the assumption of rational investors it is possible to impose restrictions on
the process representing investors’ expectations, i.e. the information process.
Hence, with the information process the distribution of the cash flow is given
and from the assumptions on investors’ preferences the characteristics of the
pricing kernel are given, too. Thus, the asset price process can be derived
from the underlying assumptions.
In this paper we follow the approach of Franke, Stapleton, Subrahmanyam.
While Franke, Stapleton, Subrahmanyam emphasize the importance of the
utility function or more precisely the elasticity of the pricing kernel our task
is to show the influence of the variations in expectations, i.e. the influence
of the volatility of the information process on the asset price process. We
extend their approach in that we allow for a second risk factor driving the
process of investors’ expectations. Hence, in our model the volatility of the
information process may be stochastic. Further we will give an economic jus-
tification for the generalization. We are arguing that introducing stochastic
volatility of the information process is a sensible assumption. To see this
consider a stochastic process with only one risk factor, e.g. the geometric
Brownian motion. In this case, the uncertainty about the stock price in T is
an only time dependent deterministic function. It is sensible to assume, that
this uncertainty may also be a stochastic function since this uncertainty is
driven by exogenous shocks. Unexpected news announcements may be seen
as one of these exogenous shocks. We will turn to this point again in section
3.
With our approach we are able to link explicitly financial markets phe-
nomena to the process of investors’ expectations. We will show that many
properties of asset price processes and especially empirically documented
properties of the risk premia can be explained by the characteristics of the
volatility of the information process. Further, we give an economic justifi-
cation for stochastic volatility asset models and we discuss the justification
of specifications of stochastic volatility by relating them to the process of
investors’ expectations.
The organization of this paper is as follows. The next section gives a short
review on related papers. In section 3 we discuss the viability of information
processes under the assumption of rational expectations. In section 4 we give
a brief characterization of the pricing kernel. In section 5 we derive viable as-
set price processes with the modern technique of forward-backward stochastic
differential equations (an outstanding overview on backward stochastic dif-
ferential equations and forward-backward stochastic differential equations is