A thesis submitted for the degree of
Doctor of Philosophy
2013 / This thesis presents a range of related pricing kernel models that are driven by
incomplete information about a series of future unknowns. These unknowns may,
for instance, represent fundamental macroeconomic, political or social random
variables that are revealed at future times. They may also represent latent or
hidden factors that are revealed asymptotically. We adopt the information-based
approach of Brody, Hughston and Macrina (BHM) to model the information processes
associated with the random variables. The market filtration is generated
collectively by these information processes. By directly modelling the pricing
kernel, we generate information-sensitive arbitrage-free models for the term structure
of interest rates, the excess rate of return required by investors, and security
prices. The pricing kernel is modelled by a supermartingale to ensure that nominal
interest rates remain non-negative. To begin with, we primarily investigate
finite-time pricing kernel models that are sensitive to Brownian bridge information.
The BHM framework for the pricing of credit-risky instruments is extended
to a stochastic interest rate setting. In addition, we construct recovery models,
which take into consideration information about, for example, the state of the
economy at the time of default. We examine various explicit examples of analytically
tractable information-driven pricing kernel models. We develop a model
that shares many of the features of the rational lognormal model, and investigate
examples of heat kernel models. It is shown that these models may result
in discount bonds and interest rates being bounded by deterministic functions.
In certain situations, incoming information about random variables may exhibit
jumps. To this end, we construct a more general class of nite-time pricing kernel
models that are driven by Levy random bridges. Finally, we model the aggregate
impact of uncertainties on a nancial market by randomised mixtures of
Levy and Markov processes respectively. It is assumed that market participants
have incomplete information about the underlying random mixture. We apply
results from non-linear ltering theory and construct Flesaker-Hughston models
and in nite-time heat kernel models based on these randomised mixtures.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/12926 |
| Date | 30 July 2013 |
| Creators | Parbhoo, Priyanka Anjali |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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