  The main purpose of this paper is to extend the information-based
asset-pricing framework of Brody-Hughston-Macrina to a more general set-up. We
include a wider class of models for market information and in contrast to the
original paper, we consider a model in which a credit risky asset is modelled
in the presence of a default time. Instead of using only a Brownian bridge as a
noise, we consider another important type of noise. We model the flow of
information about a default bond with given random repayments at a
predetermined maturity date by the so called market information process, this
process is the sum of two terms, namely the cash flow induced by the repayment
at maturity and a noise, a stochastic process set up by adding a Brownian
bridge with length equal to the maturity date and a drift, linear in time,
multiplied by a time changed L\'evy process. In this model the information
concerning the random cash-flow is modelled explicitly but the default time of
the company is not since the payment is contractually set to take place at
maturity only. We suggest a model, in which the cash flow and the time of
bankruptcy are both modelled, which covers contracts, e.g. defaultable bonds,
to be paid at hit. From a theoretical point of view, this paper deals with
conditions, which allow to keep the Markov property, when we replace the
pinning point in the Brownian bridge by a process. For this purpose, we first
study the basic mathematical properties of a bridge between two Brownian
motions.
