Optimal bond portfolios with fixed time to maturity
(English)Article in journal (Refereed) Submitted
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 L´evy processes associated with the OU processes. This allows us to calculate the efficient mean-variance portfolio. We exemplify the results by a case study on U.S. Treasury bonds.
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.
Interest rate models, rolling horizon bonds, generalised Ornstein-Uhlenbeck processes, affine term structure, mean variance portfolio
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:su:diva-57751OAI: oai:DiVA.org:su-57751DiVA: diva2:417705