EUROPT 2024
Abstract Submission

277. Parametric optimisation applied to a fitting problem in finance

Invited abstract in session FB-3: In memory of Georg Still - part 3, stream In memory of Georg Still.

Friday, 10:05 - 11:20
Room: M:J

Authors (first author is the speaker)

1. Ralf Werner
Institut für Mathematik, Universität Augsburg
2. Dirk Banholzer
School of Mathematics, University of Southampton
3. Joerg Fliege
University of Southampton

Abstract

The Nelson-Siegel and the Svensson model are two of the most widely used models for the term structure of interest rates. Even though the models are quite simple and intuitive, fitting them to market data is numerically challenging and various difficulties have been reported.
For this reason a novel mathematical analysis of the fitting problem based on parametric optimisation is carried out. It is based on the known observation that the fitting problem can be formulated as a separable nonlinear least-squares problem, in which the linear parameters can be
eliminated. We specifically provide a thorough discussion on the conditioning of the inner part of the reformulated problem and show that many of the reported difficulties encountered when solving it are inherent to the problem formulation and cannot be tackled by choosing a particular optimisation algorithm.
Our stability analysis provides novel insights that we then use to show that some of the ill-conditioning of the problem can be avoided, and that a suitably chosen penalty approach can be used to take care of the remaining ill-conditioning.
As our numerical results indicate, this approach has indeed the expected impact, while being independent of the choice of a particular optimisation algorithm. As a side benefit, we establish smoothness and differentiability properties of the reduced objective function, which for the first time puts global optimisation methods for the reduced problem on a sound mathematical basis

Keywords

Status: accepted

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