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Yield_Curve_fitting.jl
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Yield_Curve_fitting.jl
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### A Pluto.jl notebook ###
# v0.19.5
using Markdown
using InteractiveUtils
# ╔═╡ c80cb8c4-ee67-11ec-0816-77676878d2af
using Yields
# ╔═╡ e7f43088-a92d-43f3-8584-756cfbd9fda2
using Plots
# ╔═╡ ceb370fb-ad7f-46b7-bb10-bcb177d7f5fb
md" # Fitting Yield Curves to rates
Given rates and maturities, we can fit the yield curves with different techniques.
Below, we specify that the rates should be interpreted as `Continuous`ly compounded zero rates:
"
# ╔═╡ 619e758c-460f-4784-ad88-9ea1518f0d4a
rates = Continuous.([0.01, 0.01, 0.03, 0.05, 0.07, 0.16, 0.35, 0.92, 1.40, 1.74, 2.31, 2.41] ./ 100)
# ╔═╡ 509cf67d-bc6f-414b-8e99-418df34d8137
mats = [1/12, 2/12, 3/12, 6/12, 1, 2, 3, 5, 7, 10, 20, 30]
# ╔═╡ c0b65e7f-ab23-43e8-820c-f62417013785
ns = Yields.Zero(NelsonSiegel(),rates,mats);
# ╔═╡ c3a86b0d-b677-47dc-8d13-0e1933b99aaa
nss = Yields.Zero(NelsonSiegelSvensson(),rates,mats);
# ╔═╡ 040d3fff-a2cd-484c-9b5d-49d3375996fa
b = Yields.Zero(Bootstrap(),rates,mats);
# ╔═╡ b495b6ec-28c9-49d7-bf56-1b9e0e7f4213
bl = Yields.Zero(Bootstrap(Yields.LinearSpline()),rates,mats);
# ╔═╡ 501b3c90-8fa2-4b00-b04e-6d67ddddf52f
md" That's it! We've fit the rates using four different techniques. These can now be used in a variety of ways, such as calculating the `present_value`, `duration`, or `convexity` of different cashflows if you imported [ActuaryUtilities.jl](https://github.com/JuliaActuary/ActuaryUtilities.jl)"
# ╔═╡ e55da4f6-1ba0-4e91-b005-22d6c5689570
md"## Visualizing the results"
# ╔═╡ e0385d98-53e1-44e7-b225-c69edc20cf9e
# ╔═╡ 1d04f511-9954-4634-9e2b-5bad6a81ac90
"""
plot the given curve onto the given plot figure
"""
function curveplot!(plot_fig,curve;label="",alpha=alpha)
maturities = 0.25:0.25:40
f(x) = rate(Yields.zero(curve,x))
plot!(plot_fig,maturities,f,label=label,line=3,alpha=alpha)
end
# ╔═╡ 26187930-cade-49c3-8517-3105242d4c28
"""
a function to plot the curves, given different alpha transparency for each of the lines (used when creating animiation)
"""
function p(alpha=[1,1,1,1])
theme(:wong2)
p = plot(legend=:topleft,xlabel="Tenor",ylabel="Continuous yield",grid=false)
scatter!(
mats,
Yields.rate.(Continuous().(rates)),
label = "Given zero rates"
)
curveplot!(p,b,label="Bootstrap (Spline)",alpha=alpha[1])
curveplot!(p,bl,label="Bootstrap (Linear)",alpha=alpha[2])
curveplot!(p,ns, label = "NelsonSiegel",alpha=alpha[3])
curveplot!(p,nss, label = "NelsonSiegelSvensson",alpha=alpha[4])
lens!([0, 3.5], [0.0, .0045], inset = (1, bbox(.5, 0.5, 0.4, 0.4)))
end
# ╔═╡ b25427c5-fd08-4c07-ae23-e9aedb005c17
p()
# ╔═╡ 1b647af0-2d90-424a-8b24-4a9f48d511aa
anim = let
a = [1,.25,.25,.25]
anim = @animate for i in 1:4
a = circshift(a,1) # shift the transparency
p(a)
end
anim
end
# ╔═╡ 24f70673-74fb-4818-8f7c-25b90a70e688
gif(anim,"anim_fps2.gif",fps=2)
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
Yields = "d7e99b2f-e7f3-4d9e-9f01-2338fc023ad3"
[compat]
Plots = "~1.30.1"
Yields = "~3.0.1"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
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