### Doctoral Thesis Defense, Optimization and Systems Theory

Friday, February 16, 2001, 10.00, Kollegiesalen, Administration building,
Valhallavägen 79, KTH

**Camilla Landén**

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On the term structure of forwards, futures and interest rates

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Akademisk avhandling
som med tillstånd av Kungliga Tekniska Högskolan framlägges
till offentlig granskning för avläggande av teknologie
doktorsexamen fredagen den 16 februari 2001 kl 10.00 i Kollegiesalen,
Administrationsbyggnaden, Kungliga Tekniska Högskolan,
Valhallavägen 79.
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This thesis consists of four papers which all treat term structures,
either of forwards and futures or of interest rates.

In the first paper we consider a diffusion type model for the short
rate, where the the drift and diffusion coefficients are modulated by
an underlying Markov process. The main objective of the paper is to
study 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 we investigate 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 satisfies a stochastic differential 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 a multi-dimensional Wiener process and a general marked
point process. For an infinite dimensional model of HJM-type of the
futures and forward prices we study properties of the futures and
forward convenience yield. We also study affine term structures,
general pricing of futures options, and the problem of fitting a
finite 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 by a multi-dimensional Wiener
process and the volatility is a smooth functional of the present
forward rate curve. Building on earlier results in the field,
concerning when such a model can be realized by a finite dimensional
Markovian state space model, we present a general method to actually
construct such a realization.

Calendar of seminars

*Last update: January 24, 2001 by
Anders Forsgren,
anders.forsgren@math.kth.se.
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