1 Introduction
In the last decades much empirical work has been done on time series of
asset prices. Many studies report mean reversion in stock returns [see Fama
and French [9]; Poterba, Summers [28]], predictability of the equity premium
and other "anomalies”. Empirical research on options suggests significant
mispricing compared to theoretical option prices, especially compared to the
Black-Scholes model (see Canina, Figlewski [4]; Jackwerth, Rubinstein [20];
Rubinstein [29] and for an outstanding survey Ghysels, Harvey, Renault [13]).
Most of these well documented facts still lack a sound theoretical explana-
tion. While the smile effect, for example, can be explained with stochastic
volatility models the stochastic process of the volatility is usually exoge-
neously given. Only few models address the basic economic question why
volatility is stochastic. Thus, usually a somewhat arbitrary volatility process
is introduced.1
Many theoretical papers have already investigated the viability of sto-
chastic processes for asset prices, i.e. the consistency with an equilibrium.
A common framework for the investigation is a representative investor econ-
omy. Basically, as was shown for example by Decamps, Lazrak [6] an equi-
librium in a representative investor economy implies that the pricing kernel
is a deterministic function of wealth. Hence, not every arbitrage free asset
price process is consistent with such an equilibrium, since the existence of a
strict positive pricing kernel is sufficient to ensure the absence of arbitrage
possibilities. The assumption of arbitrage free markets does not imply that
the pricing kernel is a deterministic function of wealth. Whether certain
asset price processes are consistent with an equilibrium in a representative
investor economy has been analyzed for example in Bick [1]; Bick [2]; He,
Leland [14] and Pham, Touzi [27]. Franke, Stapleton, Subrahmanyam [12]
choose a slightly different, more constructive approach to investigate the via-
bility of asset price processes. Instead of starting with the stochastic process
of asset prices, they take the process of investors’ expectations of the future
cash flow as given. They further assume that the asset pays no dividends.
Since the price is completely described by the distribution of the cash flow
and by investors’ preferences it is possible to construct any viable asset price
process from the characteristics of information processes and preferences. By
1For models that are able to generate stochastic volatility see David [5] and Veronesi
[32].