Source: Bundesbank
Non-technical summary
Research Question
The term structure of interest rates, i.e. the representation of the interest rates in dependence of the maturity, may have a complex course. Usually, it is increasing, meaning rates (per year) are higher for longer maturities. Depending on the horizon, the term structure can be modelled with a different number of parameters. The representation with more parameters increases the precision, but also increases the complexity, which may hamper the search for closed-form solutions for relevant variables. How many parameters are therefore optimal for which purpose and application?
Contribution
We present a model for the term structure of interest rates that depends on two parameters, namely one parameter for the short-term interest level and one parameter for the slope. This model makes it possible to derive closed-form solutions for important values of risk management (present value, duration and convexity) and we give a new interpretation to the convexity, namely as the sensitivity of a bond with respect to the slope of the term structure.
Results
In our study of Germany (period 1975-2023), we show empirically that the term structure of German government bonds can be well described by the presented model if the horizon is about one year (or longer). In different applications, we estimate the contribution of maturity transformation to the German banks’ interest income to about 12% and we deduce an estimate for the probability of the interest hike in 2022/23.