Free-form interest rate term structure decomposition: a 2nd order optimization problem

Brian Barnard


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The paper discusses an interest rate term structure decomposition method that breaks from the conventional, in that it does not superimpose any model, form or structure on the decomposition output – hence, the term free-form. The premise is simple: if the model does not presuppose any structure beforehand, and if the structure underlying the input data is indeed that implemented and applied by conventional models1, and if the model is not internally constrained by method itself, such that its model power can hardly be drawn into question, it should have no problem surfacing such structures. On the other hand, if the structure underlying the input data in fact does not necessarily follow a presupposed structure, the model should achieve greater modelling accuracy, and offer greater explanatory power. This in itself may also offer a better reflection on cases and scenarios where the modelling residual is significant, for instance, in the case of modelling (corporate) vanilla bonds2.
To realize such a model, a 2nd (higher) order or nested optimization problem – a series of optimizations pertaining to the same problem, and resulting from floating one or more constraints – is defined, and solved. The model is applied to a simulated term structure, as well as a market sample of government vanilla bonds, and the results are discussed.
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