Abstract:
We study interest rate models where the term structure is given by an
affine relation and in particular where the driving stochastic
processes are so-called generalised Ornstein-Uhlenbeck processes.

For many institutional investors it is natural to consider investment
in bonds where the time to maturity of the bonds in the portfolio is
kept fixed over time. We show that the return and variance of such a
portfolio of bonds which are continuously rolled over, also called
rolling horizon bonds, can be expressed using the cumulant generating
functions of the background driving Lévy processes associated with the
OU processes. This allows us to calculate the efficient mean-variance
portfolio.

We also show that if the short rate, in a risk-neutral setting, is
given by a linear combination of generalised OU processes, the implied
term structure can be expressed in terms of the cumulant generating
functions. This makes it possible to quite easily see what kind of
term structures can be generated with a particular short rate dynamics