On the term structure of forwards, futures and interest rates
This thesis consists of four papers which all treat term structures, either
of forwards and futures or of interest rates.
In the rst paper we consider a di usion type model for the short
rate, where the the drift and di usion coe cients are modulated by an
underlying Markov process. The main objective ofthepaperistostudy
how bond pricing can be carried out in this framework, both when the
underlying Markov process is observable and when it is not.
In the second paper weinvestigate when a model of the Heath-Jarrow-
Morton-type (HJM) for the futures prices generically implies a Markovian
spot price, that is when no matter which initial term structure is used
for the futures prices, the spot price implied by the futures prices always
satis es a stochastic di erential equation.
In the third paper we investigate the term structure of forward and
futures prices for models in which the price processes are assumed to
be driven by amulti-dimensional Wiener process and a general marked
point process. For an in nite dimensional model of HJM-type of the
futures and forward prices we study properties of the futures and forward
convenience yield. We also study a ne term structures, general pricing
of futures options, and the problem of tting a nite dimensional factor
model to an observed initial futures price curve.
In the fourth paper we consider interest rate models of the HJM-type,
where the forward rates are driven byamulti-dimensional Wiener process
and the volatility is a smooth functional of the presentforwardratecurve.
Building on earlier results in the eld, concerning when such a model
can be realized by a nite dimensional Markovian state space model, we
present a general method to actually construct such a realization.
School:Kungliga Tekniska högskolan
Source Type:Doctoral Dissertation
Keywords:MATHEMATICS; Applied mathematics; Optimization, systems theory; Term structure; Markovian realizations; affine term structures.
Date of Publication:01/01/2001