,7 @@ function _bootstrap_inner(rates, maturities, settlement_frequency, interpolation
discount_vec[1] = discount(Constant(rates[1]), maturities[1])

for t = 2:length(maturities)
@show t
if isnothing(settlement_frequency[t])
# no settlement before maturity
discount_vec[t] = discount(Constant(rates[t]), maturities[t])
Expand All @@ -95,70 +96,34 @@ function _bootstrap_inner(rates, maturities, settlement_frequency, interpolation
cfs[end] += 1

function pv(v_guess)
v = interpolation_function([[0.0]; maturities[1:t]], vcat(1.0, discount_vec[1:t-1], v_guess...))
@show "here1"
@show typeof(v_guess)
pv_inner(v_guess)
end

function pv(v_guess::U{T}) where {T<:NonlinearSolve.ForwardDiff.Dual,U<:AbstractArray}
@show "here2"
pv_inner(v_guess.value)
end

function pv_inner(v_guess)
v = interpolation_function(vcat(1.0, discount_vec[1:t-1], only(v_guess)),[[0.0]; maturities[1:t]])
return sum(v.(times) .* cfs)
end
target_pv = sum(map(t2 -> discount(Constant(rates[t]), t2), times) .* cfs)
root_func(v_guess) = pv(v_guess) - target_pv
root_func′(v_guess) = ForwardDiff.derivative(root_func, v_guess)
discount_vec[t] = solve(root_func, root_func′, rate(rates[t]))
f(u,p) = pv(u) .- p
# root_func(v_guess) = pv(v_guess) - target_pv
# root_func′(v_guess) = ForwardDiff.derivative(root_func, v_guess)
# discount_vec[t] = solve(root_func, root_func′, rate(rates[t]))
probN = NonlinearProblem{false}(f,@SVector[rate(rates[t])],target_pv)
discount_vec[t] = NonlinearSolve.solve(probN,NewtonRaphson(),tol=1e-9)
end

end
zero_vec = -log.(clamp.(discount_vec,0.00001,1)) ./ maturities
return interpolation_function([0.0; maturities], [first(zero_vec); zero_vec])
end

# the ad-hoc approach to extrapoliatons is based on suggestion by author of
# BSplineKit at https://github.com/jipolanco/BSplineKit.jl/issues/19
# this should not be exposed directly to user
struct _Extrap{I,L,R}
int::I # the BSplineKit interpolation
left::L # a tuple of (boundary, extrapolation function)
right::R # a tuple of (boundary, extrapolation function)
end

function _wrap_spline(itp)

S = BSplineKit.spline(itp) # spline passing through data points
B = BSplineKit.basis(S) # B-spline basis

a, b = BSplineKit.boundaries(B) # left and right boundaries

# For now, we construct the full spline S′(x).
# There are faster ways of doing this that should be implemented...
S′ = diff(S, BSplineKit.Derivative(1))

return _Extrap(itp,
(boundary = a, func = x->S(a) + S′(a)*(x-a)),
(boundary = b, func = x->S(b) + S′(b)*(x-b)),

)
end

function _interp(e::_Extrap,x)
if x <= e.left.boundary
return e.left.func(x)
elseif x >= e.right.boundary
return e.right.func(x)
else
return e.int(x)
end
end

function linear_interp(xs, ys)
int = BSplineKit.interpolate(xs, ys, BSplineKit.BSplineOrder(2))
e = _wrap_spline(int)
return x -> _interp(e, x)
end

function cubic_interp(xs, ys)
order = min(length(xs),3) # in case the length of xs is less than the spline order
int = BSplineKit.interpolate(xs, ys, BSplineKit.BSplineOrder(order))
e = _wrap_spline(int)
return x -> _interp(e, x)
end

# used to display simple type name in show method
# https://stackoverflow.com/questions/70043313/get-simple-name-of-type-in-julia?noredirect=1#comment123823820_70043313
name(::Type{T}) where {T} = (isempty(T.parameters) ? T : T.name.wrapper)
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