Add Nelson-Siegel and Smoothing Spline Yield Curve fitting

[alecloudenback]

Seems like a good reference:

• https://www.bis.org/publ/bppdf/bispap25.pdf
• https://onriskandreturn.com/2019/12/01/nelson-siegel-yield-curve-model/

Three related variants:

• Nelson-Siegel
• Nelson-Seigel-Svensson
• Smoothing Splines

This could be good first issue for someone familiar with the above methods already.

[alecloudenback]

Related article: https://www.soa.org/sections/financial-reporting/financial-reporting-newsletter/2022/february/fr-2022-02-perelman/

[leeyuntien]

Would like to contribute to this issue. Please advise next steps. Thanks!

[kasperrisager]

A good first step would be to make a struct that holds the data for the Nelson-Siegel parametrisation and methods for computing discount and zero rate correctly. Add in some tests. You can get inspired by the Smith-Wilson implementation. The open a draft pr.

[leeyuntien]

Tried to implement and added NelsonSiegelSvensson.jl and SmoothingSplines.jl whose approach might be debatable but please advise how these can be uploaded/pulled for a review.

[alecloudenback]

Awesome! Check out this article about creating a pull request: https://www.digitalocean.com/community/tutorials/how-to-create-a-pull-request-on-github

A PR will allow the automated tests/checks to occur and makes it easy to review the changes.

[alecloudenback]

Two of three will be completed in #116

[leeyuntien]

I have seen there are two spline methods in bootstrapping, do we still need smoothing splines? In this reference https://www.bis.org/publ/bppdf/bispap25.pdf it seems to talk about cubic splines, so smoothing splines here would mean cubic splines, or splines with even higher degrees? Thanks.

Seems like a good reference:

• https://www.bis.org/publ/bppdf/bispap25.pdf
• https://onriskandreturn.com/2019/12/01/nelson-siegel-yield-curve-model/

Three related variants:

• Nelson-Siegel
• Nelson-Seigel-Svensson
• Smoothing Splines

This could be good first issue for someone familiar with the above methods already.

[alecloudenback]

My understanding is that "smoothing splines" refers to fitting (minimizing error) of a starting spline model, whereas the existing methods fit simple splines through bootstrapped points (for the given points, the model error is zero).

[alecloudenback]

I was looking at DataInterpolations.jl and think that maybe it has smoothing spline fitting built in?

[leeyuntien]

I think you are right, and there are examples showing how to call the BSpline functions. https://htmlpreview.github.io/?https://github.com/PumasAI/DataInterpolations.jl/blob/v2.0.0/example/DataInterpolations.html.