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Another interesting decision has been made, this time for my paper titled:
“Beyond Nelson-Siegel and splines: A model-agnostic Machine Learning framework for discount curve calibration, interpolation and extrapolation”. By European Actuarial Journal. First time, 7 years ago, it was for Swap curve construction for insurance pricing, based on no arbitrage short rate models – which works perfectly. I might decide to publish the review one day.
I think, as it’s been suggested to me (after being, institutionally and not only, knocked down several times), that documenting even the subtle harassment is important, especially when my reality (and reality in general) is questioned in order to create auto-prophecies.
What is astonishing (suprisingly only to me, so far) is that people do not hesitate to write absurdities down, even when facing compelling receipts that will remain written virtually forever. Is this the era of post-truth I’ve been hearing about? Or is there another hidden reality that I am not aware of (which doesn’t even justify the gigantic institutional, and not only, gaslighting)?
The paper introduces a general machine learning framework for yield curve modeling, in which classical parametric models such as Nelson-Siegel and Svensson serve as special cases within a broader class of functional regression approaches. By linearizing the bond pricing/swap valuation equation, I reformulate the estimation of spot rates as a supervised regression problem, where the response variable is derived from observed bond prices and cash flows, and the regressors are constructed as flexible functions of time-to-maturities. I show that this formulation supports a wide range of modeling strategies — including polynomial expansions, Laguerre polynomials, kernel methods, and regularized linearmodels — all within a unified framework that could preserve economic interpretability. This enables not only curve calibration but also static interpolation and extrapolation. By abstracting away from any fixed parametric structure, my framework bridges the gap between traditional yield curve modeling and modern supervised learning, offering a robust, extensible, and data-driven tool for financial applications ranging from asset pricing to regulatory (?) reporting.
The reviewer says:
”
-
The approach is based on a linearization of the exponential function, which can lead to significant errors
-
The regression uses errors that are correlated with the regressors, which leads to model misspecification
Therefore, I cannot recommend this paper for publication.
“
Ok, so:
- which can lead to significant errors: in theory yes. But in pratice? Have you read the paper? Have you seen the residuals? Have you seen the images? Have you seen the comparison with other published papers? The residuals are less than 1e-18.
- what if I use independent Gaussian or whatever specification of errors instead? Or remove the errors altogether? The reviewer does not even suggest that. He just says “which leads to model misspecification”.
Based on the paper (at least on swaps data, for bond data, could be discussed: what if I use independent Gaussian or whatever specification of errors instead?) linked below + the magnitude of the residuals (< 1e-18) + the images + the comparison with other high-profile published papers, could anyone see what they are talking about? That couldn’t be improved?
At least recognize the novelty and suggest ways to improve, instead of opposing hate and shadow, arbitrary rules. Have you seen that before? Bootstrapping the yield curve + interpolation + extrapolation (almost the same as I did in Swap curve construction for insurance pricing, based on no arbitrage short rate models) all at once? With a model-agnostic approach, meaning a lot of flexibility based on various model capacities? Couldn’t this paper be at least improved?. This is a generalization of many existing approaches. While it’s grotesque to name names, which I won’t, I can see a lot of papers in this same journal which could easily be master’s dissertations. A lot of “[Place any existing- sophisticated-model-created-by-someone else here] applied to insurance” indeed.
From P.22 in:
“@article{andersen2007discount,
title={Discount curve construction with tension splines},
author={Andersen, Leif},
journal={Review of Derivatives Research},
volume={10},
number={3},
pages={227–267},
year={2007},
publisher={Springer}
}”
From my paper:
From P. 242 in “@misc{anderseninterest,
title={Interest Rate Modeling, 2010},
author={Andersen, L and Piterbarg, V},
publisher={Atlantic Financial Press: London}
}”
From my paper:
CAN YOU SPOT THE MODEL MISSPECIFICATION?
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Analysis and Future Implications of the Machine Learning Framework for Yield Curve Modelling
The original text discusses a proposed Machine Learning framework for yield curve modelling as in the paper titled ‘Beyond Nelson-Siegel and splines: A model-agnostic Machine Learning framework for discount curve calibration, interpolation and extrapolation’. The framework proposed in the paper presents a technique for bond pricing and swap valuation that reformulates the estimation of spot rates as a supervised regression problem. This new approach is an extension of classical parametric models and accommodates a wide range of modelling strategies.
Long-term Implications
This framework bridges the gap between traditional yield curve modelling and modern supervised learning, offering a robust, flexible, and data-driven tool for financial applications. The range of applications it may provide includes asset pricing to regulatory reporting. As this machine learning model is flexible and can be tailored to any specifications, financial analysts and economists could use it to develop more robust and accurate methods for yield curve modelling and predicting economic trends. This makes it a potentially valuable tool for institutions engaging in economic forecasting and financial decision-making.
Possible Future Developments
While the paper highlights the promise of this method, the proposed approach faced criticism for potential significant errors due to the model’s linearization of the exponential function and correlated errors with the regressors leading to model misspecification. These criticisms must be addressed in future developments of the model. More rigorous testing, refinement of the model and independent validation could lead to wider acceptance and use of the framework in the finance and economics industry.
Actionable Advice
- Authors should take criticism into consideration and work on refining their model to address the issues raised – i.e., the occurrence of significant errors caused by the method’s linearization of the exponential function, and model misspecification due to correlated errors with regression variables.
- Future research should focus on refining the model and enhancing its robustness, flexibility, and extensibility.
- Financial institutions and economists should keep an eye on the development of this framework as it could potentially revolutionize the way yield curves are modeled, providing more accurate and reliable tools for predicting future economic trends.
Conclusion
Overall, the machine-learning framework for yield curve modelling, while criticized by some, has the potential to be a significant tool in the realm of financial economics. However, for the full potential to be realized, authors need to work on improving and refining their model, addressing the issues currently associated with it. For financial practitioners, this signifies an exciting development on the horizon, indicating that future yield curve modelling could possess more accurate and potent predictive power than ever before.