Interest Rate Term Structure Decomposition: An Axiomatic Structural Approach

Abstract

The paper examines an axiomatic structural approach to term structure decomposition. From this perspective, term structure decomposition is modelled as an non-parsimonious optimization problem, with the structure delineated by constraints related to the likely attributes thereof, rather than by a linear combination of splines or functions. The motivation for the model lies in its perceived flexibility or power. Also, the model is seen as a likely candidate to implement issue-level term structure decomposition. Consequently, issue-level term structure decomposition is also briefly introduced. The power of the model is tested on a simulated and market sample. Even though it may go against notions of structure smoothness, the relationship or correlation between structure smoothness, goodness of fit, and systematic/ unsystematic risk is also touched on.

Interest Rate Term Structure Decomposition at the Instrument Level

“…Inequality constraints are added to prevent negative issue (equation 2.c), and portfolio (equation 2.d) forward rates. The initial solution of equation 8 of Barnard (2019) would also function in this case. Here, issue value is predominantly derived from discounting issue coupons against issue discount factors ( ), not portfolio discount factors ( ), and the optimization primarily optimizes issue discount factors, not portfolio discount factors per se.…”

“…Here, issue value is predominantly derived from discounting issue coupons against issue discount factors ( ), not portfolio discount factors ( ), and the optimization primarily optimizes issue discount factors, not portfolio discount factors per se. Barnard (2019) discusses term structure decomposition as as optimization problem, and it is also further covered subsequently.…”

“…In order to introduce structure smoothness to equation set 2, the axiomatic structural approaches of Barnard (2019) may be considered. Barnard (2019) notes that the premise that the resultant portfolio term structure optimizes goodness of fit against structure smoothness, may already stipulate sufficient information to decompose a term structure, without necessarily stipulating a set of basis functions or splines, as conventional models do. Rather, it may simply be stated as a general optimization problem, by including constraints to guide the structure or smoothness thereof (Boyd and Vandenberghe, 2004).…”

“…introduces and reviews term structure decomposition, its purpose and objective, the applicable models used to decompose term structures, and offers a brief comparison of these -their performance, strengths and weaknesses. Barnard (2019) also introduces an axiomatic structural approach as term structure decomposition method. In addition, the premises of term structure decomposition at the instrument level are also introduced.…”

“…Next, the theoretical model thereof is stated. Barnard (2019) notes that instrument-level term structure decomposition implies that a term structure is decomposed for each issue or instrument. Furthermore, hypothetically, the portfolio term structure is not directly decomposed, but derived from the issue term structures instead.…”