This paper considers the dynamics of conditional second moments result
ing from a statistical description of agents' attitudes and behaviour
in a noise trader/infection framework. In general, the dynamics of sec
ond moments of state variables (e.g. prices) can be seen to exhibit au
toregressive structures. Conforming to well-known empirical findings,
volatility can change over time, shocks to volatility have lasting eff
ects and mean-reversion in second moments is observed. Thus, this kind
of market microstructure modelling can contribute to explain the regu
larities in variances found in data from asset markets and foreign exc
hange markets.