In financial markets, the information that traders have about an asset is reflected in its
price. The arrival of new information then leads to price changes. The ‘information-based
framework’ of Brody, Hughston and Macrina (BHM) isolates the emergence of
information, and examines its role as a driver of price dynamics. This approach has
led to the development of new models that capture a broad range of price behaviour.
This thesis extends the work of BHM by introducing a wider class of processes for the
generation of the market filtration. In the BHM framework, each asset is associated
with a collection of random cash flows. The asset price is the sum of the discounted
expectations of the cash flows. Expectations are taken with respect (i) an appropriate
measure, and (ii) the filtration generated by a set of so-called information processes that
carry noisy or imperfect market information about the cash flows. To model the flow
of information, we introduce a class of processes termed Levy random bridges (LRBs),
generalising the Brownian and gamma information processes of BHM. Conditioned on
its terminal value, an LRB is identical in law to a Levy bridge. We consider in detail
the case where the asset generates a single cash flow XT at a fixed date T. The flow
of information about XT is modelled by an LRB with random terminal value XT.
An explicit expression for the price process is found by working out the discounted
conditional expectation of XT with respect to the natural filtration of the LRB. New
models are constructed using information processes related to the Poisson process, the
Cauchy process, the stable-1/2 subordinator, the variance-gamma process, and the
normal inverse-Gaussian process. These are applied to the valuation of credit-risky
bonds, vanilla and exotic options, and non-life insurance liabilities
